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Carrier Injection in Optically Bistable
Optoelectronic InSb Device
Abdul-hussain .K.Iltaif and Baha'a .A.M.Al-Hilli
Ministry of science and technology Abstract In this study, the required injected carrier's number, current, and voltage to achieve switching dynamics in n-type InSb has been calculated theoretically. It is found that the required injected concentration at room temperature is much larger than that at liquid nitrogen temperature and the applied bias voltage and current increase linearly with increasing the injected concentration .Results show that ,the relation between the logarithm of the current versus applied bias is linear .At ٧٧ K, for an applied bias of ١٤٣ mV the entire injection requirements to achieve switching dynamics are satisfied by ٠٦ mA compared with a requirement in the range of amperes for contacts which are not fabricated to be injecting. Thus, the efficiency of injection increases considerably when a p+-n junction was used. Also, the required power to achieve switching in InSb increased as temperature increased.
!) # $%( ! . ( !% ) * ( +
*, + ) - + .(. ) / 01 0 + ! -( * (. ( * 2 + 3 + 4, 5 *
. ) *3 + 01.0 *, + ) - ! 5
mV 678 $ ( + 0 + ! 9,; mA 0 ! $0 /< = ! +. ( ( > + )? (
< * 3 p+-n . 0 ) + ! @K AA *B ) - + .( .899 k
Introduction Semiconductors are a group of materials having conductivities between those of metals and insulators [١]. The III-V semiconductors, which are compound semiconductors comprising elements from the third and fifth groups of the periodic table. Typical examples are InSb, InAs, InP, GaP, GaAs, GaSb, and AlSb [٢]. InSb has the highest electron mobility of all known semiconductors [٣]. The high mobility of InSb may allow it to play an important role in very high speed electronics [٤].
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The conductivity of semiconductors can be varied over orders of magnitude by changes in temperature, optical excitation, and impurity content [٥]. In the case of optical excitation, a light is shined on a semiconductor. If the photon energyνh of the light is greater than the band gap energy gE of the semiconductor, whereh is the Planck constant andν is the optical frequency, the photon is absorbed by the semiconductor and an electron-hole pair is generated. The optical excitation increases the electron and hole concentrations above their equilibrium values. These additional carriers are called excess carriers. The process of introducing excess carriers is called carrier injection [٦]. Early work on carrier injection in InSb was directed towards the creation of an InSb laser diode. Bistable switching is achieved by a combination of optical holding power and an electrically injected switching signal. This forms the basis of the electrical switch ON of the optically bistable optoelectronic device [٧]. The aim of the present work is to study, theoretically, the required injected carriers number, current and voltage to initiate switching by using an external switching pulse (such as CO pulse and CO٢ pulse). Theoretical bases: ١. Temperature Dependences The band gap and the intrinsic carrier concentration both of which are temperature-dependent. The intrinsic carrier concentration is given by [٨]:
kTEvci
geNNn /2 −= (١) Where Nc is the effective density of state in the conduction band, and Nv is the effective density of state in the valence band.
2/312108 TNc ×≈ cm-٣
2/315104.1 TNv ×≈ cm-٣
eV500
10624.0
24
+×−=
−
T
TEg
and k =٥-١٠×٨٦٢ eV/K. Injection Requirements ٢. At thermal equilibrium: NcNv=ni² (٢) And when extra carrier injected to the semiconductor, the non equilibrium condition will be occur: NcNv>ni² (٣) In this study we used the optical excitation method to inject extra carriers. The required injected concentration is given by [٩]:
(٤)ντα
h
Ip
p
n =∆
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whereα is the absorption coefficient, I is the incident intensity, pτ is the
lifetime of holes, and νh (eV) =١٢٤/ λ(µm). ٣. Voltage Requirements The built in potential which is the voltage difference between the p and n layers is: V=Vn-Vp=KT/q ln (NAND/ni²) (٥) Where Vn is the voltage of n layer, q is the electron charge, Vp is the voltage of p layer and NA,ND accepter and donor carrier concentrations respectively. The required applied bias to achieve a switch is [٦]:
+
∆= 1ln
no
n
p
p
q
kTV (٦)
Where din Nnp /20 = and =dN ١٠١٤ cm-٣.
٤. Current Requirements The required current is given by [١٠]:
I )1( /0 −= kTqV
p
npe
L
pAqD=
p
np
L
pDAq ∆ (٤)
where =A ١mm٢-١٠= ٢ cm٢, pD is the hole diffusion coefficient, and pL is the diffusion length of holes. ٥. Results and discussion By using eqn. (١),the intrinsic carrier concentration in InSb have been
calculated for two different temperatures (٧٧K and ٣٠٠K), the results are
shown in table (١).
Table (١) .Band gap and intrinsic carrier concentration values.
At ٧٧ K, 00 ndn pNn >>= and )(0 diin Nnnp <<<< , and this means that the sample is n-type, while at ٣٠٠ K, non pn <<0 and in np >>0 , so the sample is p-type (above ١٥٠ K the pure n-type InSb sample is intrinsic and become p-type by injection of holes).Also, the injected carrier concentrations to achieve switching in InSb (eqn.٢) is ١٠١٤ (cm-٣) at ٧٧K while it becomes ١٠١٩ (cm-٣) at ٣٠٠K as shown in table(٢).
2in gE qkTkT /, T
(cm-٦) (eV) (eV),(V) K) ٧٧ ٠٠٠٦٦ ٠٢٣ ١٠١٨× ٣٨ ٣٠٠ ٠٠٢٥٩ ٠١٧ ١٠٣٢×٤٣
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Table ٢ .The injected concentration calculated from eqn.( ٢) T α I
pτ λ νh np∆
(K) (cm-١) (W/ m٢) (s) (µm) (eV) (J) (cm-
٣) ٨٠ ٧٧
(١١،١٢) ٠٢ ٥٥ ٦-١٠×٢ ٠٠٢٨
٣ ١٠×٠٣٧-
١٩ ١٠١٤
٣٠٠
١٠٤×٩ (١٣) ١٠ (١٣)
٠١ ١٠٦ (١٤) ٧-١٠×٢٢
١٠×٠١٩-
١٩ ١٠١٩
From this table, the photon energy of the CO laser is of the order of gE at ٧٧
K ( gEh =ν , single-photon absorption), while the photon energy of the CO٢
laser is larger than half the band gap at ٣٠٠ K ( νh2 > gE , two-photon absorption). For different injected carrier concentrations ,voltage required to achieve switching have been calculated for ٧٧K and ٣٠٠K as shown in table (٣) and Fig.(١). Table ٣ .Voltage as a function of injected concentration for a given temperature.
V (mV) T (K) np∆
(cm-٣) ٧٧
٣٠٠
١٤٣ ١٠١٤ ١٥٨ ١٠١٥ ١٧٤ ١٠١٦ ١٨٩ ١٠١٧ ٢٠٤ ١٠١٨ ٣١ ٢١٩ ١٠١٩ ٨٣ ٢٣٤ ١٠٢٠ ١٤١ ٢٥٠ ١٠٢١ ٢٠١ ٢٦٥ ١٠٢٢
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Fig.١ Dependence of applied voltage on the injected concentration This figure indicate that the applied voltage is a linear function of the injected concentration when the temperature remains constant (i.e., 0np is constant) according to eqn.(٣) and the voltage change is qkT /3.2 (١٥ mV at
=T ٧٧ K and ٦٠ mV at =T ٣٠٠ K) for qkTV />> . From eqn.(٤), the required current was calculated and the results are shown in tables ٤،٥ and Fig.(٢).
Table ٤. Current calculated from eqn.(٤)
Table ٥ .Current as a function of injected concentration for a given temperature.
T pµ pp q
kTD µ= pτ
ppp DL τ= I np∆/
(K) (cm٢/V-s) (cm٢/s) (s) (cm) (mA/ cm-٣)
٤٠٠٠ ٧٧ (١٥)
١٠×٢ ٢٦-
٦ ١٤-١٠× ٠٦ ٤-١٠×٧٢
٣٠٠
٨٠٠ (١٥)
١٠×٢ ٢١-
٧ ١٤-١٠×١٧ ٤-١٠×٢٠
T (K)
٣٠٠ ٧٧
∆ pn (cm-
٣) I(mA) log (I) I(mA) log (I)
٠٢- ٠٦ ١٠١٤ ٠٨ ٦ ١٠١٥ ١٨ ٦٠ ١٠١٦
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Fig. ٢ Shows a plot of log I as a function of np∆ . It is evident from table ٥ and Fig. ٢ that the current I is a linear function of np∆ when both the diffusion coefficient pD and the diffusion
length pL are constants (i.e., the temperature is constant) according to Eq.٤.Therefore, for an increase in np∆ by a factor of ten, there is a corresponding increase in I by the same factor. The minimum required power (P=IV) to achieve switching for minimum value of current and voltage at ٧٧K and ٣٠٠K were ٨٥٨µW and ١٠٦×٥٢٧
µW respectively. From the previous results ,the current –voltage characteristics were plotted as shown in Figs.(٣ and ٤),and that the relation between I &V is linear when T is constant according to eqn.(٤) .From these figures we note that the rate of current increase is constant. At T (K) for every decade change of current, the voltage change is qkT /3.2 . The logI versus V curve is a straight line as shown in Fig.٥.The slope of this straight line is
1)/3.2(/43.0 −= qkTkTq and this result is in agreement with Fig.( ٦) [١٦].
٢٨ ١٠٢×٦ ١٠١٧ ٣٨ ١٠٣×٦ ١٠١٨ ٥٢ ١٠٤×١٧ ٤٨ ١٠٤×٦ ١٠١٩ ٦٢ ١٠٥×١٧ ٥٨ ١٠٥×٦ ١٠٢٠ ٧٢ ١٠٦×١٧ ٦٨ ١٠٦×٦ ١٠٢١ ٨٢ ١٠٧×١٧ ٧٨ ١٠٧×٦ ١٠٢٢
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Fig. ٣ Ideal current-voltage characteristic (linear plot) at ٧٧ K.
Fig.٤ Ideal current-voltage characteristic (linear plot) at ٣٠٠ K.
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Fig. ٥ Ideal current-voltage characteristics (semilog plot).
(a) linear scale (b)semi logarithmic scale
Fig. ٦ Ideal current-voltage characteristics (١٦). Conclusions ١. The required injected concentration at ٧٧ K is smaller than that at ٣٠٠ K by five orders of magnitude. ٢. The minimum voltage required to achieve a switch is ١٤٣ mV at ٧٧ K and ٣١ mV at ٣٠٠ K. The minimum current is ٠٦ mA at ٧٧ K compared with ١٧٠ A at ٣٠٠ K. ٣. The minimum power at ٧٧ K is much smaller than that at ٣٠٠ K. Therefore, from the application point of view, ٧٧ K is the best.
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٤. At ٧٧ K, for an applied bias of ١٤٣ mV our entire injection requirements are satisfied by only ٠٦ mA, this compares with a requirement in the range of amperes for contacts which are not fabricated to be injecting. Thus we can increase the efficiency of injection considerably by using a p+-n junction. References ١. Neamen, D.A., ١٩٩٢, Semiconductor Physics and Devices: Basic Principles, Irwin, and Homewood, IL. ٢. Ibach, H. and H. Lüth, ١٩٩٦, Solid-State Physics: An Introduction to Theory and Experiment, Springer-Verlag. ٣. Weiss, H., ١٩٦٦, Semiconductors and Semimetals, Vol.١, ed. by R.K. Willardson and A.C. Beer, Academic Press, New York. ٤. www.onr.navy.mil/sci_tech/information ٥. Streetman, B.G. and S. Banerjee, ٢٠٠٠, Solid State Electronic Devices, ٥th ed., Prentice Hall, Englewood Cliffs, New Jersey. ٦. Sze, S.M., ١٩٨٥, Semiconductor Devices: Physics and Technology, Wiley, New York. ٧. Mackenzie, H.A., A. Iltaif, J.I.L. Hughes, J.J. Hunter, and D. Ronaldson, ١٩٨٩, OSA Proceedings on Photonic Switching, Vol.٣, ed. by J.E. Midwinter and H.S. Hinton. Optical Society of America. ٨. www.ioffe.rssi.ru/SVA/NSM/Semicond/InSb/bandstr.html
C. Omar, M.A., 6CAD, Elementary Solid State Physics, Addison-Wesley.
69. Millman, J. and C.C. Halkias, 6C;A, Electronic Devices and Circuits, McGraw-Hill, New York.
66. Miller, D.A.B., S.D. Smith, and C.T. Seaton, 6CE6, IEEE J. Quant. Elec.,
QEF6A86GF86A.
6G. Miller, D.A.B., 6CE6, IEEE J. Quant. Elec., QEF6A89;F866.
68. Ji, W., A.K. Kar, P.L. Chua, and A.C. Walker,6CEA,IEEE J. Quant. Elec.,
QEFG8, 6CE;F6CC6.
67. Al-Attar, H.A., H.A. Mackenzie, F.A.P. Tooley, and A.C. Walker, 6CE;,
IEEE J. Quant. Elec., QEFGG ;;8F;A9 .
6D. * B H36CCC @I<1 I I B IJ KIL ( /<I (3 M ( 51 ) <M(.
6;. Howe and Sodini, G998, ocw.mit.edu/NR/rdonlyres/
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Effect of Incident Ray Angle and Optical lens on
Solar Cell Performance
Oday Mazin Abdul-Munaim
Department of Physics-College of Science AL-Mustansiriyah University
Abstract: Silicon solar cell (p-n junction type) was used in this research an active area of ٢٢٤ cm٢ with for measuring the voltage and current values were for different angles of incident ray (θ). a comparison between (θ) and (θF) when a fresnel lenses with an active area of ٦٤ cm٢ were used at ٢٦°C with average value during the measurements. The maximum values of voltage and current (VMAX ,IMAX ) for each incident angle was measured and thus the filling factor (F.F) , was also measured through determination of IS.c and Vo. c for closed and open of solar cell circuit . In results indicated The filling factor was proportional with (I MPP,V MPP) depending on ability of charge distribution for P-N silicon system with increasing or decreasing depletion layer , obtaining current about ٣ ٦٢ Amp with lens and this is a large magnitude with respect of ١ ٣ Amp with incident angles(٠°).
: أم "2,س 0/ ا".)" وا",ر P-N Junction ) silicon (*(ع '& ه$ا ا"! خ
3,' مB(٠º=θ)واA@اء م2,ر* ب6 0 ا"=اوی ، )θ( '& زوای, م. ٢٢٤cm٢"8, 67 م,ح) fº(θ=اام 3,ت ٠ D3 3,' ح@ارة ٦٤ E*@'cm٢ ب,حAل درIخ C ºل 3,م ٢٦Jآ
,ر وا".(". خIل أA@اء ا"2,,ت " MNJ")( وت ی ا"2/ اIMAX,VMAX P"$2(ط ،آ "ER زاوی م6 خIل ت ی F.F( /0(ح,ب 3,مE ا"MءT"ا " )IS.c , Vo.c ( اU@ة ا"8R@ب,U ا".(ح"
V"واT"ا " 2. Bدي م@X ERTء بM I MPP ,V)بZU,* [D ا"! أن ا"V@ '& م2ار 3,مE ا"MPP) م,ND" D T"ا Bت(زی R(ن '& زی,دة و*2^,ن ح,A= ا"[8 بP-N ،,8D ب,\3,د 3M 0,ب"
٦٢ ٣'& ا" ^(ل 3M ت,ر م2ار_ Amp"م دة وا 67 م,حJ"د ا)A)آ,*] اآ!@ م6 ب &٣ ١م2ار Amp2(ط D3 زاوی(ح ا"" ٠°°°°) . (
Introduction: In ١٩٨٧ has been involved in photovoltaic concentrator technology for space applications for the past ١٩ years ago. In addition, latest space concentrator module uses a small (٨ ٥ cm wide aperture) silicone Fresnel lens to focus Sunlight at ٨X concentration onto radiation-cooled triplejunction photovoltaic cells [١]. In ١٩٩٤ l.james[٢] use the program to perform optical ray tracing with the properties of a proprietary Fresnel lens as an input to determine the intensity distribution of the light falling upon the top, middle, and bottom cells of the ٣
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Junction cell. In ١٩٩٧ King and Kratochvil, exhibits a somewhat different response to the angle of incidence and note that the incident angle effect response for the mono-crystalline, polycrystalline, and silicon film BIPV panels are almost identical. This is attributed to the fact that the glazing associated with these panels is identical, ٦ mm low iron glass [٣]. In ٢٠٠١, O’Neill and McDanal working on the development of a new high-efficiency concentrator module using multi-junction (MJ) cells,as part of the DOE/NCPV High Performance Photovoltaics Initiative [٤] ,Various tyoes of compounds were studied with silicon by Ganguly & Han in order to show it’s effect on solar cell efficiency average and the latter’s relation with temperature at (٤٥º& ٠º) incident angle [٥]. The Stan, Aiken develop work is the integration of a high-efficiency triple-junction(٣J) solar cell into a Fresnel lens-based concentrating array operating at average concentration ratios on the order of ٤٠٠X ,when effect of heat appetite to incident ray it slightly due to the glass of panel have a thermal scattering [٦]. Input parameters required by these models include the photovoltaic cell current and voltage at maximum power conditions, open circuit voltage, short circuit and the changes in incident angle coefficients associated with the short circuit current and open circuit voltage. a model used within Fresnel lens to show the variety filling factor (F.F) with other angle. The Aim of the research is to determine the best incidence angle in order to get a high performance. Practical part: Current and voltage values were calculated for each angle by using the basic parameters of a PV cell is fairly easy. All you need is the solar cell have ٢٥ ٢٢% maxima Efficiency, a Volt Ohmmeter (with a DC Amps scale), constant resistors (٢ ٥ohm), Sincere light, Fresnel lens and P.C I.R Adapter contact with the system of solar cell a sunny day (see fig. ١). The arched lens has an aperture width of ٨ ٥cm and focal length of ٩ ٢cm measured from the top of the arch.
Fresnel lens + Sincere light (Ra.d) ٦٤cm٢ Solar cell - - + I.R Adapter
٥ m range A
V R Ω
P.C
sun
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Fig (١) The system of solar cell with P.C I.R Adapter mode
The diode has the I-V characteristic that we following Fig (٢). If we do not connect the cell to anything, current from the current source just circulates back around through the diode. A voltage is created across the diode. This is the open circuit condition. If we short the cell, all of the current is diverted away from the diode and flows through the short. Voltage output is zero. This is the short circuit condition. Real solar cells have characteristics that degrade their performance compared to the ideal. In particular, their wiring has some resistance to the flow of current. This is represented electrically by a resistor in series. Likewise, there is some resistance that is in parallel with the current source and diode that drains some amount of power from the cell. To be more complete, then, the equivalent circuit looks like the following Fig (٣). The Is.c of this cell in full sunlight is about ١ ٣ amps. Its Vo.c is about ٣ ٤ volts. To know (I MPP,V MPP) value with or without lenses, it must determine the solar incidence angle, and when measurement the ( Is.c , Vo.c )values. A typical current-voltage characteristic curve taken from reference for a solar cell shown in Fig (٤) [٦]. Unlike the fuel cell, it is possible to measure a short circuit current (maximum current/zero voltage at conditions of no resistance) without damaging the device. The short circuit current varies with the strength (Intensity) of the light source as mentioned previously. However, the non-load voltage (a function mainly of the semiconductor materials used in the solar cell) is only weakly affected by light strength. Output Power (product of the voltage and current) can be determined from these curves. Maximum power point MMP (voltage and current corresponding to maximum power), filling factor commonly used to describe solar panel performance. Filling factor, (F.F) is defined as:
nlCS
MMPMPP
VI
VIFF
××
=.
. …………. (١) [٨-٧]
Where subscript MPP stands for “at maximum power point”, s.c “short circuit” and “non- load”. Optimal operation of the solar cell occurs when the power required by the load is close to the MPP. The Efficiency indicates what fraction of the power irradiated onto the solar cell is converted to electrical power by the cell when the cell is operating at its maximum power point equal : output power(electrical) / input power(light) This is done through the following Equation: [٦]
εsolar %100.
.. ×××=
AeffR
VI
da
cocs …………. (٢)
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Where: Aeff: Active area for solar cell (٦٤cm٢ in Fresnel lens). Rad: Incident ray density which can be considered sometimes as input power (Pin) and equal ٩٦٩٣١ in active area ٦٤cm٢ , therefore Pout = Is.c × Vo.c / Area of Cell [٩،١٠]. From equation (٢) can determined and investigate the solar cell efficiency use in search. Result & Discussion: When the solar cell is pointing to the sun, the output voltage was measured .It was ٣ ٤ volt when the circuit was opened (i.e VO.C). Then the DC current was measured and it was ١ ٣ Amp when the circuit was closed (i.e IS.C) . These values of voltage and current were measure at (٠°) incident ray angle without optical lens. Table ١ shows the effect of incident ray angle and optical lens on the output characteristics of the solar cell .The data shows a small variation in output I and V with change of incident ray angle. While there is a large increment in output values with presence of optical lens see figure ٦. This, simplify, is due to the concentration of solar radiation on solar cell surface while is mean an increments in input power. The effect of incidence angle can be represented by figure ٥, which matched with P-V characteristic in figure ٤. The point at which the curve intersects the y-axis represents the short circuit condition. While it represents an open circuit condition when the curve intersects the x- axis . and also calculated the (F.F) value from Equation (١) or through computers (P.C) program connection by I.R adapter with the system solar method to determination (F.F) show in table ٣. Same behavior was found in variation of VO.C and IS.C with angles of incident ray as show in table ٢ .Based on these values , the filling factor values were found (see table ٣ ) Conclusions: ١- Essentially the increasing and decreasing in the value of the current and Voltage dependent to the incidence angle for the sun ray during the year and the heat temperature . ٢- The using of the tracing and concentrating systems lead to get better performance of solar cell ٣- The effect of temperature increasing was bounded at depletion layer between (P-N) that caused a difficultly transportation of electrons at high temperature, the depletion layer is large for this reason must amount of temper scattered that applied the cell .
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٤- The amount of performance is became small in case of deposition large amount of dust on cell surface , and then the increasing thermal global between it and dust layer on it , at this reason must keeping the same
amount of intensity along the procedure especially at incident angle( ٠° ) . Table (١) : (V-I) Values for different incidence angle with and without optical lens
f : use the fresnll lens to measure the angle with an active area of ٦٤ cm٢
Degree angle (θ)
V volt I amp Degree angle (θ)
V volt I amp
٠ ٤٥ ٠ ٣٤٣ ٠٥٥ ٤٢٥ ٠٣١ ٣٣٩ ١٣٥ ٤٢ ٠٥ ٣٣٣ ٢٦ ٤٠٥ ٠٧٦ ٣٢٨ ٣١٥ ٣٩١ ٠٩٣ ٣٢٦ ٣٢٥ ٣٨٥ ١٠٦ ٣١ ٣٥٣ ٣٦ ١٢٢ ٢٧٦ ٣٥٤ ٢٧ ١٢٦ ٢٦٨ ٣٥٥ ٢٠٣ ١٢٧ ٢٣١ ٣٥٨ ١٣٧ ١٢٩ ١٩٦
٠º
١٣ ٠
٠ºf
٣٦٢ ٠ ٠ ٣٣٨ ٠ ٣٤٣ ٠٢٣ ٣٣١ ٠٢٨ ٣٣٧ ٠٥٧ ٣٢٣ ٠٤٦ ٣٣٢ ٠٦٩ ٣٢٦ ٠٧ ٣٢٧ ٠٧٥ ٢٩٧ ٠٩١ ٣١٢ ٠٨ ٢٩٦ ١ ٢٩٧ ١ ٢٧٨ ١١٦ ٢٧٥ ١٠٧ ٢٥ ١١٩ ٢٦٣ ١١ ٢٢٨ ١٢٤ ٢١٣ ١١٢ ١٩٢ ١٢٥ ١٣٧
١٥º
١٢٦ ٠
٣٠º
١١٣ ٠ ٠ ٣٢٧ ٠ ٣٣٣ ٠١٩ ٣١٧ ٠٢ ٣٢٨ ٠٤ ٣٠٤ ٠٤٢ ٣١٧ ٠٥٣ ٢٨٥ ٠٦٥ ٣٠١ ٠٥٨ ٢٧١ ٠٧٩ ٢٨٢ ٠٦ ٢٤٩ ٠٨٦ ٢٥٠ ٠٦١ ٢٣٨ ٠٨٧ ٢٤٦ ٠٦٢ ٢٣ ٠٨٩ ٢٣٥ ٠٦٣ ٢٢٨ ٠٩٠ ٢٢٤ ٠٦٥ ١٩٦ ٠٩١ ١٨
٤٥º
٠٩٢ ٠
٦٠º
٠٦٦ ٠
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Table (٢):IS.C and VO.C Values for different incidence angle with and without optical lens
Table (٣): F.F Values for different incidence angle with and without optical lens
Fig (٢) the I-V diode circuit condition Fig (٣) the equivalent circuit
θº IS.C Amp VO.C volt
٠ºf ٤٢٥ ٣٦٢
٠º ٣٤٣ ١٣
١٥º ٣٤٢ ١٢٦
٣٠º ٣٣٨ ١١٢
٤٥º ٣٣٣ ٠٩٢
٦٠º ٣٢٧ ٠٦٥
θº IS.C Amp VO.C volt F.F
٠ºf ٠٨٢ ٣٦ ٣٥٣
٠º ٠٧٥ ٢٦٨ ١٢٦
١٥º ٠٧٤ ٢٧٥ ١١٦
٣٠º ٠٧٣ ٢٧٨ ١
٤٥º ٠٧٢ ٢٨٢ ٠٧٩
٦٠º ٠٧ ٢٨٥ ٠٥٣
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Figure (٤): Representative solar cell performance curves at varying light intensities[٦]
Fig (٦): I-V characteristic of solar cell by use Fresnel-Lens in ( ٠°°°° )
Fig (٥): solar cell in Full Sunlight-Angular Variation
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References : [١]Piszczor .M.F., and M.J. O’Neill, “Development of a Dome Fresnel Lens/Gallium Arsenide Photovoltaic Concentrator for Space plications” ,١٩th IEEE-PVSC, ١٩٨٧. [٢]James .L. ,"Effects of Concentrator Chromatic Aberrations on Multi- junction Cells”, First World Conference on Photovoltaic Energy Conversionpp. (١٩٩٤),١٨٠٢-١٧٩٩ . [٣]Hunter Fanney, A. Mark W. Davis, “Short-term characterization of building integrated photovoltaic panels”, heat transfer and alternative, National institute of standards and technology,Jun ١٩-١٥, Reno, Nevada, ٢٠٠٢ [٤]Neill M.J. O’ and. McDanal A.J, “Development of Terrestrial Concentrator Modules Using High-Efficiency Multi-Junction Solar Cells” ,Entech, Inc. ٢٠٠١. [٥]Ston M. ,D.Aiken , “progress report on the integration of the Emcore Triple-Junction solar cell in to a high concentration Rattio Fresnel- Based Receiver”,٢٠٠٣. [٦]King D.L., Kratochvil J.A., and Boyson W.E, “Measuring Solar Spectral and Angle-of-Incidence Effects on Photovoltaic Modules and Solar Irradiance Sensors”, Proc. ٢٦th IEEE Photovoltaic Specialists Conference,Anaheim, CA, pp. ١١١٦،١٩٩٧-١١١٣. [٧]. Bahnemann D., Berge C., and F. Pujiuala-Kruger, Thames& Kosmos “Fuel Cell Car & Experiment Kit Lab Manual”, (٢٠٠١). [٨]James Kachadorian, Chelsea Green publishing Co., “The Passive solar House: Using solar Design to heat and cool your home”, ١٩٩٧. [٩]Tom starrs and Howard wenger, “Energy Efficiency and Renewable Energy”, U.S.Department of Energy,December,P.٢٠٠٣ ,٢. [١٠]Cotal . Lillington H., .D., Ermer J., King R., Karam N., Kurtz S., D. Friedman, Olson J., Ward J., Duda A., Emery K., and Moriarty T.,“Triple-Junction Solar Cell Efficiencies above ٣٢٪” , The Promise and Challenges of their Applications in High-Concentration-Ratio PV Systems, Proceedings of the ٢٨th IEEE PV Specialists Conference, September ١٩-١٩, Anchorage, Al, pp. ٩٦٠،٢٠٠٢-٩٥٥.
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Abstract: The developed in digital TV and digital transmission and receiving systems and highly using the computer in information communication around the world that causes to increasing requirements to analysis the different media information, especially the TV media information. So, to analysis TV films must be cut it efficiently to determine the different shots, to be used in various applications like data compression and extract TV image information. In this paper we devoted to study the operation of cutting (partitioning) the TV scenes by introducing an algorithm depend on simple approaches to analysis the TV clips, this by determining criteria of compute the rate of elements that will be changed between the successive frames . the results of this criteria compared with the results of minimum mean square differences between the successive frames. The results shown that the introduced algorithm give high efficient way to determine the separated frames between different shots. Where this algorithm are high stationary in determine the separated frames for long range of thresholds of testing amount of high difference between the frames.
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AlgorithmAlgorithmAlgorithmAlgorithm((((١) : ) : ) : ) : FFFFindindindindinginginging the separated frames between video shots the separated frames between video shots the separated frames between video shots the separated frames between video shots InPutInPutInPutInPut : Image frames (current frame ft, and previous frame ft-١), and the threshold value Th . OutPut OutPut OutPut OutPut : (Mean Square Difference MSD , and Rate of number of changed pixels RNCP) between the two frames
١. Input the current frame ft( ), and the previous frame ft-١(). ٢. Input threshold value Th. ٣. Put Square difference SDF=٠
Put Number of Changed pixels NCP=٠ ٤. For y=١ to ImageFrame_Hieght ٥. For x=١ to ImageFrame_Width ٦. Compute the square difference of current pixel (x,y) between the two frames (ft,and ft-
١). i.e CDF=[ft(x,y)-ft-١(x,y)]
٢ ٧. Check CDF if it has high value or not (i.e. the pixel (x,y) changed or not).
IF CDF≥Th THEN Comput i) SDF = SDF + CDF ii) NCP = NCP + ١ ENDIF
٨. NEXT x: NEXT y ٩. Compute MSD by using ( MSD=SDF/NCP) ١٠. Compute RNCP by using
(RNCP=NCP/(ImageFrame_Hieght*ImageFrame_Width) ١١. The OutPut results (MSD, and RNCP) End algorithm
Notes: This algorithm iteritvely performed for the successive video frames, and repeated for
different Th values.
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>.)
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Refrences ١. Nada, A. A., "Homogeneous Image Compression Using Quadtree", M.Sc Thesis, Babylon University, October,(١٩٩٨). ٢. Lars Bretzner, " Multi-Scale Feature Tracking and Motion estimation", M.Sc. thesis, Stockholm Univ. ١٩٩٩. ٣. Yurong Li, " Motion Tracking in active vision system", M.Sc. thesis, Univ. Of Louisville, ١٩٩٩. ٤. Banerji A.S., Brag-neto U., and Goutsias J., " Non-Linear Techniques for Automatic Target Detection, Recognition",http://w٣antd-mist-gov/html files//Project-Atr.Html, ٢٠٠٢.
0
5000
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0 10 20 30 40 50 60 70 80
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a b
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٥. Zoran Zfivkovic, "Motion Detection and Object Tracking in Image Sequences", PhD. Thesis, College Voor Promoties Univ. of Twente, ٢٠٠٣. ٦. Musa Kadhum Muhsen Al-Aujany," Astudy of Simulation of Motion and Orientation of Moving Images " PhD. Thesis, Physics Dept., College of Sciences, Al-Mustansiriyah Univ.,٢٠٠٦. ٧. Kuhttan Abbas Noman "Algorithm of image operation that using in still image", PhD. Thesis, Physics Dept., College of Sciences, Al-Mustansiriyah Univ.,٢٠٠٦. ٨. http : // www. Maxim-ic.com /appnotes. Cfm /appnote-number /٧٣٤ . update (٢٠٠١). ٩. Tnku Acharya and Ajoy K. Ray, "Image Processing Principles and Applications",Willy Interscience, A John Wiley & Sons, Inc., Publication, ٢٠٠٥. ١٠. http: //micro.magnet. fsu. Edu / primer / digital imaging / video basics . htm /. update (٢٠٠٤). ١١. Xilinx Solutions for the Broadcast Chain ,"Digital Video &Image Processing" ,at www.xilinx.com, [email protected], See in ٢٠٠٨. ١٢. Doug Black barn [email protected] . update (٢٠٠٤). ١٣. Umbaugh, S.E. , "Computer vision and image processing", prentice Hall PTR , Upper Saddle River, USA,(١٩٩٨). ١٤. John C. Russ, "IMAGE PROCESSING Handbook" The Fifth Edition, CRC Press is an imprint of Taylor & Francis Group, an Informa business, ٢٠٠٧. ١٥. Digital Creation Labs Incorporated ٢٠٠٤ Rev ١٠ April ٢٠٠٤ http //www.digital creation labs.com . update (٢٠٠٣).
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2.0E-02
0 50 100 150 200 250
*(L)D ( I S + 3 #5(gray level) I (Probability) )<I ? % aF )<I <.bF 3 )< o30=θ P . M <J M3 > 1 * (N , . 3(.
(a)
(b)
(a)
0.E+00
2.E-04
4.E-04
6.E-04
8.E-04
1.E-03
0 45 90 135 180 225 270 315 360
NM
SE
(b)
0.E+00
2.E-04
4.E-04
6.E-04
8.E-04
1.E-03
0 45 90 135 180 225 270 315 360Θ in degrees
NM
SE
(c)
0.E+00
2.E-04
4.E-04
6.E-04
8.E-04
1.E-03
0 45 90 135 180 225 270 315 360Θ in degrees
NM
SE
*(L)7 (H + 3 #5 Θ + 4 [01 NMSE ? % )< aF 1 J , . * (N .bF 01 , . * (N 1 .cF 3( , . * (N 1 .
Θ in degrees
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b. U % + 4 [01 *
*(L + #5(;) ? I01 /I *I3 U % * 3 + 3 + H H 3NMSEU % * 3 (9,DF6) (x) B I
(y) O * (LJ / ! M( :
• +NMSE + I3 I #< U(3 U % * 3 * ( )< - 5 + * ( . )< %< )< 5 *!
U % * 3 * (. • ! +( 3 O *(L ! +( OB [01 M (;) *I >I
[01 OB +( * .(Sx=9,;) H (9,99GDD) + >I e *<(9,999EC) (Sx=9,A7) +I *B > =1B ) [01 (
(9,99GDD) - =1B ) R ( . . IB Q 01 %<) I< I( @L < 0 3 + +(
)< (*(L !(E) (9,;) (9,A) * ! ( (6) . Y < / + $ X + O1 (Sxy=9,A) H )3.07( ×
B (Sxy=9,;) H ! )4.07( × X * ! #5 $ X (G) H (G) (Sxy=9,;) (6,E) (Sxy=9,A) $ X B +B
! ) > HWNMSE M! +( / - *L NMSE $0 )( e 5B )< ( >.
• , I. * (Id I01 , . * (N + *5!B 3( , . * (N +( JNMSE@! .
• NMSE + ( %< +( )( )< (X,Y) + J %< / 0 I I <I / + $ )
(. • < ( 001 + $ 0 - +B ( 001 + O
*I IM 0 *I 001 - +B * +( +( 3 < <J
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! + U % * 3 * ( )< 5 e 0 +( + @ (B B H U % * 3 + ( P.
*(L(;) Q3 U % * 3 + 3 #5 Sx U % + 4 [01 NMSE ? % )<aF (N 1 J , . * .bF 01 , . * (N 1 .cF 1
3( , . * (N.
NM
SE
Sx 0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
NM
SE
NM
SE
Sx Sx (a) )b( (c)
Sxy
Sxy
Sxy
0.0E+00
1.0E-03
2.0E-03
3.0E-03
4.0E-03
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0.0E+00
1.0E-03
2.0E-03
3.0E-03
4.0E-03
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0.0E+00
1.0E-03
2.0E-03
3.0E-03
4.0E-03
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
NM
SE
NM
SE
NM
SE
*(L)A ( 3 + 3 #5 Q3 *0 U % *SxyU % + 4 [01 NMSE )< ? % aF J , . * (N 1 .bF 01 , . * (N 1 .cF 1
3( , . * (N.
(a)
(b)
(c)
y x y( sy=٠٦) y( sy=٠٧) x(sx=٠٦
) x(sx=٠٧
)
٠٧ ٠٦ ٠٧ ٠٦ ١ ١
١٤ ١٢ ٠٧ ٠٦ ٢ ١
٢١ ١٨ ٠٧ ٠٦ ٣ ١
٢٨ ٢٤ ٠٧ ٠٦ ٤ ١
٣٥ ٣ ٠٧ ٠٦ ٥ ١
٤٢ ٣٦ ٠٧ ٠٦ ٦ ١
٤٩ ٤٢ ٠٧ ٠٦ ٧ ١
*(6) 0 (x,y) sy=9,;,sy=9,A,sx=9,; , sx=9,A
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0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8
Sxy=٠ ٧
Sxy=٠ ٦
m O
*(L(E) < 3 0L %< #5 OM Sxy=9,A ,Sxy=9,;
dx(sx=٠٦) dx(sx=٠٧)
٠٣ ٠٤
٠٤ ٠٢
٠١ ٠٢
٠٢ ٠٤
٠٥ ٠
٠٢ ٠٤
٠١ ٠٢
sam=٢ sam=١٨
*(G)0 $ (x,y) sx=9,; , sx=9,A.
0.0E+00
5.0E-03
1.0E-02
1.5E-02
2.0E-02
0 50 100 150 200 250
Pro
babi
lity
Gray level
*(L)C ( S + 3 #5(gray level) (Probability) )< )< - ? % 3 U %)4.0( =XS P . M > M <J 1 * (N , . 3(.
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0.0E+00
5.0E-03
1.0E-02
1.5E-02
2.0E-02
0 50 100 150 200 250
Pro
babi
lity
Gray level
*(LI)69 ( I SI +I I3 #I5(gray level) I (Probability) )< )< - ? % 3 U %)4.1( =XS .
P M > M <J 1 * (N , . 3(.
0.0E+00
5.0E-03
1.0E-02
1.5E-02
2.0E-02
0 50 100 150 200 250
Pro
babi
lity
Gray level
*(LI)66 ( I SI +I I3 #I5(gray level) I (Probability) )< )< - ? % 3 U %)4.0( =xyS .
P M > M <J 1 * (N , . 3(.
0.0E+00
5.0E-03
1.0E-02
1.5E-02
2.0E-02
0 50 100 150 200 250
Pro
babi
lity
Gray level
*(LI)6G ( I SI +I I3 #I5(gray level) I (Probability) )< )< - ? % 3% U )4.1( =xyS .
P M > M <J 1 * (N , . 3(.
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5.)
MO > U % ? 4, + NMSE + I , . * ( 01 , . * ( + *5! 3( , . * ( )I > O! * ( $0 + ( 001 O /
? . )< 3 *< + * 3 +( U % < / + ( 0 + .(.
References ١.James D. Foley “Computer Graphic”, Addison-Wesley Professional , Aug. (١٩٩٥). ٢. Hang Zhong, “Computer Graphic using Java ٢D and ٣D”, Pearson Prentice Hall (٢٠٠٦). ٣.J. P. Macey,“ Intro. To CGT”,(see in ٢٠٠٤),http://www.notes slid impoj.p/lo٤.pdf ٤.John C. Russ," Image processing Handbook", Taylor & Francis Group, LLC(٢٠٠٧). ٥.National Central Univ“ Image Fundamentals”,(see in ٢٠٠٧) , http://www.ip.csie.ncu.edu.tw/course/ip/ip٦٠٢p.pdf .“ Image Representation and Manipulation ” (see in ٢٠٠٧), http://www.scince ura.ni/~rein/machinevision/chap٢-٢u.pdf .S.J. Sangwine and R. E.N. Horne“ The color image processing Handbook”, Chapman & Hall (١٩٩٨). . Bruce A.Draper, "Geometric Image Manipulation ",(see in ),http:www.Homepajes.inf,ed.ac.uk/rbt/
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!) !(4 &=D 9A 0!E4
B! $) 9 ! !)
+ *,– ! ( – 0! ") G :
0 , +(N ,5 K ) .d * *3 ! H > < @L + +(N * + @1 +( , M,L 0 0 %M(.
H , M( * > < – Z M *< 0 (J + R J *, .
Abstract In this paper, transition rates for the photoexcitation and photoejection of an electron initially bound by its image charge to a plane infinite wall, impenetrable to the electron , and the electromagnetic wave is incident at an arbitrary angle, has been calculated. The electric field of intrest is parallel to z-axis for perfect conductive wall and liquid Helium wall.
:
g !),5 ) .N K ( 5J , +(N , M #0 L )< 0 . > +( #0 +z !
` K< *%L + R z<9 . M F +(V(z)=-ZeG/z *( z>9
)1(4
1
+∈−∈=Z + ∈ ( *3 . .
M $0 + ! T 1 *(L <. 6. *< +(N $1) @P Lmurium( [6] @! H ∞∈=
-4
1=Z +(N * + $1 * 2 +( H +∞=)(ZV z<9.
G. * . *, M =6,9DA ∈ Z=9,99;C *, M ! [G] V(Z)= 6 (eV) *( z≤9(L 0 +(N ( *
+ ZG Ry .(J > ;×69F7 (eV) @ Q + /0 - e 5B +(N * + $1 * 2 +( . !.
( > ! 5N F [ + ! 0 ( M( )F+(P ( 3
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Z [8]. 6. ( U *.
G. O 2 H 1) *0 > H 1 ( + + 2 >O +( > H3.(
8. 3 > M 2 e 3 ( + 3 ! e$0N > .3 H V / * 3 +( R *. ! . + 3 + +
3 H , 0 , . - ) - T, <1 RM 4, K 0 3LP * * .( 0 , . ! 1 M<
* ( @ L 3J .. /5 !s-state > s-state 3 ! .( + + 2 > 3J .. 30 / ! .( + e.( 1 +( +(N
+ e.( K1 1 * 3 + O K !1 - * 3 M L 3J .. .
!H:
H ! ( +( +(N +x-yI (z<9) 1 kh - ! @( ! 0L / ) 3 0 K< H
01 3 . > +(N ( ! ) z e 3 ! (L 3 * + M *<]7[.
0)(16
1
2
2
2
22
=Ψ
Ε−+− zU
z
e
dz
d
me οπεh …………..(6)
*. me +(N (e +(N L ћ > - . Gπ، ψ )<E)< +(N M 0 )(zU M
*(L > @ ( +( H +(N @! - H #0 + ]D[.
( ) ( )( ) ( )
>+−+∈
+−∈−
≤≤+=
ioo
o
im
Z Z tZZ4
1
1
2
ZZ4
gU
ZZ0 AGZZU ………(٢)
G / . Z = Zo M )< H / *. Z=9 / ) #0 Zi )< H / *. Uº 3 > @ ` H 0 t +3 #0 > 3 ) - +g (∈), M( 0
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3 >03 ];[.
( )1
1 g
+∈−∈=∈ ....................(٣)
0 z<9*(L > ( + ! ]A.[ ( ) ∑=ψ
k
ikZkeCZ …………..(٤)
k 3 b
2
2
g π= k= b(L . *. Ck . .
ψ 0 + + / *< M! ( z<9 0 z≥9 M ψnk(z) .
) *, M #0 0 > - + +(N + * + MO , M( * 0Grimes and Brown ]E[.
1 ( 3 / *1 +(d ,5 K * *3 > zH kh - , +( ψnk(z) 0
m
kE
2
22h=
( ) ( ) 22 EnEn MEρπ h=Γ …………..(D)
)(Eρ ( 3 ! 0 ) ! .( *(L > ( )kLmE 2/)( hπρ = ……………(;)
+(k 3 +]C[ hkinmEk 2= ……………..(A)
Bkin EhE −= ν ……………..(E)
EUEB −= ο ……………..(C)
*.νh 0 + 0 BE 0 0 EnM( * !< < ]G[
nkEkEn zWM ΨΨ= )( …………….(69)
( )(zW *(L > ( ) zezW ℑ−= β …………….(66)
*.ℑe ( , M( * β *(L > ( )[ ] γβ sin1
2
1wR+= ……………..(6G)
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*.( )wR U (3 * 3w γ0 . Iz>9 #< / *< 1)( =wR Q3 3 .(B S
/5 K L1)( =wR Iw H< *B0)( =wRw H< > M J e 5 +( H *, M) *B +(
< ( /50)( =wR] 6.[
+ OE P 3 +(d ( 0 ! 0 e 0! > +(N ( /z * + w 3 0 K3(66)
> 3x y > ( *(L > MO + 0 +(N > 0 zI >03
−==
οan
eZw
m
kE
2
2222
22h
h …………..(68)
οa 0 K< n=6G8. , <=:
! +(N ,5 + ) .d * *3 L Q%s-
state ]D [ + 3 Y0 *. OJCu,Ni,Ag (666) (996) )< 0 0 S6,SG . *. SJ 3
*%Lφ + > ( 0 Eg ! ( Vg H ! F ε < + 1B ! ]69 [ * ! 5 ((6)Q3 !
* *3 Q% +3 *( . -. "Cu(---) :
)< +(N M 0 * *3 L *J > (6G,DA6;; (eV) , M( * .[
+ 0 0 * ! M53(G) . +( MO + : 6. * *31EΓ+ 0 , M( * ) 1)( =wR 0)( =wR. G. *(L +(6) * *3 + O 1EΓ 1)( =wR * *3 + (
0)( =wR0 + 0 . . 8. * *3 + O1EΓ *(L ! #5 ( 0 % % (G).
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7. * *3 *1EΓ + 0 )1)( =wR 0)( =wR ( * ! #5(G).
. . "Cu(II-):
)< +(N M 0 !S6 SG > ( 6G,D7C7 (eV) 68,99A7 (eV) > * *3 U J1EΓ
2EΓ * ! + ( (8) . _ 21 EE ΓΓ 4, / ( > - + 3]C . [
3 . "Ni(---): +(N M 0 )< S6 SG > (
68,8CEC (eV) 68,E6A6 (eV) * ! + ( * *3 (7) . *(L(8) K1 + 21 EE ΓΓ + 1)( =wR0)( =wR.
5 . "Ni(II-):
( )< +(N M 0 68,D;C7 (eV) 68,E897
(eV) I S6 SG * > (D) R 4, + . *(L (7) * *3 + #52EΓ +3 #0 Ni(996) * *3 + ( 2EΓ #0
+3Ni(666). 6 . "Ag(---) " Ag(II-):
+3 #0 ( )< +(N M 0Ag(666) 66,A;CC (eV) * ! 4, (;) #0 Ag(996) 66,EEC6
(eV) * ! M, (A) . *(L(D)* *3 #5 1EΓ ( + + + 3 Y0 *(
0 + * * 3 + 360=γ + 0)(3.4 eVh =ν * , M(Ve 002.0=ℑ.
):
+ + *1 : 6. * *31EΓ+ 0 , M( * ) 1)( =wR 0)( =wR. G. * *31EΓ 1)( =wR * *3 + ( 0)( =wR 0 .
0 +.
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8. * *3 *1EΓ + 0 ) 1)( =wR 0)( =wR. 7. * *31EΓ0 % % . D. * *32EΓ +3 #0 Ni(996) * *3 + ( 2EΓ +3 #0
Ni(666). ;. * *31EΓ I )1)( =wR ( +3Ni(996) + 3 * *3 (
M +3 * *3 Cu(666). *)6:( ! ( ! H *%L + > ( 0
+ ` H 0 U° Uo= Eg –Vg + φ + εF εF (eV) φ (eV) Vg (eV) Eg (eV) نJ"ا
١١٦ ٣٧ ٥٢ ٠٩ ١٤ Ni(١١١)
١٤٧ ٣٤ ٥٢ ٢٥٣- ١٣٩٧ Ni(٠٠١)
١٠٣ ٢٥٥ ٤٧٤ ٠٨٥ ١٣٣٤ Cu(١١١)
١٣٤٥ ٣٠٥ ٤٥٩ ١٨- ١٣١٩ Cu(٠٠١)
٩٦٤ ٢١٥ ٤٧٤ ٠٣١ ١٢٥٤ Ag(١١١)
١٢١ ٢٥٣ ٤٦ ١٧٨- ١٣٣٩ Ag(٠٠١)
*)G :(* *3 + 1EΓ 0 % , M( * +! 0) ℑe(a.u) νh (eV) γ )sin(1 γβ =Γ(a.u) )sin5.0(1 γβ ×=Γa.u
٥-١٠×٢٠٦٩٣ ٥-١٠×٨٢٧٧٥ ٣٠ ٤٣
٦-١٠×٧٨٧٨٠ ٦٠ ٤٣
٥-١٠×٦٧٧٦٩ ٩٠ ٤٣ ٠٠٠٢
٥-١٠×١٨٩٠٤ ٥-١٠×٧٥٦١٩ ٣٠ ٥
٤-١٠×١٨٦٢٤ ٤-١٠×٧٤٤٩٧ ٣٠ ٤٣ ٠٠٠٦
٤-١٠×٥١٧٣٤ ٣-١٠×٢٠٦٩٣ ٣٠ ٤٣ ٠٠١
٢-١٠×١٨٦٢٤ ٢-١٠×٧٤٤٩٧ ٣٠ ٤٣ ٠٠٦
٢-١٠×٥١٧٣٤ ١-١٠×٢٠٦٩٣ ٣٠ ٤٣ ٠١
١-١٠×٨٢٧٧٥ ٣٣١١٠ ٣٠ ٤٣ ٠٤
١٢٩٣٣ ٥١٧٣٤ ٣٠ ٤٣
١-١٠×٤٩٢٣٨ ٦٠ ٤٣
٤٢٣٥٥ ٩٠ ٤٣ ٠٥
١٨١٥ ٤٧٢٦٢ ٣٠ ٥
*)8(:* *3 + 1EΓ * *32EΓ +I3 IM Cu (٠٠١) * I% , M(.Cu (٠٠١) 3.4=νh (eV) 60=γ
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ℑe(a.u) )(sin1 γΓ(a.u) )(sin2 γΓ
(a.u) 21 EE lΓΓ )sin5.0(1 γ×Γ
)sin5.0(2 γ×Γ 21 EE lΓΓ
٣-١٠×٤١٨٤٨ ٤-١٠×٩٢٥١٥ ٦-١٠×٣٨٧١٦ ٣-١٠×٤١٨٤٧ ٣-١٠×٣٧٠٠٦ ٥-١٠×١٥٤٨٦ ٠٠٠٢
٣-١٠×٤١٨٥٠ ٢-١٠×٢٣١٢٨ ٥-١٠×٩٦٧٩٠ ٣-١٠×٤١٨٤٨ ٢-١٠×٩٢٥١٥ ٤-١٠×٣٨٧١٦ ٠٠١
٣-١٠×٤١٨٤٨ ٢-١٠×٩٢٥١٥ ٤-١٠×٣٨٧١٦ ٣-١٠×٤١٨٤٧ ١-١٠×٣٧٠٠٦ ٣-١٠×١٥٤٨٦ ٠٠٢
٣-١٠×٤١٨٤٨ ١-١٠×٢٠٨١٦ ٤-١٠×٨٧١١١ ٤-١٠×٤١٨٤٨ ١-١٠×٨٣٢٦٤ ٣-١٠×٣٤٨٤٤ ٠٠٣
٣-١٠×٤١٨٤٧ ١-١٠×٥٧٨٢٢ ٣-١٠×٢٤١٩٧ ٠٠٥
٣-١٠×٤١٨٥٠ ٢٣١٢٨ ٣-١٠×٩٦٧٩٠ ٠١
*)7( :* *3 + 1EΓ * *32EΓ +3 M Ni (١١١) *
% , M(.Ni (١١١) 3.4=νh (eV) 60=γ
ℑe(a.u) )(sin1 γΓ(a.u) )(sin2 γΓ(a.u) 21 EE lΓΓ )sin5.0(1 γ×Γ )sin5.0(2 γ×Γ 21 EE lΓΓ
٣-١٠×٦٢٨٠٨ ٤-١٠×٨٦٤٠٨ ٦-١٠×٥٤٢٧١ ٣-١٠×٦٢٨٠٧ ٣-١٠×٣٤٥٦٣ ٥-١٠×٢١٧٠٨ ٠٠٠٢
٣-١٠×٦٢٨٠٤ ٢-١٠×٢١٦٠٢ ٤-١٠×١٣٥٦٧ ٣-١٠×٦٢٨٠٨ ٢-١٠×٨٦٤٠٨ ٤-١٠×٥٤٢٧١ ٠٠١
٣-١٠×٦٢٨٠٨ ٢-١٠×٨٦٤٠٨ ٤-١٠×٥٤٢٧١ ٣-١٠×٦٢٨٠٧ ١-١٠×٣٤٥٦٣ ٣-١٠×٢١٧٠٨ ٠٠٢
٣-١٠×٦٢٨١١ ١-١٠×١٩٤٤١ ٣-١٠×١٢٢١١ ٣-١٠×٦٢٨٠٨ ١-١٠×٧٧٧٦٧ ٣-١٠×٤٨٨٤٤ ٠٠٣
٣-١٠×٦٢٨٠٧ ١-١٠×٥٤٠٠٥ ٣-١٠×٣٣٩١٩ ٣-١٠×٦٢٨٠٤ ٢١٦٠٢ ٢-١٠×١٣٥٦٧ ٠٠٥
٣-١٠×٦٢٨٠٤ ٢١٦٠٢ ٢-١٠×١٣٥٦٧ ٣-١٠×٦٢٨٠٨ ٨٦٤٠٨ ٢-١٠×٥٤٢٧١ ٠١
*)D(: *3 +* 1EΓ * *32EΓ +3 M Ni (٠٠١) *
% , M( . 3.4=νh (eV) 60=γ
ℑe (a.u) )(sin1 γΓ
(a.u) )(sin2 γΓ(a.u) 21 EE lΓΓ )sin5.0(1 γ×Γ )sin5.0(2 γ×Γ 21 EE lΓΓ
٣-١٠×٧٦٤٠٩ ٣-١٠×٤٣١٨٦ ٥-١٠×٣٢٩٩٨ ٣-١٠×٧٦٤١٠ ٢-١٠×١٧٢٧٤ ٤-١٠×١٣١٩٩ ٠٠٠٢
٣-١٠×٧٦٤١٣ ١-١٠×١٠٧٩٦ ٤-١٠×٨٢٤٩٥ ٣-١٠×٧٦٤٠٩ ١-١٠×٣١٨٦ز٤ ٣-١٠×٣٢٩٩٨ ٠٠١
٣-١٠×٧٦٤٠٩ ١-١٠×٤٣١٨٦ ٣-١٠×٣٢٩٩٨ ٣-١٠×٧٦٤١٠ ١٧٢٧٤ ٢-١٠×١٣١٩٩ ٠٠٢
٣-١٠×٧٦٤٠٩ ١-١٠×٩٧١٦٩ ٣-١٠×٧٤٢٤٦ ٣-١٠×٧٦٤٠٩ ٣٨٨٦٧ ٢-١٠×٢٩٦٩٨ ٠٠٣
٣-١٠×٧٦٤٠٧ ٢٦٩٩١ ٢-١٠×٢٠٦٢٣ ٣-١٠×٧٦٤٠٩ ١٠٧٩٦٥ ٢-١٠×٨٢٤٩٥ ٠٠٥
٣-١٠×٧٦٤٠٩ ١٠٧٩٦٥ ٢-١٠×٨٢٤٩٥ ٣-١٠×٧٦٤٠٨ ٤٣١٨٦٣ ١-١٠×٣٢٩٩٨ ٠١
*);( :* *3 + 1EΓ +3 Ag (١١١) % , M( * . Ag (١١١) 3.4=νh (eV) 60=γ
ℑe (a.u) )sin(1 γβ =ΓE (a.u) )sin5.0(1 γβ ×=ΓE (a.u)
٥-١٠×١٣٩٢٤ ٥-١٠×٥٥٦٩٨ ٠٠٠٢
٤-١٠×٣٤٨١١ ٣-١٠×١٣٩٢٤ ٠٠١
٣-١٠×١٣٩٢٤ ٣-١٠×٥٥٦٩٨ ٠٠٢
٣-١٠×٣١٣٣٠ ٢-١٠×١٢٥٣٢ ٠٠٣
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٣-١٠×٨٧٠٢٩ ٢-١٠×٣٤٨١١ ٠٠٥
٢-١٠×٣٤٨١١ ١-١٠×١٣٩٢٤ ٠١
١-١٠×٣١٣٣٠ ١٢٥٣٢ ٠٣
١-١٠×٨٧٠٢٩ ٣٤٨١١ ٠٥
*)A :( * *3 +1EΓ +3 Ag (٠٠١) % , M( * . Ag (٠٠١) 3.4=νh (eV) 60=γ
ℑe (a.u) )sin(1 γβ =ΓE (a.u) )sin5.0(1 γβ ×=ΓE (a.u)
٥-١٠×١٢١٦٩ ٥-١٠×٤٨٦٧٨ ٠٠٠٢
٤-١٠×٣٠٤٢٤ ٣-١٠×١٢١٦٩ ٠٠١
٣-١٠×١٢١٦٩ ٣-١٠×٤٨٦٧٨ ٠٠٢
٣-١٠×٢٧٣٨١ ٢-١٠×١٠٩٥٢ ٠٠٣
٣-١٠×٧٦٠٦٠ ٢-١٠×٣٠٤٢٤ ٠٠٥
٢-١٠×٣٠٤٢٤ ١-١٠×١٢١٦٩ ٠١
١-١٠×٢٧٣٨١ ١٠٩٥٢ ٠٣
١-١٠×٧٦٠٦٠ ٣٠٤٢٤ ٠٥
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
0 0.1 0.2 0.3 0.4 0.5 0.6
B=0.5*sin( )B=sin( )
*(L)6 : ( .W 1 * * *3 #5β1 .
γ
γ
ℑe (a.u)
1EΓ
(a.u)
γβ
γβ
sin
sin2
1
=
=
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1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
0 0.1 0.2 0.3 0.4 0.5 0.6
=30 =60 =90
6.2804E-03
6.2805E-03
6.2806E-03
6.2807E-03
6.2808E-03
6.2809E-03
6.2810E-03
6.2811E-03
0 0.02 0.04 0.06 0.08 0.1 0.12
B=sin( )B=0.5*sin( )
γ γ
γ
γ
γ
ℑe
ℑe
(a.u)
(a.u)
1EΓ
2
1
E
E
ΓΓ
*(L)G :(.W 1 * * *3 #5 0 90,60,30=γ
*(L)8 :( K1 #521 EE ΓΓ β1 .W 1 * /.
(a.u)
γβ
γβ
sin2
1
sin
=
=
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1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0 0.02 0.04 0.06 0.08 0.1 0.12
Ni(001)
Ni(111)
12.7198312.5494
13.3989
13.5694
11.769911.8891
0.E+00
2.E-05
4.E-05
6.E-05
8.E-05
1.E-04
1.E-04
1.E-04
11.5 12 12.5 13 13.5 14
*(L)D :( * *3 % *.1EΓ I )1)( =wR ( +( M 0 /
* *3 ( + 3 H + 3 )< . + )(3.4 eVh =ν 60=γ Ve 002.0=ℑ.
ℑe (a.u)
2EΓ
*(L)7:(+ +M .W 1 * * *3 #5Ni(996) Ni(666)
E (eV)
1EΓ
(a.u)
(a.u)
Ni(٠٠١)
Ni(١١١)
Ag(١١١)
Ag(٠٠١)
Cu(٠٠١) Cu(١١١)
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Reference
6. R.Shakeshaft and L.Spruch, phys. Rev.A GGE66 (6CE9).
G. M.A. Woolf and G.W. Rayfield, phys.Rev.Lett.6D, G8D (6C;D).
8. R.Shakeshaft and L.Spruch, phys. Rev.A 86, 6D8D (6CED). 7. Ludwig Bartels ,S.W.Hla, A. Kuhnle, G.Meyer, J.R.Manson and K.H.Rieder,
phys. Rev. B;A, G9D76; (G998). D. Jabbar M.Khalef. Thesis , Basrah , Iraq, ٢٠٠٠. ;. D. Straub and F. J. Himpsel, Phys. Rev. B (١٩٨٦) ٢٢٥٦ ,٣٣. ٧. Kittel in introduction to Solid State Physics sixth edition p (١٩٨٦) ٥٢٩.
E. C.C.Grimes and T.R. Brown, phys.Rev.Lett. 8G, GE9 (6CA7). C. K. Giesen, F. Hage, F.J.Himpsel , H.J.Riess and W.Steinmann , phys. Rev. B
8D, CA6 (6CEA). ١٠. P.M. Echeniqe and J.B. Pendry, Prog. Surf. Sci . (١٩٩٠) ١١١ ,٣٢.
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JK 0! !( C" !E?ZnS
( ! 0!DB!! &= /.) @ !D* L *. 9 &, *** L ) )***
* ! ") / ! ( /+ *,
** !, BA ") / * " ( /+ *,
*** +( * @!( / * " ( /+( *,
II( LII2 5II -IIZnS HII , II( II II0
II ( 3IIL /3LII >II II5(Cs68A) ? LII% QII3 + +IIZnS LI2 RIM <I T1 % > HW X 3L . /3LI I +
-I ( T < * 3 % > HWZnS )I I 0 +I I% I( ! XI YI +IL + . < <I I0 *I
KII0 =II II! )5II LII2J RIIM II )899FC99nm.(
Abstract Thin transparent film of ZnS have been using chemical spray
pyrolysis technique. These film have been exposed to gamma rays. It was found that the as deposited films affected by γ - radiation Cs which lead to change in the optical properties.
The irradiation change the absorption coefficient of ZnS also a change in optical forbidden gap for direct allowed and forbidden transition were abserved. Transmission and absorption spectra have been recorded in the wavelength range (nm).
- .
LI2J I 1I ) I I( H ( 30 3 +I 3 !3 M $0 + I I I, ( I, TI1
30 M(L M<1 > *< 3< I I RI IB I I 1I I! /I /I I I +I I +L3 + ! (
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+LI3 +I +I U I1 3 K< ! 0< J (P IMB I( )MJ + 3 ( ! 1) I 3I I ( I, (
L 1 /< ! 1 ( . I +I LI2J I< +I KLI( I ,5 , M( M<1 I( I I30 >I KI3 +(
R LJ 0 + I, I0 I! T <I KI0 I + < K0 + $! I! >IP W! I( I ! + ( B
T <I I0 I! T <I KI0 I + M +(! *< T <I *I 3 I +I )I(! I03 I Jα ( I 0 )I )
*5I I IL I1 I< ! % B ) 0 !3 + I I )I( )I! I 0 ?5I 0 +( +P * !
=1J 0 / ) I )I I 0 L 1 )? ( + - +P I -I IL I1 IM <I ) +( L 1 )? ( OB
)! 0 6,DeV [6]. +I I < S N * ! MB L2J 3 3 O
( U ! T, <1 *5!B 03 5 1 $,0 I + M $I0 =IP HI , ( 0 3 - 1 )MJ
L2J 5 ! 1 MG] –[8 Z 2 > 0 R : 1 )MJ K ( 0 ? LI% 5 (P I0 I
=1B $0 1 M *< +( L2B > *< (P I< 3 ( % B ) S $0 + - 1 ,5 , M( < I + L2B 5 0 3 ? L% ( ! 1
=1B $0 5 3 M<] [ 7 . L2B 5 )ZnS ( R 1 I. +I 1 S $< )L L2B > *< 0
* ( 3LB + 1 >P M53. ..&!) "
L2B 5ZnS) ( - ( 1)Zn ( j! ( @.68;,GEgm\mol ) 99% (IL *I +I )M General purpose Reagent BDH-Limited
Poole England P )(9,;E6gm ! - ( ) + D9ml ? I +I
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- 0 * > *< . I! )I $I ( *( N +( -(M Q + 0 5B / * ( *(L N +B Q% *
K1)HCl ( ) 01 > /5 + $, * #<[!GD + ([ (L 0 ? ) P - ( * U * > *< - *
UI 5I @ $ [L + . ) + @ *<! ( < B S 3 0D9ml I I . *I / - ( * +
89ml 0 * > *< - L2B ZnS J * $! : OHCOZnSClNH2OH3)NH(CsZnCl 2242222 +↑++→++
!"# !" !# $%
&!'# $ ( )*+ ,- ZnS./ !0 12 :
↑+↑++ →++ OHHClNHZnSOHZnsClNH Co
23300
24 222
L2J - U 3 * g * ) + 0 1 @ X + + M! O + ([69F7 gm gI I I3 M 3 .
) 3B ) ! .( $! !3 + ? L% - D] [;, . =I I! K 0 1 L2J < <(899_C99)
!% ) ! / . 1 H ( ! ) 3 0 3LJ 0)(ASTM_system .
) ? L% /3L67 e ( 3L (Cs68A). 3. , <=
*(L #5)6 ( ? L% B *0 < < + 3ZnS +( /3L 3 * % *3 I3 I 0 ! )%< *0J ( < <
< < < % *3 +( T < ! + )( *0J e% /3L 3 < < * . *(L !)G ( +I( /3L 3 + O
)( *0J * )%< *0J ( % . I T < * 3α( T < 0 ! 3 1 ] [ A:
(١) d/A303.2=α
A < < d? L% - .
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*(L )8 ( +( /3L 3 * ? L% + 0 T < * 3 + 3 *. ,0 0 %< + 0 / T < * 3 % 0 !
3 0 T < * 3 % *3 T < ! + 3 +>697 α( )L ( *< > * .
)L ) 0 )E( g L2 ZnS 1I /3LI I3 * 3] [E: (٢) r
g )Eh(Bh −ν=να
(B) > 3 . . r = 6/GY L * ! . r = 8/GX L * ! .
*(L )7 ( + 3 *.2( )hα ν +I(B I /3L 3 * ? L% + 0 ) 0 )E( g /3LI 3 )! 0 Y L *
)9,6eV. ( *(L #5)D ( 3 *I ? L% + 0 I3 ) 0 > *< M /3L)E( g I3 IM I X L *
/3L . T <I ! .B * > = /3L + O*< > *< + +( ( + ] [C .
5. )
? L% T < * 3ZnS @ ( 3L /3L >P ? L% Q3 * /3L * .
? L% < < + <ZnS M33L 3 . /3L 3 )L ( ) 0.
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!:N
[-] Martin A.G.,"Solar cells operating principles technology", (6CEG).
[.] A.K.Abass, Z.A.Ahmed and R.E.Taheir, phy. Stat. sol. (a) CA, (6CE;).
[3] A.K. Abass, Solid state communications , ;6, D9A, (6CEA).
[5] O.P. Agnihotri, M.T.Mohammed , A.K. Abass and K.I.Arshak, Solid state
comun.,7A6CD, (6CE8). [6] A.K.Abass ,F.Y.M.Al-Eithan and R.H.M.ISHO, phys.stat.sol.(a)EC , GGD,(6CED). [8] H.A.Jassem, Department of physics, college of science ,university of Basrah,
Basrah- Iraq
[:] A.K.Abass ,A. K. Husen and R.H.M.ISHO, J. Appl. phys. Vol. DE, No.
7,(6CED).
[;] Y. N. Al- Jammal, Solid stste Physics, Published by Al-Mousul University,
Arabic Version, (6CC9).
[>] T. K. Subramanyam and S. Uthanna, Physical Properties of ZnO Films Prepared by dc Reactive Magnetron Sputtering of different Sputtering Processes, Cryst.
Res. Techol., Vol. 8D, pp. 66C8, (6CCD).
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)(: (A) ZnS
)(: (T) ZnS
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)(: ! (αααα) " # ZnS
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)$(: # %& (Eg) '( ) *+ ZnS
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),(: # %& (Eg) ) *+ - ZnS
, ! , ( ! !
) I,6 – . MeV ( ! P
&" ! ! < B / @!
& $" /(
KM +B + +I 0 ( 0L - > K3 1 0L = 0 :
) G78Pu G76Pu G8CU G8AU G8DU G88Th G86Th( 0 0 + = U ) .(9,D - G MeV 0LI I +
! .W * 3 0L 0L 53 /0 *1 + I I 0 =I +5 0L 0L + O -
0 ) MeVG F 9,D ( 0 ) T . I I RI ! 0 ! 3 3,(Fitting Method) +I( IM1 +
0 I I 0 ( 0L !3 B W 9,D – G MeV) (1 0L =.
Abstract The aim of this study is to study the behavior of fission probability as function of neutrons energy of various fission nucleuses (٢٣١Th, ٢٣٣Th, ٢٣٥U, ٢٣٧U, ٢٣٩U, ٢٤١Pu, ٢٤٣Pu) at the same energy range of descending neutrons (٠٥ to ٢ MeV). The fission probability is considered as a principal effective factor in measuring the fission cross section of fissing materials. In this work we found that, the fissing materials at the energy range of descending neutrons decreased as a result of increasing neutron energy. In this study, we conclude the empirical relations has been calculated by the fitting
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method in which the probability fission value can be estimated as a function for neutrons energy (٠٥MeV-٢MeV) and for various fission nucleuses.
B!H )Theory
3 ! H 0L < B 6C87. 0L L(B +I + + 3 *)(Hahn + )(Strassemann 6C8C +[ O
3 < H * K< + < K P +3 ( ( [6] . k (B = +B !A>ED) ( ! +
I.(J = - ) >P ) HW T M! +( *( 0 0 [G] . > ( ! + + >P ) H 0L H * !
0L OL (fission fragments) + 3 *I( I I 0L 3 H (G,D neutrons) )! 5 3 ( )sec10 15−≅ 0LB *([8] . I * I + ) 3 0L 53 /0
e. R 0L :PaG87) 8He,P (ThG8G . 0 +B ( I I +I + > 3 0L 53 /0
0Lfission probability) ( ( ) +( 53 /0 >)Compound
nucleus formation cross section ( 3 >03 [7] :
)1.(......................................................................nfcnf P×= σσ
+P ( )nfσ : 0L 53 /0 )( cσ :( ) +( 53 /0 ( )nfP : 0L ( ) 1 +B M0 +( M
( =1J * + 0L 3 ( M! +( 0L ) [D] : ( ) ( ) ( ) )2.(......................................../∑∑=
jj nfnf jNjNjPP πππ
+B ( )j,π > *. T <I I I *I I, M + +B (( )πjN , M ) *. ( )j,π +B ( )πjPnf I *I.
RIM M ( ) M * 0L ) )3 1 0L0 ) +( 53 /0 +B ( I 3 +I @ I +I( ( [;]:
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( ) )3.........(....................4/22
0
2
Γ+−
ΓΓ=
∗EE
ac Dπσ
*. aΓ ( ) +( ) R * , - 1 +B . +( J * + 3 ! 0L ) M ( =1 Γ -
( 1 ( * / H * M! +( . D 4M 0 ) * . ( )∗
0E ( 0 M[ M 3 +( M( M 0 0 >P ! 5N <J ) . + (aΓΓ I ) 1
H 0LI HI * + ) ) * ! 1 ) X[A]. 3 +B8G6 +( B0 I 0LI 53 /0 M
1 + H 0L * HJ 0L M =I Q3 3 4, 35 0 ( 0L R +( 0L+ .
<=
)L 3 1 ! 3 + @<1 4, 3
(LA- 76CE , Los Alamos scientific laboratory) I I ! [E] I3 RM /3L ? ( S - 5 ( = !I I
- + .3 3 0 K0 -I I IM! e )L =1 3 1 4, > 3 K
0L 53 /0nfσ 3 1 I53 /I0 )I ( )barn ( ) +(cσ 3 + * ! + )6 : (
)١(ج3ول
اد ا\+ر1 ا(,#"!1 )" 1OآC)اة اG ا# .CEا T+$)[٨]ا
Pu243 Pu243
Pu241 Pu241
U239
U239 U237
U237U235
U235
Th233
Th233
Th231
Th231
Target Nucleus
( )bnfσ
( )bcσ
( )bnfσ ( )bcσ ( )bnfσ ( )bcσ ( )bnfσ ( )bcσ
( )bnfσ ( )bcσ
( )bnfσ ( )bcσ
( )bnfσ
( )bcσ
nE
(MeV)
٠٥ ٣٦٥ ٠٧٦٦٥ ٣٦٥ ٠٢١١٧ ٣٦٥ ١٧٨٨٥ ٣٦٥ ٠٨٧٦ ٣٦٦ ٠٧٦٨٦ ٣٦٦ ١٩٠٣٢ ٣٦٧ ١٧٩٨٣
٠٦ ٣٦٢ ٠٣٩٠٩ ٣٦٣ ٠٢١٧٨ ٣٦٣ ١٥٩٧٢ ٣٦٤ ٠٨٧٣٦ ٣٦٤ ٠٧٨٢ ٣٦٤ ١٧٨٣٦ ٣٦٥ ١٧٨٨٣
٠٧ ٣٦١ ٠٣٥٠١ ٣٦٢ ٠١٨٤٦ ٣٦٢ ١٥٥٦٦ ٣٦٣ ١٥٢٤٦ ٣٦٣ ٠٦٨٩٧ ٣٦٣ ١٧٤٢٤ ٣٦٤ ١٥٦٥٢
٠٨ ٣٦٢ ٠٢٩٦٨ ٣٦٣ ٠١٦٣٣ ٣٦٣ ١٥٢٤٦ ٣٦٣ ٠٧٩٨٦ ٣٦٤ ٠٦٩١٦ ٣٦٣ ١٧٤٢٤ ٣٦٥ ١٤٩٦٥
١٠ ٣٦٣ ٠٢٥٧٧ ٣٦٤ ٠١٤٥٦ ٣٦٣ ١٤٨٨٣ ٣٦٤ ٠٧٢٨ ٣٦٥ ٠٦٢٠٥ ٣٦٥ ١٧١٥٥ ٣٦٦ ١٤٦٤
١٢٥ ٣٧٨ ٠٢٥٣٢ ٣٦٩ ٠١٢٩١ ٣٦٧ ١٤٣١٣ ٣٦٧ ٠٦٩٧٣ ٣٦٨ ٠٦٢٥٦ ٣٦٩ ١٨٤٥ ٣٦٩ ١٥١٢٩
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2008١٥ ٣٧٢ ٠٢١٩٤ ٣٧٣ ٠١٢٣٠ ٣٧٠ ١٤٠٦٠ ٣٧٠ ٠٦٦٦ ٣٧١ ٠٥٥٦٥ ٣٧٢ ١٧٨٥٦ ٣٧٢ ١٤٨٨
١٧٥ ٣٧٣ ٠٢٠٥١ ٣٧٤ ٠١٢٣٤ ٣٧٠ ١٤٠٦٠ ٣٧٠ ٠٦٦٦ ٣٧٢ ٠٥٥٨ ٣٧٢ ١٦٣٦٨ ٣٧٢ ١٣٧٦٤
٢٠ ٣٧٥ ٠٢١٣٧ ٣٧٦ ٠١٢٠٣ ٣٧١ ١٣٧٢٧ ٣٧٠ ٠٦٦٦ ٣٧٢ ٠٥٢٠٨ ٣٧٢ ١٥٩٩٦ ٣٧٣ ١٣٠٥٥
+ *)6 ( 3 $0)6 ( 3)G ( 0L * ! 0L )G: (
)). (
P ! ! *, 9,D – G MeV). (
Pu٢٤٣ Pu٢٤١ U٢٣٩ U٢٣٧ U٢٣٥ Th٢٣٣ Th٢٣١ Target Nucleus
Pnf Pnf Pnf Pnf Pnf Pnf Pnf En
(MeV) ٠ ٠ ٤٩ ٠ ٥٢ ٠ ٢١ ٠ ٢٤ ٠ ٤٩ ٠ ٠٥٨ ٠ ٢١ ٥ ٠ ٠ ٤٩ ٠ ٤٩ ٠ ٢٠ ٠ ٢٤ ٠ ٤٤ ٠ ٠٦٠ ٠ ١٠٨ ٦ ٠ ٠ ٤٣ ٠ ٤٨ ٠ ١٩ ٠ ٤٢ ٠ ٤٣ ٠ ٠٥١ ٠ ٠٩٧ ٧ ٠ ٠ ٤١ ٠ ٤٨ ٠ ١٩ ٠ ٢٢ ٠ ٤٢ ٠ ٠٤٥ ٠ ٠٨٢ ٨ ٠ ٠ ٤٠ ٠ ٤٧ ٠ ١٧ ٠ ٢٠ ٠ ٤١ ٠ ٠٤٠ ١ ٠٧١ ٠ ٠ ٠ ٤١ ٠ ٥٠ ٠ ١٧ ٠ ١٩ ٠ ٣٩ ٠ ٠٣٥ ١ ٠٦٧ ٢٥ ٠ ٠ ٤٠ ٠ ٤٨ ٠ ١٥ ٠ ١٨ ٠ ٣٨ ٠ ٠٣٣ ١ ٠٥٩ ٥ ٠ ٠ ٣٧ ٠ ٤٤ ٠ ١٥ ٠ ١٨ ٠ ٣٨ ٠ ٠٣٣ ١ ٠٥٥ ٧٥ ٠ ٠ ٣٥ ٠ ٤٣ ٠ ١٤ ٠ ١٨ ٠ ٣٧ ٠ ٠٣٢ ٢ ٠٥٧
* + M < 4, + 3 )G ( 03 H *(L +( 0 0 ( 0L 9,D – G MeV) ( 0LI =
1)G78Pu G76Pu G8CU G8AU G8DU G88Th G86Th( *(L ! 5 )6 .(
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(Fitting equation) ش-, (١):()%' ا&% ا$#رآا ا وت ا ام د ا
y = -0.0418x + 0.5236
y = -0.0791x + 0.5054
y = -0.0636x + 0.4835
y = 0.3186e-0.3322x
y = -0.0447x + 0.2246
y = 0.1707e-0.6588x
y = -0.0187x + 0.0640
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2 2.5En(MeV)
Pf
Th(231)
Th(233)
U(235)
U(237)
U(239)
Pu(241)
Pu(243)
Linear (Pu(241))
Linear (Pu(243))
Linear (U(235))
Expon. (U(237))
Linear (U(239))
Expon. (Th(231))
Linear (Th(233))
()- ( = " * , ! , ( ! (Fitting equation)
0 3 S ? (fitting method) *(L + 3)6 ( 0 =09,D – G MeV) ( ( 1 0L = :
)(6688.0231 1707.0 MeVE
nfnePTh −=⇒
064.0)(187.0233 +−=⇒ MeVEPTh nnf
( ) 4835.00636.0235 +−=⇒ MeVEPU nnf
( ) 5054.00791.0243 +−=⇒ MeVEPPu nnf
( )MeVE
nfnePU 3322.0237 3186.0 −=⇒
( ) 2246.00447.0239 +−=⇒ MeVEPU nnf
( ) 5236.00418.0241 +−=⇒ MeVEPPu nnf
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!3 W (P ! ), ! 03 ! M RB 3 +B =I +I5 1 0L = 0 0 ( 0L
9,D– G MeV) ( 0L . ,:
3 /0 ! ).W M *3 0L RI + I 0L H * + 3 H 0L 53
> 3 ?) (selection rules HI 1I > e $ ( I( 0L O O H 1 O H
I *(LI ! + ( 0L < 3 + 3 0 + 0)G ( )A, B, C, D, E, F, H ( I + OI @I1 +I H >
T 0L + I3 1 0L = 0 0 ) * ( ) +( )( cσ 0 -I *I +B +( M
3 *1 + - O + 0L 0 ))G ( I + +I I )I * + Q% O O * ( H 1 > 3 0L I1[ I O I O + ( H 1 O + $ 0L
0L 2 e1 e * P )I3 M ( ) - > * . >I ) % + 3 * B ( 3LB 3 * - 5J
* M <J( )pn, ) I /I *I 0 +B ( ) ( ) ( ) ( ) ( ) ( )fnnnnnpnnn ,,2,,,,,,,,, γα′ RIB +
I 0 + / +( +( 1I *I IO I2 *I. H-( O *(L ! + K1 )G( R IB +
0 + 0 + U > ) +( 0L + ! (
Pnf *( 1 +( + O - =1 + 1 +( ) *( 0L ).
*(L)G : ( 0L = 0 0 ( 0L +
1.
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Th٢٣٢
B
٠
٠٠١
٠٠٢
٠٠٣
٠٠٤
٠٠٥
٠٠٦
٠٠٧
٢٥ ٢ ١٥ ١ ٠٥ ٠
Pnf
En(MeV)
Th٢٣١
A
٠
٠٠٥
٠١
٠١٥
٠٢
٠٢٥
٢٥ ٢ ١٥ ١ ٠٥ ٠
Pnf
En(MeV)
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U٢٣٧
D
٠
٠٠٥
٠١
٠١٥
٠٢
٠٢٥
٠٣
٢٥ ٢ ١٥ ١ ٠٥ ٠
P
En(MeV)
U٢٣٥
C
٠
٠١
٠٢
٠٣
٠٤
٠٥
٠٦
٢٥ ٢ ١٥ ١ ٠٥ ٠
Pnf
En(MeV)
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Pu٢٤١
F
٠
٠١
٠٢
٠٣
٠٤
٠٥
٠٦
٢٥ ٢ ١٥ ١ ٠٥ ٠
Pnf
En(MeV)
U٢٣٩
E
٠
٠٠٥
٠١
٠١٥
٠٢
٠٢٥
٢٥ ٢ ١٥ ١ ٠٥ ٠
Pnf
En(MeV)
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):
6. 0L ( )nfP 0 0 . G. 0L ( )nfP . 0L K1 3 K1
G78Pu) G76Pu G8CU G8AU G8DU G88Th G86Th(. 8. 0L 53 /0( )nfσ 0L > 3 ( )nfP )I +(
(( )cσ ( 0 > B *(L 3 H (E)M ( ) . 7. 0L +( *3 $ !B +5( )nfP )I I 0 I
+ 0 (neutron generators) > * . -(G,DMeV,67MeV).
References [١] E.C. pollard and W.L. Davidson ," Applied Nuclear physics " second Edition, John and sons , Inc .New york, (١٩٥٣). [٢] DiIorio ,G.J., "Direct physical measurement of mass yields in thermal fission of Uranium – ٢٣٥" Ph. D. thesis, University of Illinois at Urbana – champaign, (١٩٧٦). [٣] J.M. Carpenter, "Neutron Production, Moderation and Characterization of Sources" (٢٠٠٤). [٤] M. petit, M. Aiche, Determination of The neutron cross _ section for ٢٣٣pa from ٠٥ MeV To ١٠ MeV, CEN Bodeaux, Bp ٣٣١٧٥ ,١٢٠ France,(٢٠٠٢).
Pu٢٤٣
H
٠
٠١
٠٢
٠٣
٠٤
٠٥
٠٦
٢٥ ٢ ١٥ ١ ٠٥ ٠
Pnf
En(MeV)
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[٥] J.D Cramen and H.C. Britt, neutron fission cross_ section for ٢٣١Th- ٢٣٢Th- ٢٣٥U and ٢٤٣Pu from ٠٥ MeV to ٢٢٥ MeV using (t,pf) Reactions, Nuclear Science and Engineering ١٨٧-١٧٧ (١٩٧٠) ٤١. [٦] Harald enge, ''Introduction to nuclear physics" Addison- Wesley publishing company, (١٩٨٣). [٧] J.csikai "hand book of fast neutron generators " volume ٢, Inc., florida,(١٩٨٧). [٨] C.L. Dunford and P.F. Rose "neutron cross section " volume (١٩٨٨),٢.
! D B!! &A !Q ! !(Nd:glass) "
! R! &!
/ . .B$ S */* .* .& !E *# / ***.* ." ***
* )( ") /!( ! ! *,.
** 0! ) ( * " /+ 0!=
***! ") /* " ( /+ *,
KM >P 3 ! 5(Nd:glass) I% I )I ) / 5 ) ( * 3 . 3 + KL( * 3 $0 )
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0 S * 3 KL ( ,5 I *1I 0* 3) <I YI < ( U !2! ( .
IM H<I = I 5I >I ) Nd:glass( I3N (7*699mm) ( * 3(n=6,D86) . I( *I 3 I% 3 4,
. 3 HW 3 + ( ,5 )L. + + < 4, *1 + ) ( 5I *1
(Nd:Glass) . ABSTRACT This research deals with study of thermal lens generation in rod of (Nd:Glass) laser due to refractive index changing for rod material with temperature , measurements of thermal lens consist of several ways, non-interferometry method by using pin-photodiode and interferometry method by using : photographic cat film, Camera. Experimental optical setup for this method consist of (Nd:Glass) rod
( φ7*699mm) with refractive index (n=6,D86). The results of refractive index changing & light intensity had been compared for to cases and determine focal length for thermal lens . From studying the result of this research, there is thermal lens generation (i.e. diverge lens) inside rod of (Nd:Glass) laser.
E U ")!:
< *( L L +P 1B + *1 " 3 " I! +3J = > I I 3 +[! - 5 "
. * ,5 ? P " " I I * J * + 3 .[ X5 . ! 6CCC + *( L (Dmitriy
I. Kovsh, David J. Hagan and Eric W. Van Stryland) [6] <I ! / TI *, I 0I ! 3 5 L 5 S ! 3
< " >P HW ( * 3 % I 3 *, *1. L [G] (Ginitc Institute of Manufacturing Technology) I
! +. +G999 " I *1I 0 .[ +ONd: YVO7 0 @15 H " 1 .
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H< $! U * ) ) ! .[ + 4 ( 1 (Camera). + *( L U !Rudiger Paschotta,Jurg
Aus der Au and [8]Ursula Keller I I! .[ +O e 0 M15 3 ) I M 3 + *(
. !G996 *I( (Akihiko Nishimura, Kastsuaki Akaoka and others) [7] I. " I!( J. Nuclear Science and Technology, Vol. 8E Dec.G996) +I
! .[Ytterbium Phosphate Glass) ( 1I IO(
Shack- Hartmann wavefront sensor) + 3 U ( Y M % U (699 Hz). +I *I( LI(Isao
Matsushima, Hidehiko Yashiro& Toshihisa [D]Tomie) " M3 + < 3 ( (AIST) + !G99G ! 3 +O
(Ti:sapphir) I 1I I + Q3 .[ +P I I + I *0 + < #< 3 HW *0 +P
2 0 )( ) 1 H X 3L ) . I c 3 " I I!G997 L ( International School of Photonics) [;] I3 .[I +I
.[ ) O + ) + S *1 .
!! !E?: Thermal Effect
3 *%L M .W + ?B < * ( +P c5 X 3L H T < + ) ) + / + [ .[
5 #0 ) + ) +1 +P )5 ( >P O + H X 3L < L >P HW 5 )
( * 3 % > +3 MN ) *1. + * +( ( c5 )? ( 5 ! ) + )( ( +P -(
c5 + 0( /5 S ) +P H ) 3L . (
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IO I2 )I / ( 5 ! < L +P :F 6. ( * 3 % 3.
G. M S (. 8. < L5 0 ( MO .
5 3 .[ R + *( . HW *0 1 @[( *. 5 +[! O +( ) ) P
))% ( % 3B0 ( ( * 3 . *(L(6) *. 1 H< O +O < 3 + 001(O.S) H
% HW 3 .(f)
((-) ! &% *" ! DH ! .
!! " :Thermal Lens
L L K IM ) S ( + 4 < ( * 3 K1 > )3.
) $! +P[ Tm-T9]3 .[ H 0 #0 ( + . ) .[ . - :F
6. 0 @ M RLα . G. ( * 3 0 K< ) Sdn/dT. 8. ,5 .[ Cr,φ .
3 + @ *< ( * 3 ( % + 3 /0 ]A[ :F n(r,φ)= n(9)[6-Q/GK(6/Gn9* dn/dT+n9
G α Cr,φ)rG]……….(6)
+P : n(r,φ) = K< % ( * 3 H0.
O.S
O.S
M١ f M٢
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Q = ) (. n(9) =H 0 ! ( * 3.
K = H *< * 3. α = 0 * 3. dn/dT = ( * 3 H * 3. Cr,φ = * 3,5 .
( L ( * 3 % > 3 MN ) .[ / ( HW *0 3 >P 5 @ M ) H0 K<(
]A[:F f(r,φ) = Ka/Pa[6/G dn/dT+ Cr,φn9
8+ αr9o n9F6p/L] F6 …( G)
+P : r9 = 5 0 K<. A =5 53 /0 . Pa = 5 ! ) ( ).
) .[ ( * 3 % X5 * K[dn/dT] )I3 ) +P3 ( * 3 % > M ]A[:F
∆nT= [Tr-T9]dn/dT ……….(8)
+P Tr 0 K< *0 > ) *. r , T9 ( ! ) 5. * 3 % +P K - <<1 3 +
J +( ) > 3 ( 3 (J U .
!! " B!Q :
0 _ HW *0 +P He-Ne0 * U 5 *1 X 3L 3 ) HW *0 +( ( " < 3J >
,5 KL ( 1 3 U . e 3 HW *0 ( ]E[ ]C[:F
a feq7 + b feqG + c feq +d = 9…………(7)
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a = 7λG/ πG DG ……………..(D)
b = DG(6-d6/ ( f6-d6))-Wd …………(;)
c = - G Db(L+d6f6/ ( f6-d6)) ………(A)
d = DG(L+d6/( f6-d6)) ……………(E)
d6 = d`+ l/Gn ……………….(C)
6/feq = 6/fR + 6/f6- d6/ f6fR …………(69)
a, b,c,d =. . feq = O j! ( HW *0.
D = 5 0[7mm] . d ` =3 5 + ! . f6 = 3 HW *0. Wd = X 3L 0. L => 3 + ! . < (pinhole) . l = 5 *069cm .
n = 5 ( * 3. " V=!
3 .[ U $0 ) > : (6) ,5 KL ( 1 *1 0. (G)1 *1 0 : a F 3 ( (Camera).
bF U < Y (Cat film) . *(L(G) <I I 5 *1 . 3 #5
1 : (6)3 ( .
(G) ,5 Photodiode. (8) U < Y Cat film.
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((.) ! D, E !! " ! !) .
K !:
&=D 9( * !! " !: (Pin- Photodiode)
>J 0 3 .[ + KL( *1 0 > R X 3L He-Ne) ( 5 *1( Nd:Glass) I @ +! *1 (9FG99 9C) ! 1 X 3L )L % O (Pin-Photodiode) X (
RSF89E) .! % U HW 3 ( % $L 1 0 R 3B > )3 3 3 5 S 1 3 )
.
He-Ne laser B-E
l d`
L
Monitor
Scope
He-Ne laser
BE Rode
F
PD
١
٢
Photographic film
٣
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((3)E !! " @ &!) B! ! .
E !:
!! " !* ! :
6. < (Camera . G. U < YCat film .
. *J @ U (3 + ) *1 B + KL( 0 R ! X 3L RB +0 =P 1 5(He-Ne) 5 >
(Nd-Glass) @ +! *1 X5 ( 9FG99 9 C) *1 B U ) 3 HW *0 >P L J % +P 1 .
*(L(7) ( 1 3 .
<=
eF X 3L )L U ) He-Ne:(
camera
Ne-He BE
Rode inside oven
Filter
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)L % +PHe-Ne 5 *1 R (Nd:Glass) ? .P 3 @1 5 ) 3 >P L M * ]69.[
5 +1 !(Nd:Glass) ) > !% ) + G99˚C X 3L )L O He-Ne I I( Q I1 BI
L )>P 3 ) (*(L #5 (.(D)
*(L(D)) / X 3L )L % .
e .F% $L 1 0 ! U : % +P / B S >P P L S 1 X 3L /0 0 ! 3LJ
5 + 1(Nd:Glass)5 *1 3 (W .
0
2
4
6
8
1.5 1.58 1.66 1.74pro
pe
bea
m in
ten
sity
(m
v)
T=٠ ٢٠ C T=٢٥٠ C
0
2
4
6
8
10
12
14
16
18
20
0 50 100 150 200 250
Temperature C
Pro
be
bea
m in
tensi
ty [m
v]
٠C
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((8) 0!! )! ! W" 0 C W" ! % !# .
/ X 3L )L + : * X 3L )L ? .P *< % !3 Q% +1 3
) .[ 5 + 1 ,5 3LZ.
*(L(A)* X 3L )L % (6) ? .P(G)3 (8)+1 . e . .F 3 3 ( 1: ( 1 U !(Camera) 3LJ U (3 + ) *1 B *
3 >P L 1 J % +P 5 . *J @ + . * (LJ(E) *1 0 J < *. *J J R + Q3 P O
) % / RL . !E? U D B! ! V! !# ) K !# )! 7
! D, 0 !! " U B!Q E A !!.
(K) ; (K ! 0!! )! .
0
2
4
6
8
10
0 4 8 12 16 20 24
time [ms]
١
٢
٣
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(-) T=.8IC (.) T=58IC
(3) T=88IC (5) T=;8IC
(6) T=-.IIC (8) T=-5IIC
(:) T=-:IIC (;) T=.IIIC
e 3F U < Y 1 3 :
U < Y 1 0 R ! Cat film) ( #5 M Q% *1 B * ) ) J *< %.
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((>) 0!! )! @ X * /
)(-) B!Q ! Fr) ( @ "!H "0!! )! 9 .
, )
(6) +P X 3L )L (He-Ne) e< 5 ! ) ( * =1B ) ) )L B 3 X 3L )L M! 3 >.
Fr cm !H" Fr cm "* 0!! )!I C
N-I,I-8
N>,35
N;,>-
N;,I.
-I,5;5
NI,5.3
NI,5-5
NI,3I>
6I
:I
>I
-3I
*Fr = !! " B!Q " * ! * )&=D 9( (
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(G) X 3L /0 0 ! % + (He-Ne) LI 5 *1 ( 3LJ S > I 3 > R > HW )
S 5 *1. (8) ) 3 ( H< RL *1 B + P O
( 1 - @ L(Camera) U Y 1 B ( Cat film). (7) *1 + 0 > HW *0 3 O 4,
J >P / 4, K1 - + O *1:F (a) 1 H< K< (He-Ne) . (b) 3LZ + < ! 3LB + X 5 M1 + ) . (c) 1 U + ) U 01 U HL3 %
). (d) I0 S 1 M 0 J / U ) + X 5 +. (D) M / e O 3 HW 3 *1 0 1 e
3 ( 1 HW 3 U >P 3 .
!
[6] D. I. Kovsh, D. J. Hagan, J. Optics Express, Vol. 7, No.E, pp.F86DF8GA,
6CCC.
[G] P. Xiaoyuan, A. Asund, Gintic Institute Of Manufacturing Technology,
A6 Nanyang, Drive,Singapore ;8E9AD(G999).
[8] R. Paschotta, J. Ausder Au , and U. Keller, IEEE J. Of Selected Topics in
Quant. Elect., Vol.;, No.7 (G999).
[7] A. Nishimura, K. Akaoka, J. Nuclear Science& Technology, Vol. 8E, No. 6G,
G996.
[D] I. Matsushima, H. Yashivo & T. Tomie, National Institute of Advanced
Industrial Science &Technology(AIST), (G99G).
[;] International School of Photonics (ISP), (G997).
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[A] W. Koechner “Solid-State Laser Engineering”Springer-verlag, ( New
York Inc.), 6CA;.
[E] J.S.Uppal, J. C. Monga, IEEE J. of Elect., Vol. QEFGG, No.6G, 6CE;.
[C] N.Subhash & Sathiauandan, IEEE J. of Quan. Elect.,Vol.QEFG9, No. G,
6CE7.
[69] Y.R.Shen“ Principle of Nonlinear Optics” John Wiley & Sons, Inc.,
6CE7.
V ! " [" A/B! * +E
&)
! ")N* " ( N + *,
: N
+ J $ J 3 Y0 ) ! % * µm)6 ( - 1 ? .P M< 0 ! .(
1)) H0B *( > J 0 ! .( +P 4, MOB )69AW/mG ( =1J < $0 M H 3 - >P ! 5P
.[ = H $ *1 + #0 @L )M< Y . S 1 . 30 3 $ % + Q3 B
1 ) . 5 + ( )µm 6,; ( *< ! *)µm 9,7. ( Abstract:- A theoretical study has been made for studying and analysis the change in the temperature of some metals at its surface and at some depth not exceed (١ µm) during laser welding process. This study was made to calculate the necessary energy density for melting . Also comparison between laser and the other industrial methods for welding was made for penetration depth ,the results indicated that melting energy density was (١٠٧W/cm٢) and the laser welding process is the best in which the penetration depth was dependet on the type of material and it was ( ١٦ µm) for Ag and( ٠٤µm) for Fe .
:N
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! < )! >O3 0 < )( +P 5 . ( 0 ! .( + ( >P . + +<
H M 0 - 0 ( 3 U J +(L 0 - T ) 1 B > B 3 1[6].
=1J % >P ! 5P 0 K< 5 *0 + *( .[ +P HW M< N + !3 >P )1 *< + ( ! 1
0 )M< ) + *1 + 1 $% . $% % Y . > 3 - Y . > 0 .
)Keyhole Weld ( * ! ( 0 )6 ( nL ! 1 * . =3 ! 1 B O
)M< Y0 )? ( +30 *< 0)Joining efficiency ( U )mmG/k J (+ () v d/p.(+P v /0 d -p
0 ).* )G ( 1 < 1 Q3 )? ( +. [G]
*)6 ( =1B < / H [G].
آ!ءة ا"Lم ا"0 ري) ٢(ج3ول [٢].
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>B *. H .[ 0 +1 ) *[ )? ( )Heat affected
zone ( - #< MB P .( >B )? ( $0 Q3 +P O H M 3 % ! .! 3 ! = 4, )6F
8mmG/kj ( -( ?Z =1B < 5 1 HB - ?J ! + ! *.J H.
! ( H ! + +6CE8 * + Williams @! ) 4, M5 3 M< -
M< 0 Q 0 ) ) [8] . !6CCD + 1 * + H /0 Q2 + . [8] Daueliog
* 7:F ,M 0 + ! . /0 *. < 0 / !
)MJ P X P M1 3 >P ! 5P 1:[7]
6 – ! ( 3 > )( 0 0 ( *(L)6. (
GF + *J /< (Dmm) M (3 + - 3 #0 / B )MJ K >P H )0 M 2 + ? 02 ! 5P *5 1 5P
*(L ! ( (3 3LJ > )G. ( 8F 1 T < K0 +5 3 1 .
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K "Q B! * &% 0!E:N
6F T, <1 :F ) + *( . B 5 3 1 0 B *0 0 . GF ( T, <1 :F < 3 / / ? *(L . 8F % T, <1 :F + 0%5 >P ! 5P + < % X . 7F) T, <1 :F0 ) X #.
()- ( ! (![3].
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().( !/ ! H * [.].
()3 ( G= ))* \ &% K " (.[.]
B!H ):N
T1 3 0 O3 ! * 3 +( / H * H L)α( M o ) )( )698cmF
6 ( ! % , M < +(! O 5 + + ( _! .(B B )[D] .
S - T ٠
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+ )S ( #0 ) )T 9 ( I!% ) )z ( I $I *I. + H)t.(x k > < L *. [;]. +P 5! P[H= I(6-R)] ) H + 3 *..R I *I.
> 0 X 3L )L #0 (3 [;] .
( #0 ) ! % +(:
+()S ( 3 + #0 )7 (HBz=9 ) ( [01 +(
=1B $ B + .( >B +( #0 ) +P O 3 ) , M HB 5 + ! 5 + >)tp ( +( HB)tp t< <9 (
3 ( +()6([A] .
(٥)
!$ V:N
3 +)6 ( *< +P >P ) + ! +1 + ( > M< 0 )H0B * ( ) #<) ( ! % +( - ,
H $ >P ( ) [D] .
#0 + % ) +( Tb ) M< ) Tm (
5 + H $ >3 :
3 Q3)7 ( 3 !)A ( 4:
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( +( $ )Z m( [ ( :
()5 (B! A V[3] .
<= : N
-N B! A V D ( 0 0!! )! !#
-a U #0 ) %)z=9 ( 5 + >P ( *(L ! O ( )D ( ) 1 + #5 H )GEEDk ( + +3
) =1B $ B / < 4, H[8].
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( )6( D ( @ 0!! )! &% !#(H=-I: W/cm.) .
bF K1 $ U ) % *(L ! ( );( + @I! OI HI M< +( - + @. +( ( + - 0! M<
) B (68D;k).
()8 ( ( @ 0!! )! &% !#0 V .
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.NS ! U , ! A V *H/ )7 . + >P ! 5P ) T1 + *( > 3 H $ +P
.( T1 + 3 +( H H(Km) +(!H >O3 ) (Sm) *(L ! O ( AE) ( [C].
(): (@ B! A V B!! !) ,".
*(L)E (D & B! A V B!! !) ,".
):N
6F 3 B H H0B * >P ) ) /! > T < K0 +5 3 ! +( 0 3LB T < *1 +
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1 *5 H ? 3LZCoG B Nd-YaG *. < <9,CA3LJ 1 +( 0 )L + - , K0 +5 M (3.
GF M< ) +(6E9EK >P *< 0 ! .( 0 )D869
J/cmG (>P *< 5 + *( * (6D79J/cmG) +( - J ! > ) M< ) C8Gk 30 > 3 - ( )
H. 8F>P 0 ) +B)69E W/cmG( 3LZ + ) 1 >P HW
W. /0 ! 0 - + M - >P H.
)) !((
6 ( K K2 . ( J I2 UM" ? LIN IM UIJ G " L K[ 3 3 (>J 30$L6CCG.
٢)William, M. Steen, "Laser Material Processing" , Second Edition , New York , ١٩٩٨. ٣)Bass , M., “Laser Material Processing “ , Northland –Holland Publishing Company,١٩٩٦. ٤)Wilson, M. , and Hawkes , J.F.B. ," Lasers Principles and Applications ",Prentice Hall, ١٩٨٨.
3"، ا"آ(ر ',"s ا\حي، ا"آ(ر ',U= ا"!@0ار )٥,D^"2,ت8, ا!uر وت= ا"v0,u " ا"vNDرات م)TDم .١٩٨٥،ا"J@اق،ا"$ری
٦) Powell , J., Menzies, I. A., " Principles and Application of CO٢ Laser cutting", proc ٢nd conference. on Materials Engineering , Nov.١٩٨٥ London U.K. p.p.٢١٣-٢٠٦
٧ (x*,رب)Vی@y،" ر= ب," u"ا ]",J"ا zUا@Xذ ، "٣,v\ا vA@ت /*,vy v س مvD8"آ(ر اv"ا ،@TD"وا""| وا A@"ی~ وا@J ا\و"M ،ا"@آ= ا"J@ب& "J!u"ا ،zT١٩٩٢،دم.
٨) Caprino, G. and V. Tagliaferri , Int.J .Mach. Tools Manufact,Vol.٣٨٩ ,(٤)٢٨ -(١٩٨٧ ) ٣٩٨, Printed in Great Britain. ٩) Sparks. M. , "Theory of laser heating of solid :Metals" , J. of Appl. Phys. Vol. ١٩٧٦ ,(٣) ٤٧. ١٠)Marce Eleccion ,"Materials Processing with Laser" reprinted from IEEE Spectrum ,VOL.(١٩٧٢) ٧٢-٦٢ ,٩.
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2008
Photons Loss Simulation during Cr:YSO Passive
Q-Switched Ruby Laser Pulse Generation
Abdul-Kareem M.Salih
Physics Dep., College of Science , Thi-Qar University, Thi-Qar, Iraq.
Abstract The loss of photons behaviour during the passive Q-switching pulse built-up time has been simulated. This simulation preformed by numerical solution for four rate equations for 52
4 : SiOYCr + (Cr:YSO) as a saturable absorber material with the ruby solid state laser. The ground and the first excited state of saturable absorber and the laser cavity are the essential factors of photons absorption, concerning of saturable absorber states contribution, they show obesity behaviour according to molecules population for each state with the time and the first exited state lifetime . While laser cavity loss has a steady-state behaviour. The total loss behaviour decreases from maximum to minimum value through the generation time of the giant pulse (passive Q-switching pulse).
* 3 * 5 ? + *1 ! ) 1 ) ( B I) 1[Cr:YSO H3 * *1 + - / *3 3L < ) (
*3 3 / + 5 S . < ) * 4M H 5B H +B ? + *1 T < ! B * K 3L5 . I !
) 1 ! 3L < ) 0 ( L $3 + I MO ! +I +I H\ I, /I ! % > B ( 3 !< + + +
4M H 3 > -( + / +* . ) 1 MOB >IP >O + T ( ) 1 + + / . !< K
3 5 + *1 =%< ) * 3 * 5 . ( ١. Introduction
With the development of the laser in the early ١٩٦٠, the short laser pulses were generated and measured of the order a nanosecond (٩-١٠ sec) by Q-switching technique. The Q- switching is required for many applications of solid- state lasers, such as optical communications, laser remote sensing, pulses convey information, and many nonlinear optical experiments [٤-١]. Many different Q-switching techniques developed in the past, passive Q-switching was considerable advantages in terms of device simplicity and economy because it is requires less optical element inside the laser cavity and no outside driving circuitry[٥،٦]. This technique is depend
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on ability of the cavity to store light energy in the form of standing waves, through the controlling of the Q factor ( the ratio of energy contained in the cavity divided by the energy lost during each round trip in the cavity ). By numerical solution for coupled rate equations for Cr:YSO saturable absorber with the ruby laser, this paper study the energy lost by the simulation of photons losses in the optical switch (saturable absorber) and another kinds of losses by the cavity (γc ) during the giant pulse generation, and the effect of these losses on the giant pulse. ٢. Theory The simulation of photons losses during the passive Q-switching laser pulse generation has been performed by utilized the following rate equations model [٧]*:
nNKNKNKdtdn
caeaagagg )( γβ −−−= (١)
nNKNRdt
dNggpggp
g γγ −−= (٢)
nNKNdt
dNagaaea
ag −= γ (٣)
aeaagaae NnNK
dtdN γ−= (٤)
The parameters used in this model are defined in the table (١). At the initial time, the
* Eq. (٢) is different from Ref.[٧], the factor γp is stated in this paper for general compatible for three & four levels solid state lasers.
photon number inside the laser resonator is low, so most population of saturable absorber molecules are in the ground state Nag ,then
0aag NN ≈ and 0.0≈aeN (٥)
Where Nao is the total number of saturabel absorber molecules. At this time the absorption activity of saturabele absorber is very high (i.e.
0.0≈dtdn ) and one can predict the initial value of population inversion for laser medium ( 0gN ) , then from Eq. (١)
gcagag KNKN /)(0 γ+= (٦)
When the photon number inside the laser resonator is high, most population of saturable absorber molecules are in the excited state ( aeN ), then
0aae NN ≅ , 0.0≅agN (٧)
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At this time the absorption activity of saturable absorber is very low, then we can regard 0.0≈dtdn , also we can predict the threshold population inversion thN
g
caea
K
NK
thNγβ += (٨)
In general, the build-up time of Q-switched laser pulse is very short compared to pumping rate pR and the relaxation time of active medium gτ , then it is possible to neglect pumping rate and spontaneous decay of laser population inversion during pulse generation [٥] , then from Eq. (١) and Eq.(٢) , we get
)/()( ggpcaeaagaggdNdn NKNKNKNK
gγγβ −−−−=
∫ ∫∫ ++−−=th
g
th
g
g
g
p
p
i
N
N
N
N
N
dN
gcaeaagag
n
n
KNKNKdNdn0 0
))/)(()((1 γβγ (٩)
From Eq. (٩), the photon number reaches a peck valuepn when population
inversion gN is equivalent to thN , also agN approaches zero )0.0( ≈agN , then
∫ ∫∫ −−=th
g
th
g
g
g
p
p
i
N
N
N
NN
dN
thg
n
n
NdNdn0 0
)(1γ
but pn >> in , then
)ln((00
1g
th
p NN
thgthp NNNn −−−= γ (١٠)
After the release of the Q-switched laser pulse, the population inversion is reduced to the final value fN , this value can be utilized to calculate the output
energy of Q-switched pulse using the following equation
υγ hENgo
fg
p
fgNNNN
out ))((00
−−= (١١)
Where υh is the laser radiation energy. The peak power of the Q-switched laser output can approximately be calculated by using Eq.(١٠) as
)ln(()( 00
0
go
thgo
cg
fg
c
p
N
NN
thgthh
N
NNhn
P NNNP−−
−−−≈≅ γτυ
τυ
(١٢)
The pulse width of the Q-switched laser pulse can be calculated approximately by the following formula
P
out
PE
pulse ≈τ (١٣)
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For calculating the photons loss by the ground and excited level of saturable absorber, also the loss by the laser cavity using the following equations respectively :
Gloss= gaga KNK / (١٤)
Eloss= gaea KNK /β (١٥)
Closs= gc K/γ (١٦)
Finally the total loss of the Q-switched laser can be calculated by the following equation
Tloss= gcaeaaga KNKNK /)( γβ ++ (١٧)
٣. Numerical Simulation ٣ ١ Calculations
From this numerical study of the optical performance of Cr:YSO saturabele absorber with ruby laser, the loss of photons by each the first excited state and the ground state of the saturabele absorber material, the laser cavity losses, and the total loss have been simulated by Rung-Kuta numerical method . The published parameters values in [٨] have been depended in this study as follows
110 sec1096.7 −−×=gK , 18 sec1015.3 −−×=aK , 17 sec100.5 −×=cγ , 1sec333 −=gγ ١,16 sec1043.1 −×=aγ , ,33.0=β ,sec100.1 122 −×=pR and 16100.1 ×=aoN molecules.
٣ ٢ Results and Discussion From the study, the loss of photons due the contribution of the ground state of saturabele absorber seems the maximum part of the total loss at earlier time of pulse build-up, but it is decreasing with time and approach to minimum and constant value (shown in Fig. (١)). This behaviour depending on the molecules transferring rate from the ground to the first excited state and the first excited state lifetime. The molecules population is changing from maximum to minimum value through the pulse generation time (shown in Fig. (٢)), that is causes the decreasing the ground state absorption activity. While the saturable absorber excited state behaviour completely different from that of the ground state, it shows very low contribution in the total photons loss at earlier time of pulse build-up, but increases with the time and approaches the maximum steady-state value (shown in Fig.(١)).This behaviour related to the molecules population in the first excited state, it varies from minimum to maximum value with the time (shown in Fig. (٢)) causes the increasing in the first excited state absorption activity with time.
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Fig. (٣) shows; at the time ٥٩ nsec the population inversion approaches to the total loss value, that indicates the pulse rising time and the photon number approach to the maximum values. After this temporal interval all the laser photons are exhaust of dissipation and the pulse falling time is starting, that is clear from the decreasing of population inversion more than the decreasing of the total loss to approach minimum value of steady-state which is equal to the loss of photons by the laser cavity.
Fig (١): The time profile of photons loss by the first and ground
state of saturabele absorber, laser cavity loss , and the total loss.
Fig (٢) : The time profile of molecules population for the
first excited and ground state of saturabele absorber.
0.00 40.00 80.00 120.00 160.00
Time (nsec)
0.00E+0
4.00E+15
8.00E+15
1.20E+16
Mol
ecul
es p
opu
latio
n
Ground state
First excited state
0.00 40.00 80.00 120.00 160.00
Time (nsec)
0.00E+0
1.00E+17
2.00E+17
3.00E+17
4.00E+17
5.00E+17
Loss
of p
hoto
ns
First excited state
Ground state
Cavity loss
Total loss
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Fig (٣) : The time profile of cavity loss, total loss, Population inversion, and photon number
Table (١) : List of simples n Photon number in the laser cavity
Ng Population inversion of the laser medium
Kg =٢σg/(τr Ag ) The coupling coefficient between photons and the laser active media
σg Laser emission cross section
τr The cavity round-trip transit
Ag Effective laser beam area in the laser gain medium
Nag The ground-state population of saturabele absorber
Ka = ٢σag/(τrAa) The coupling coefficient between photons and the saturabele absorber
molecules
agσ The saturabele absorber ground –state absorption cross section
Aa The effective laser beam area on the saturabele absorber
agae σσβ /= The ratio of the excited-state absorption cross section σae to the ground-
state absorption cross section σag of the saturabele absorber
Nae Population of the first excited state of saturabele absorber
cc τγ /1= Cavity decay rate
γττ /rc = Cavity lifetime
0.00 40.00 80.00 120.00 160.00
Time (nsec)
0.00E+0
1.00E+17
2.00E+17
3.00E+17
4.00E+17
5.00E+17
Los
s, p
opu
lati
on in
vers
ion
0.00E+0
1.00E+16
2.00E+16
3.00E+16
4.00E+16
5.00E+16
Pho
ton
num
ber
Cavity loss
Population inversion
Total loss
Photon number
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210 ln2 rrl r −= αγ Total loss
0α Absorption coefficient per unit length
lr Length of laser rod
r١ and r٢ The reflectivity's of cavity mirrors
Rp The pumping rate
γg = ١/τg Decay rate of the upper laser level
τg The upper laser level lifetime
γp The population reduction factor ( bottlenecking parameter) ), γp
equal ١ for a four level and ٢ for three level laser active medium.
γa =١/τa The spontaneous relaxation rate of the saturabele absorber
References [١] Jianhui G.F. Zhou, Wenji Xie Y.L.Lam, Yihong Chen,”Pasive Q-switching of a Nd:YAG laser with a GaAs output coupler”, Society of Photo-Optics Instrumentation Engineers, .(١٩٩٩) ١٧٨٨-١٧٨٥,(١١) ٣٨. [٢] Yen-Kuang,Kuo and Yi-An Chang,” Numerical study of passive Q- switching of a Tm: YAG laser with a Ho:YLF solid-state saturable absorber “, Applied Optics, (٢٠٠٣) ١٦٩١-١٦٨٥ ,(٩) ٤٢. [٣] Hua Liu, Osmany Hornia, Y. C. Chen, and Shou-Huan Zhou, “Single-Frequency Q-switched Cr-Nd:YAG laser operating at ٩٤٦-nm wavelength”, IEEE J. of selected topics in quantum electronics, .(١٩٩٧) ٢٨-٢٦ ,(١) ٣. [٤] Yen-Kung Kuo, Horng-Min Chen, and Chia-Ching Lin,”A Theoretical study of the Cr:BeAl٢O٤ laser passively Q-switched with Cr:YSO solid state saturable absorber”, Chinese Journal of Physics, ٣٨ (٣-I), (٢٠٠٠) ٤٤٣. [٥].Sigman A.E “ Lasers “, University Science,Milivalleg, California, ١٠٠٧, ١٠٢٥ (٩٨٦ ١). [٦] Yasi Jiang, Ruikun Wu, Daniel L.Rhonehouse, Michael J. Myers, John D. Myers and Scott J. Hamlin, “Bleaching and Q-switching of U٢+ : CaF٢ at ١٥٣٥ nm “, Solid state lasers and nonlinear crystals, (١٩٩٥) ٦-١ ,٢٣٧٩. [٧] Abdul-kareem Mahdi Salih , “ Characteristics of passive Q-switching pulse through modification and solution of rate equations”, Baghdad University, M.Sc.Thesis (٢٠٠٠). [٨]Yen-Kuang Kuo, Horng-Min Chen, Jih-Yuan Chang,” Numerical study of the Cr:YSO Q-switched ruby laser”, Optical Engineering, ٢٠٣٥-٢٠٣١ (٩) ٤٠, (٢٠٠١).
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THE EFFECT OF THE Z=٥٦ SUBSHELL ON INTERACTING BOSON MODEL (IBM)
CALCULATIONS
Iman Tarik Al-Alawy
Department of physics, College of Science, Al-Mustansiriyah University
ABSTRACT
The predictions of the exact O(٦) symmetry limit of interacting boson model are reviewed for the Sn-Gd region. Evidence of the transition from O(٦) to O(٦)-SU(٥) dynamical symmetry for the deformed nuclei in the ٥٠≤Z≤٦٤ region is discussed.
In this research proposed a new scheme for IBM calculations near Z=٥٦ which involves a drastic change in the proton boson number is critically examined. It is shown that this scheme is in agreement with the experimental trends observed for the B(E٢١;٢
+-٠١+) transition probability. Energy levels and
B(E٢) are compared with IBM calculations assuming either a single Z=٦٤-٥٠ shell or a subshell at Z=٥٦. The present calculation improves agreement with experiment.
:
O *.J *. B +BO(;) , IO U S ! Sn-
Gd ( O + * * L ( O(;) ( I O I >I O(;)-
SU(D) L = ! D9≤Z≤;7 . ) 0 Q3 ! ! IBM K% + Z=D; I
HW 3 j % > H ( O ! % >e 0 R ! ( O +(.
3 4, O + .( / e ! . 0 R MO , M(B(EG;G6+F96+) . I I, M( 0 +
0B(EG) S / M (IBM) I2J Q! > Z=D9F;7 K% B Z=D; .
INTRODUCTION Arima and Iachello[١،٢] were developed the interacting boson model
(IBM) to treats the collective states of even-even nuclei in terms of a system of bosons that can occupy two states with angular momentum L=٠(s) and L=٢(d). For a given nucleus the total number of bosons, N, is given by the
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number of s-and d-bosons. The IBM has three natural limits, corresponding to the group classifications SU(٥), SU(٣), and O(٦). The first two describe anharmonic vibrator and a specific type of deformed symmetric rotor respectively. The third limit describes the gamma soft symmetry.
This model provides [٦-٣] an algebraic description of the various symmetries involved in the collective structure of the atomic nuclei. The three dynamical symmetries of the U(٦) group are SU(٥), SU(٣), and O(٦) offer analytic solutions of Hamiltonian operator. The study of the deviations from these limits in actual nuclei can provide insight into the complex nuclear structure [٨ ,٧].
To study this effects of the consequent energy gap on the structure of the nuclei in the region where the neutron number N changes from ٨٦ to ٩٢, it was found that while the effects of such a proton subshell were clearly evident for nuclei with N≤٨٨, these effects seem to vanish for N≥٩٠. The possible appearance effect of the discovered subshell closure at Z=٦٤ is developed by previous authors[١٣-٩].
In this paper we use the interacting boson model to explore for the first time the possibility that there is an effective Z=٥٦ subshell closure present in Sn-Gd nuclei, a nucleus with proton number exactly midway between the closures at Z=٥٠ and Z=٦٤, and with the number of neutrons N≤٨٨ and N≥٧٠.
It is great interest in this paper to find the links of O(٦) and O(٦)-SU(٥) of nuclei. An important step is to find the (Nπ . Nυ) dependence of the coefficients of the various interaction terms in )(ˆ IBMH and the behaviour of E(٤١
+)/E(٢١+) and E(٦١
+)/E(٢١+) ratios. We report in this paper a solution of
this intermediate problem in the O(٦) limit of the U(٦) symmetry, and discuss the transition from O(٦) to SU(٥) symmetry from the deformed nuclei in the ٥٠≤Z≤٦٤ region.
We do this by first reviewing the conditions of an exact O(٦) symmetry and the conditions of an exact SU(٥) symmetry and then test them with the experiment.
Instead of studying a single nucleus or a few nuclei, we consider the whole deformed region of ٥٠≤Z≤٦٤ and N≤٨٨ and N≥٧٠. This enables us to formulate the dependence of the coefficient of the quadrupole term and the B(E٢) values on the boson numbers Nπ and Nυ, also we consider the effect of the symmetry breaking term PP ˆ.ˆ † . IBM-DESCRIPTION
The corresponding Hamiltonian can be written as [١،٢]: ...(1) ˆˆˆ.ˆˆ)5( ˆ 2
442
331 TaTaLLanSUH d +++= ε
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It is more convenient to write it in terms of the boson energy sd εεε −= and to eliminate the s-boson degrees of freedom. Where dn is dd ˆ.ˆ † operator and LL ˆ.ˆ represent interaction in a spin dependent coupling between bosons,
3T and 4T are the octupole and the hexadecapole operators respectively, and the phenomenological parameters a١, a٣, a٤ represent the strengths of the angular momentum, octupole and hexadecapole interaction between bosons respectively.
The IBM basis states are those specified by the quantum numbers for each dynamical symmetry, group SU(٥) state which describes as[٢ ,١]:
...(2) )2(
,
)3(~,
)5(
,
)5(
],[
)6(
Ld M
O
L
O
nv
O
n
SU
N
U ⊃⊃⊃⊃
∆
where N is the total boson number nd=N, N-١،٠ ,… ,١ υ=nd, nd-١،٠ ,… ,٢ (nd=odd or even)
Where υ is the seniority, which counts the number of d-bosons not coupled to zero angular momentum.
∆n~ = is the number of d-boson triplets to zero angular momentum. L=λ, λ+٢,…,١λ-٢،٢λ (Note that ٢λ-١, is missing because of the requirement that boson may only be coupled to form symmetric states.
ML= takes integer values as -L≤ML≤L On the other hand, in O(٦) limit, the wave function typically have
several non-zero components, with varying values of the following quantum numbers [١،٢]:
...(3) )2(
,
)3(~,
)5(
,
)6(
],[
)6(
LM
O
L
O
v
OO
N
U ⊃⊃⊃⊃
∆τσ
where N, L, and ML are defined as before. σ=N,N-١ ,… ,٢ or ٠ for (N=odd or even) τ=σ,σ-١،٠ ,… ,١ τ=٣ ∆v~ +λ for v∆=٠،١,.. taking L-λ,λ+٢,…,١λ-٢،٢λ The corresponding Hamiltonian can be written as[١،٢]:
...(4) ˆˆ.ˆˆˆ)6( ˆ 2331
†0 TaLLaPPaOH ++=
where the parameter a٠ represent the strength of the pairing and PP ˆ.ˆ † represent pairing interactions between bosons . 331
ˆ,ˆ,, TLaa are defined as before.
Nuclei in a SU(٥)-O(٦) transitional region can be calculated with a Hamiltonian simply given by[١٤]:
...(5) L.Lˆ.ˆˆˆ1
†0 aPPanH d ++= ε
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It is important to note that the LL ˆ.ˆ interaction is diagonal in the basis states, the PP ˆ.ˆ † interaction contains 2±=∆ dn terms.
However, the origin of the σ and τ selection rules are quite different. This arises from the fundamental nature of the )2(ˆ ET operator which, can be written as[١،٢]:
[ ] [ ] ...(6) ˆˆˆˆˆˆˆ )2(†2
)2(††2
)2( dddSSdT E ×+×+×= βα which obeys the maintained selection rules. Where α٢ and β٢ are
parameters specifying the various terms in the corresponding operator. The IBM-٢ model leads one to consider a system of bosons of two
types, proton (neutron) bosons denoted by sπ(sυ) and dπ(dυ) with L=٠ and L=٢ respectively. The SU(٥)-O(٦) Hamiltonian is [١،٢]:
...(7) ˆ)ˆˆ(ˆπυυπ
ε MnnH dd ++= where ε is the proton and neutron d-boson energies respectively and
υπ υπ)ˆ(ˆ;)ˆ(ˆ †† ddnddn dd ×=×= .
The last term contains the Majorana operator πυM is added to the Hamiltonian in order to push up states with mixed proton-neutron symmetry (those having F-spin. Less than the maximum F<Fmax) with respect to the totally symmetric states[١٥]. This term may be written as [١٦].
( ) ( )( ) ( ) )8...( ˆˆ.ˆˆ(
ˆˆˆˆ.ˆˆˆˆˆ
3,1
)(
v
)(††v
)2(
vv
)2(††v
††v2
∑=
××+
×−××−×=
K
KK
K dddd
SddSSddSM
ππ
πππππυ
ξ
ξ
where ξK (K=١،٢،٣) are Majorana parameters for mixed symmetry states in the spectrum. The eigen values and eigen vectors are obtained by diagonalizing the Hamiltonian equation and then allowing the parameters to vary until one obtains the best fit to the experimental spectrum.
Knowing the reduced matrix elements, one can calculate the electrical quadrupole transition rates which are governed by B(E٢) values, which defined as [١،٢]:
...(9) ||ˆ||12
1);2(
2)2( LTL
LLLEB E′
+=′→ where
L, L' are the initial and final angular momentum of the state. The B(E٢) values of the ground state band are given by[١،٢]:
...(10)limit O(6)for )82)(2()5(2
2
4
1)2;2( 2
2 ++−+
+=→+ LNLNL
LLLEB α
...(11)limit SU(5)for 2
122)2;2( 2
2
+
+=→+ N
L
LLLEB α
RESULTS AND DISCUSSION
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Since Np, Nn are the numbers of valence protons or neutrons, respectively, which are counted as holes beyond the middle of a major shell and as particles up to the middle of a major shell. The bosons number is finite and conserved in a given nucleus and is simply by half the total number of valence nucleons. The product Nπ. Nυ is equal to
4
1 (Np.Nn).Moreover, the valence number counting is always done relative to
the nearest closed shells, since the bosons could be pairs of either holes or particles.
Table-١ provided an explicit definition list of the major proton shells used in the present calculations. In the A=١٢٠ region, the protons are considered to occupy a closed shell Z=٥٠ for neutron number N=٧٠, but for the (g٩/٢)p and (g٧/٢)p orbits are well separated leading to single proton shell is Z=٥٠. Similarly, in the A=١٥٢ region, the (g٧/٢)p and (d٥/٢)p orbits are well separated from the (h١١/٢)p so that the gap is omitted and the shell becomes Z=٨٢-٥٠ so that the relevant shell is Z=٦٤-٥٠.
Table-١: Definitions of the major proton shells used in the present calculations.
Mass number A Proton shell Neutron number N
٧٠ ٥٠ ١٢٠ ٧٠≤ ٦٤-٥٠ ١٥٢-١٢٠
١٣٨-١٢٠(Z≤٥٤) ٨٦> ٥٦-٥٠ ١٥٢-١٤٠(Z≤٥٤) ٨٦≤ ٦٤-٥٠ ١٥٢-١٢٦(Z≥٥٦) ٨٨-٧٠ ٦٤-٥٠
For the accuracy of our calculations, several comparison is made with experiment. The energy of the first ٢+ state, E(٢١
+), typically decreases from values near ١٣-٠٣MeV to ١٧-٠١MeV in a spherical-gamma soft phase SU(٥)-O(٦) transition. The values of the energy ratio E(+
14 )/E( +12 ) and
E( +16 )/E( +
12 ), which are tabulated in table-٢, are a direct and sensitive measure of the structure of a
Table -٢: Theoretical energy ratios compared with the experimental data for
chosen even-even isotopes. Exp.[١٧] IBM-١(pw) IBM-٢(pw)
Isotopes E( +
14 )/E( +12 ) E( +
16 )/E( +12 ) E( +
14 )/E( +12 ) E( +
16 )/E( +12 ) E( +
14 )/E( +12 ) E( +
16 )/E( +12 )
7012050Sn ٢٩١٤٢ ١٨٣٣٦ ٢٩٠٢٣ ١٨٢٤١ ٢٩٤٢١ ١٨٧٣٢
70122
52Te ٣١٢٧٤ ٢٠٩٣٤ ٣١١٦٠ ٢٠٨٢٤ ٣١٠٥٠ ٢٠٩٣١
7012454 Xe ٤٣٥٦٤ ٢٥١٣٢ ٤٣٣٢٤ ٢٥٠١١ ٤٣٧٣٤ ٢٤٨٢٢
7012656 Ba ٥٢٦٨١ ٢٧٣٤١ ٥١٧٦٩ ٢٧٦٤١ ٥٢٠٧٠ ٢٧٧٧٣
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7012858Ce ٥٦٢٧١ ٢٩٩٨٠ ٥٥٦٢٩ ٢٩١٦٤ ٥٥٨٣٧ ٢٩٢٧٦
7212250Sn ١٩٥١١ ١٩١٢٢ ١٩٦٢٣ ١٩٠١١ ١٩٨٢٥ ١٨٧٢٢
72124
52Te ٢٨٩٩٨ ٢٠١٣١ ٢٩٠٨٦ ٢٠١٤٢ ٢٨٩٨٥ ٢٠٧١٤
7212654 Xe ٤٢١٩٥ ٢٤٧١٧ ٤٢٠٨٤ ٢٤٢٣٦ ٤٢٠٩٦ ٢٤٢٤٩
7212856 Ba ٤٨٢٢١ ٢٧٠٤١ ٤٩١٥٢ ٢٧٠٣٤ ٤٩٥٤٢ ٢٦٨٦٦
7213058Ce ٥٢٣٠١ ٢٨١٤٥ ٥١٤٨١ ٢٧٧٧٩ ٥٢١٤٧ ٢٧٩٨٤
7412450Sn ١٩٣٤٨ ١،٨١٢٦ ١٩٠٣١ ١٨٤٩١ ١،٩٤٣٥ ١٨٦٣١
74126
52Te ٢٧٠٢١ ٢١٥٦١ ٢٦٩٤١ ٢١٤٥٠ ٢٦٦٥٥ ٢٠٤٣٠
7412854 Xe ٣٩٢١٦ ٢٣٧٤٣ ٣٨٧٦٥ ٢٣٠٨٧ ٣٩٢١٩ ٢٣٣٢٧
7413056 Ba ٤٥٠٣١ ٢٥٩٩٨ ٤٤٩٩١ ٢٥٨٨١ ٤٤٥٩١ ٢٥٢٤٤
7413258Ce ٤٧٧٥٦ ٢٦٥٧٧ ٤٧٣١٣ ٢٦٥٤٧ ٤٧٣٢٦ ٢٦٣٥٥
7413460 Nd ٤٨١٥١ ٢٧١١٣ ٤٨٠٦٢ ٢٧٠١٨ ٤٨٢٦٧ ٢٦٨١٥
7612650Sn …. / ٢١٦٧١ ١٨٨٨١ ١٨٢٤١ ١٨٥٢١ ١٨٩٢٦ ١١٤٥٠
76128
52Te ٣٦٨٤١ ٢٣٠٦١ ٢١٦٣٢ ١٨٨٦٢ ٢١٤٣٣ ١٩٩٧٣
7613054 Xe ٤٢٣١٤ ٢٤٩٢١ ٣٦٩٢١ ٢٣٠٧٢ ٣٦٢٦٤ ٢٢٤٧٠
7613256 Ba ٤٢٣١٤ ٢٤٩٢١ ٤٢٠٨٢ ٢٤٩٨٧ ٤١٥٨٤ ٢٤٢٧٩
7613458Ce ٤٦٧٠٢ ٢٦٢٠١ ٤٦٦٩٢ ٢٦٠٣٢ ٤٥٥٣٩ ٢٥٦٣٢
7613660 Nd ٤٦٨٢٧ ٢٦١٣٢ ٤٦٧٧١ ٢٦١٤٢ ٤٦٧٦٣ ٢٦١٣٧
78130
52Te ٢١٩٥٠ ١٩٤٦٠ ٢١٩٦٠ ١٩٤٧٢ ٢١٦٢٤ ١٩٤٥٢
7813254 Xe ٣١٦٢٦ ٢١٥٦٧ ٣١٦٨٧ ٢١٥٨٦ ٣١٦٢٨ ٢١٥٧١
7813456 Ba ٣٦٠٠١ ٢٣٥٤١ ٣٦٠٨١ ٢٣٦١٤ ٣٥٨٧٨ ٢٣١٦١
7813658Ce ٤٠٢١٧ ٢٣٧٧٦ ٤٠٠٣٨ ٢٣٨٤١ ٤٠١٢٧ ٢٣٨٠٧
7813860 Nd ٤٠٨٢٩ ٢٤٠٠٣ ٤٠٩٩٩ ٢٤٠٧١ ٤٠٩٨٦ ٢٣٩٩٧
7814062Sm ٣٨٥٠٠ ٢٣٣٤٥ ٣٨٥٠١ ٢٣٢٨٥ ٣٨٦٥١ ٢٣٤٦٧
80132
52Te ١٨٧١٢ ١٦٨٢١ ١٨٠١٣ ١٧٠١١ ١٨٢١٦ ١٧١٥٥
8013454 Xe ٢٢٧٠١ ٢٠٩٤١ ٢٢٦٩٥ ٢٠٨٣٧ ٢٢٥٩١ ٢٠٤٣٨
Table-٢: To be continued (٢/٢).
Exp.[١٧] IBM-١(pw) IBM-٢(pw) Isotopes
E( +14 )/E( +
12 ) E( +16 )/E( +
12 ) E( +14 )/E( +
12 ) E( +16 )/E( +
12 ) E( +14 )/E( +
12 ) E( +16 )/E( +
12 )
8013656 Ba ٢٧٣٨٠ ٢٢٩٤١ ٢٦٩٨٠ ٢٢٨٤٠ ٢٦٩٦٥ ٢٢٨٠٥
8013858Ce ٢٩٨٢٧ ٢٣٥٥١ ٢٩٤١٥ ٢٣٣٤١ ٢٩٠٦٥ ٢٣١٥٨
8014060 Nd ٣٠١٤١ ٢٣١٩٩ ٣٠٤٦٣ ٢٣٠٩٧ ٣٠٥٨٧ ٢٣٢٨٩
8014262Sm ٣١٨٠١ ٢٣٣٥١ ٣١٥٣٤ ٢٣٣٦٠ ٣١٥١٠ ٢٣٣٢٤
82134
52Te ١٣٣٤١ ١٢٥١١ ١٣١٢٤ ١٢١٣١ ١٣٢٢٣ ١٢٣٢٢
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8213654 Xe ١٤٦١٤ ١٣٢٢١ ١٤٥١٣ ١٣٠٣٤ ١٤٤٠٧ ١٢٩٠٥
8213856 Ba ١٤٨٨٣ ١٣٣٣٤ ١٤٨٦١ ١٣٢٣٧ ١٤٥٦٠ ١٣٢٢٣
8214058Ce ١٣٨٥٠ ١٣٣٧٠ ١٣٨٠١ ١٣٣٦٧ ١٣٢٠٧ ١٣٠٥٣
8214260 Nd ١٣٩٤٢ ١٣٢٤١ ١٣٩١٣ ١٣٢٠١ ١٤٠٢٦ ١٣٣٣٥
8214462Sm ١٣٩٨٧ ١٣١٧٨ ١٣٩٨٤ ١٣١٨٠ ١٣٩٩٥ ١٣١٩٦
8413854 Xe ٢٩٠٦٦ ١٩٢٤١ ٢٩٠٥٧ ١٩٣٠٩ ٠٥٨٩٢/.… ١٨٢٠٠
8414056 Ba ٢٧٦٤٠ ١٨٥٩٩ ٢٧٥٣٩ ١٨٤٩٢ ٠٦٠٢٣/.… ١٨٧٦٩
8414258Ce ٢٦٩٣١ ١٨٩٦٣ ٢٦٧١٥ ١٨٩٥٣ ٠٦٤١٢/.… ١٩٠١٦
8414460 Nd ٢٥٨٦٠ ١٩٠٤١ ٢٥٧٩٧ ١٩٠٢١ ٢٥٧١٩ ١٨٨٧٦
8414662Sm ٢٥٧١١ ١٨٠٣٦ ٢٥١٦٣ ١٨٢٤٣ ٢٤٢٥٠ ١٨٤٨٩
8414864Gd ٢٣٣٦٧ ١٨٧٧١ ٢٣٣٨٧ ١٨٥٦٩ ٢٣١١٥ ١٨٠٦٨
8614054 Xe ٣٤٨١٥ ٢١٥٢٨ ٣٤١٨٦ ٢١٢٥٩ ٠٣٧٦٨/.… ٢٢١٥٢
8614256 Ba ٤٠٧١٠ ٢٣٨١١ ٤٠٨٩٠ ٢٣٦٢٢ ٤٠٧٩٥ ٢٣٢٢٥
8614458Ce ٣٨٩٤٥ ٢٥٠٢١ ٣٩٩٠٥ ٢٤٧٢٥ ٣٨٣٤٤ ٢٣٦١٩
8614660 Nd ٣٤٤٨١ ٢٢٨٠١ ٣٤٣١٥ ٢٢٢٠٦ ٣٦٤٩٣ ٢٢٩٨٤
8614862Sm ٣٣٦٦٧ ٢٠٩٩٨ ٣٣٧٦٢ ٢٠٩١١ ٣٤٦٤١ ٢١٤٥١
8615064Gd ٢٩٩٠٧ ١٩٧٠٣ ٢٩٩٨٩ ١٩٨٠٦ ٣٠٣٥٣ ٢٠١٩٣
8814456 Ba ٤٩٨٠٢ ٢٩٥٦٣ ٤٩٧٠٦ ٢٩٣٤٦ ٤٨٢٥٠ ٢٦٦٠٠
8814658Ce ٤١٦٠٣ ٢٤٢٣١ ٤١٦٢٧ ٢٤٤٣٣ ٤٥٣٠٤ ٢٥٨٤٩
8814860 Nd ٣٧٣٦٢ ٢٣٧١٥ ٣٧٠٨٥ ٢٣٧١٣ ٤١٧٩٩ ٢٤٩٢٥
8815062Sm ٣٨٤١١ ٢٣١٩٤ ٣٨٣٢٠ ٢٣١٨٩ ٣٨٢٩٥ ٢٣١٥٨
8815264Gd ٣٥٠٣٢ ٢١٩٠١ ٣٥٥٦٩ ٢١٩٠٢ ٣٥٦٤٩ ٢١٩٤٠
nucleus. These quantities are ٢٠ and ٣٠ respectively for a vibrator and they are ٢٥ and ٤٥ respectively for gamma soft. Finally, to test the predications for transition rates, the B(E٢; +
12 → +10 ) values, which are a basic
measure of the collectivity of each nucleus in a region, are shown in table-٣. Figures ١ and ٢ show the experimental and the theoretical IBM calculations (present work) of E(+
14 )/E( +12 ) ratios results for all the mass (A=١٥٢-١٢٠)
regions. Similarly in figures (٣) and (٤), but, for E( +16 )/E( +
12 ) ratios. The results show a complex behaviour demonstration of each region. In all figures the calculations show, a minimum ratios value at Z=٥٦ for N=٨٦،٨٨; a sudden jump between N=٨٤ and N=٨٦،٨٨ with, now, a maximum near Z=٥٦ and a bunching of curves for N≥٨٦. Moreover, the N=٨٦-٨٤ gap is largest for Ce and progressively smaller for higher and lower Z-values.
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Table -٣: Theoretical values of B(E٢; ++ − 11 02 )compared with the available experimental data, and the behaviour for chosen even-even isotopes.
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٢٠Sn ٠ ٧٠ ٥٠
(١)٠٠٤٠ (٢٤)٠٠٦٠ (١٨)٠٠٥٢ (٦)٠٠٤٠ (٦)٠٠٣٨
[١٨] [١٩] [٢٠] [٢١] [٢٢]
٠٠٤٩٦ ٠٠٤٨٣ O(٦)
١٢٢Te ٦ ٧٠ ٥٢
(١)٠١٣٢ (٥٤)٠١٣٢ (٣٨)٠١١٦ (٢٨)٠١٧٢ (٣٠)٠١٨٨ (١٠٠)٠٤٧٠ (٦٠)٠٦٥٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٣]
٠١٢٦١ ٠١٢١٣ O(٦)
١٢٤Xe ١٠ ٧٠ ٥٤
(١٨)٠٢٩٨ (٩٢)٠٢٢٦ (٦٦)٠١٩٨ (٣٠)٠١٨٨ (٣٢)٠٢١٢ (١٨)٠٢٩٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤]
(٦)٠ ٠٢٨٨١ ٠٢٨٣٢
١٢٦Ba ١٥ ٧٠ ٥٦
(٤٢)٠٣٨٠ (١٤)٠٣٤ (٩٦)٠٢٩٠ (٥٠)٠٤٢٤ (٤٦)٠٣٨٦ ٠٣٦٦
٠٢٦١١x٣-١٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥]
٠٣٥٨١ ٠٣٥٢٢ O(٦)-SU(٥)
١٢٨Ce ٢٠ ٧٠ ٥٨
(٣٦)٠٤٣٠ (١٨)٠٤٤ (١٢)٠٣٨ (٨٠)٠٥٥٢ (٦٦)٠٤٥٥ ٠٢٠٤٠x٣-١٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٥]
٠١٨٩٢x٠٢١٣٤ ٣-١٠x٣-١٠ O(٦)-SU(٥)
١٢٢Sn ٠ ٧٢ ٥٠
(١)٠٠٣٨ (٢٤)٠٠٦٠ (١٨)٠٠٥٤ (١)٠٠٣٧ (١)٠٠٣٧
[١٨] [١٩] [٢٠] [٢١] [٢٢]
٠٠٣٧٨ ٠٠٤٠١ O(٦)
١٢٤Te ٠١١٨٤ ٠١١٥١ [١٨] (٣٠)٠١١٤ ٥ ٧٢ ٥٢ O(٦)
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(٥٠)٠١٢٤ (٣٦)٠١٠٨ (٥)٠١٠٢ (٥)٠١١٠ (٨٠)٠٣٩٠ (٤)٠١١٤
[١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٦]
Table-٣: To be continued (٢/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٢٦Xe ١٠ ٧٢ ٥٤
(٥)٠١٥٤ (٨٤)٠٢٠٦ (١٨)٠١٧٨ (٢٢)٠١٩٢ (٢٢)٠٢٠٠ (٢٨)٠٧٨١ (٥)٠١٥٤ ٠٧٨٣
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٤] [٢٥]
٠٧٨٤٧ ٠٧٨١٤ O(٦)
١٢٨Ba ١٥ ٧٢ ٥٦
(٢٢)٠٢٧٢ (١٢)٠٣٠ (٨٦)٠٢٥٦ (٣٦)٠٢٦٠ (٣٦)٠٢٦٠ ٠٢٧٢ ٠٢٧٢
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥]
٠٢٧٦٢ ٠٢٧٤١ O(٦)-SU(٥)
١٣٠Ce ٢٠ ٧٢ ٥٨
(١٨)٠٣٤٦ (١٤)٠٣٦ (١)٠٣ (٥)٠٣٢ (٥٤)٠٣٤٤ ٠٣٤٠١
٠٢١٩٥x٣-١٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥]
٠٣٤٠٨ ٠٣٤٥٤ O(٦)-SU(٥)
١٢٤Sn ٠ ٧٤ ٥٠
(١)٠٠٣٣ (٢٤)٠٠٦٠ (١٨)٠٠٥٢ (١)٠٠٣٧ (١)٠٠٢٠
[١٨] [١٩] [٢٠] [٢١] [٢٢]
٠٠٤٦٢ ٠٠٤٠١ O(٦)
١٢٦Te ٤ ٧٤ ٥٢
(٢)٠٠٩٥ (٤٦)٠١١٢ (٣٢)٠٠٩٦ (٦)٠٠٩١ (٧)٠١٠٥ (٣٧)٠٥٣٢ (٦٤)٠٣٢٠ ٠٢١٩٥x٣-١٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٣] [٢٥]
٠٥٧١٨ ٠٥١٩٢ O(٦)
١٢٨Xe ٨ ٧٤ ٥٤
(٨)٠١٥١ (٧٤)٠١٨٠ (٥٠)٠١٥٤ (١٨)٠١٥٦
[١٨] [١٩] [٢٠] [٢١]
٠١٤٣٧ ٠١٢٤١ O(٦)
.................................................................... .............. ٧٠٦
NO. 33 33 ………..….… JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
EDUCATIO
NEDUCATIO
NEDUCATIO
NEDUCATIO
N2008
2008
2008
2008
(١٨)٠١٦٠ (٨)٠١٥٠ ٠٩٣٩x٤-١٠
[٢٢] [٢٤] [٢٥]
Table-٣: To be continued (٣/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٣٠Ba ١٢ ٧٤ ٥٦
(٢٨)٠٢٥٧ (٩٨)٠٢٣٨ (٦٦)٠٢٠٢ (٣٠)٠٢٥٤ (٣٢)٠٢٦٤ (١٨)٠٧٥ ٠٢٥٨ ١٢١
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٤] [٢٥]
٠٢١٨٣ ٠٢٥٠٩ O(٦)-SU(٥)
١٣٢Ce ١٦ ٧٤ ٥٨
(٢٨)٠٣٥٤ (١٢)٠٢٨ (٧٨)٠٢٣٤ (٤٨)٠٣١٦ (٤٦)٠٣١٢ ٠٣٧٦٠ ٠٣٧٦٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥]
٠٣٧٥١ ٠٣٦٤١ SU(٥)-O(٦)
١٣٤Nd ٢٠ ٧٤ ٦٠ (١٤)٠٣٢ (٩٠)٠٢٧٢ ٠١٣١٠x٤-١٠
[١٩] [٢٠] [٢٥]
٠١٣٧٨x٠١٤٠٣ ٤-١٠x٤-١٠ SU(٥)-O(٦)
١٢٦Sn ٠ ٧٦ ٥٠
(٢٤)٠٠٦٠ (١٨)٠٠٥٢ (١)٠٠٣١ (٢)٠٠١٥
[١٩] [٢٠] [٢١] [٢٢]
٠٠٥٥٣ ٠٠٥٨٢ O(٦)
١٢٨Te ٣ ٧٦ ٥٢
(١)٠٠٧٧ (٤٠)٠١٠٠ (٢٨)٠٠٨٤ (٨)٠٠٨١ (٩)٠٠٨٦ (٥٦)٠٢٨٠ (٣٣)٠٤١٢ (١٥)٣١١
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٣] [٢٧]
٠٣٨٠١ ٠٣٧٥١ O(٦)
١٣٠Xe ٦ ٧٦ ٥٤
(١٠)٠١٣٠ (٦٠)٠١٤٨ (٤٢)٠١٢٤ (١٢)٠١١٦ (١٠)٠١٠٨ (٢٥)٠٦٥ (١)٠١٣
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٤]
٠٦٣٢١ ٠٦٣١٥ O(٦)
١٣٢Ba ٠٧٣٣١ ٠٧٢٦٠ [١٨] (١٢)٠١٧٢ ٩ ٧٦ ٥٦ O(٦)-SU(٥)
.......................................... .......................................... ٧٠٧
NO. 33 33 ………..….… JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
EDUCATIO
NEDUCATIO
NEDUCATIO
NEDUCATIO
N2008
2008
2008
2008
(٧٤)٠١٨٢ (٥٠)٠١٥٢ (٢٦)٠١٨٨ (٢٤)٠١٧٤ (١٨)٠٧٢ ٠١٧٢ ٠٧٢
[١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٤] [٢٥]
Table-٣: To be continued (٤/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٣٤Ce ١٢ ٧٦ ٥٨
(١٨)٠٢٠٦ (٩)٠٢٢ (٦٠)٠١٨٢ (٣٦)٠٢٣٦ (٤٠)٠٢٦٨ ٠٢١٣٠ ٠٢١٣٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥]
٠٢٠٤٩ ٠٢١٧٩ SU(٥)-O(٦)
١٣٦Nd ١٥ ٧٦ ٦٠ (١)٠٢٦ (٧٠)٠٢١٢ ٠١٥٤x٤-١٠
[١٩] [٢٠] [٢٥]
٠١٥٩٣x٠١٥٧٢ ٤-١٠x٤-١٠ SU(٥)-O(٦)
١٢٨Sn ٠ ٧٨ ٥٠ (٢٤)٠٠٥٨ (١٦)٠٠٥٠
[١٩] [٢٠]
٠٠٥٦٨ ٠٠٥٣٤ O(٦)
١٣٠Te ٢ ٧٨ ٥٢
(٢)٠٠٥٩ (٣٦)٠٠٨٨ (٢٤)٠٠٧٤ (٦)٠٠٦١ (٤)٠٠٣٩ (٥٢)٠٢٦٠ (٣٠)٠٣٤٠ ٠٢٩١
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٣] [٢٥]
٠٢٧١٨ ٠٢٩١٤ O(٦)
١٣٢Xe ٤ ٧٨ ٥٤
(٦)٠٠٩٣ (٤٨)٠١١٨ (٣٢)٠٠٩٨ (١٢)٠١٠٠ (١٤)٠١١٠ (٩٧)٠٣١٢ (٦)٠٠٩٢
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٤]
٠٠٨٦ ٠٣١٢١ O(٦)
١٣٤Ba ٦ ٧٨ ٥٦
(٣)٠١٣٦ (٥٦)٠١٤٠ (٣٨)٠١١٦ (١٨)٠١١٦ (١٨)٠١٢٠ ٠١٣٦ ٠١٣٦ (٨)٢٩
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥] [٢٧]
٠١٣٥٧ ٠١٣٤٩ O(٦)-SU(٥)
١٣٦Ce ٨ ٧٨ ٥٨ (٦٦)٠١٦٢ (٤٤)٠١٣٤
[١٩] [٢٠]
٠١٤٢٦ ٠١٤٣٩ SU(٥)-O(٦)
.................................................................... .............. ٧٠٨
NO. 33 33 ………..….… JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
EDUCATIO
NEDUCATIO
NEDUCATIO
NEDUCATIO
N2008
2008
2008
2008
(١٨)٠١٥٨ (٢٢)٠١٧٠ ٠١٤٢x٣-١٠
[٢١] [٢٢] [٢٥]
١٣٨Nd ١٠ ٧٨ ٦٠ (٧٦)٠١٨٤ (٥)٠١٥
٠١٥٧٥x٤-١٠
[١٩] [٢٠] [٢٥]
٠١٥٨٨x٠١٥٦٧ ٤-١٠x٤-١٠ SU(٥)-O(٦)
Table-٣: To be continued (٥/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٤٠Sm ١٢ ٧٨ ٦٢ (٧٠)٠٣٢٨ (١٢)٠٣٠ (٨)٠٢٤
[١٨] [١٩] [٢٠]
٠٣١٤٢ ٠٣٣٤١ SU(٥)-O(٦)
١٤٢Gd ١٤ ٧٨ ٦٤ (٨٤)٠٢٠٦ (٥٤)٠١٦٤
[١٩] [٢٠]
٠١٧٤٨ ٠١٨٦٤ SU(٥)-O(٦)
١٣٠Sn ٠ ٨٠ ٥٠ (٢٢)٠٠٥٦ (١٦)٠٠٤٨
[١٩] [٢٠]
٠٠٤٥٨ ٠٠٤٣٦ O(٦)
١٣٢Te ١ ٨٠ ٥٢
(٣٠)٠٠٧٦ (٢٠)٠٠٦٢ (٧)٠٠٤٨ (١٤)٠٠٣٦
[١٩] [٢٠] [٢١] [٢٢]
٠٠٦٦٨ ٠٠٥٦٢ O(٦)
١٣٤Xe ٢ ٨٠ ٥٤
(١٢)٠٠٦٨ (٣٨)٠٠٩٢ (٢٦)٠٠٧٦ (١٨)٠٠٥٨ (١٦)٠٠٥٤ (١٢)٠٠٧٢
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤]
٠٠٧١١ ٠٠٧٢٣ O(٦)
١٣٦Ba ٣ ٨٠ ٥٦
(١)٠٠٨٠ (٤٢)٠١٠٢ (٢٨)٠٠٨٤ (٣٦)٠٠٩٨ (٣٤)٠٠٩٤ ٠٠١٥٥ ٠٠٧٢
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٤] [٢٥]
٠٠٧٥٤٥ ٠٠٧٣٦ SU(٥)-O(٦)
١٣٨Ce ٤ ٨٠ ٥٨
(٤٦)٠١١٤ (١٦)٠٠٩٤ (٧٨)٠١٢١ (٢٤)٠٠٩٤
[١٩] [٢٠] [٢١] [٢٢]
٠١١٨٤ ٠١١٤٢ SU(٥)-O(٦)
١٤٠Nd ٥ ٨٠ ٦٠ (٥٠)٠١٢٤ (٣٢)٠١٠٠ ٠١٥٧٥x٤-١٠
[١٩] [٢٠] [٢٥]
٠١٦٢٧x٠١٥٣٤ ٤-١٠x٤-١٠ SU(٥)-O(٦)
١٤٢Sm ٦ ٨٠ ٦٢ (٧٨)٠١٩٢ (٥٢)٠١٥٤ ٠٢٦٣x٤-١٠
[١٩] [٢٠] [٢٥]
٠١٦٦٢ ٠١٦٣٧ SU(٥)-O(٦)
١٤٤Gd ٧ ٨٠ ٦٤ (٦٠)٠١٤٤ (٣٨)٠١١٤
[١٩] [٢٠]
٠١٤٦٦ ٠١٤٢٦ SU(٥)-O(٦)
.......................................... .......................................... ٧٠٩
NO. 33 33 ………..….… JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
EDUCATIO
NEDUCATIO
NEDUCATIO
NEDUCATIO
N2008
2008
2008
2008
١٣٢Sn ٠ ٨٢ ٥٠ (٦٨)٠٠١٧ (٥)٠٠١٤
[١٩] [٢٠]
٠٠١٢٩ ٠٠١٣١ O(٦)
١٣٤Te ٠ ٨٢ ٥٢ (٢٤)٠٠٥٦ (١٦)٠٠٤٨
[١٩] [٢٠]
٠٠٥٩٢ ٠٠٦٣١ O(٦)
١٣٦Xe ٠ ٨٢ ٥٤
(١٦)٠٠٣٦ (٢٤)٠٠٦٠ (١٦)٠٠٤٨ (٧٨)٠٠٤٤ (٦٠)٠٠٣٣
[١٨] [١٩] [٢٠] [٢١] [٢٢]
٠٠٢٩٩ ٠٠٣١١ O(٦)
Table-٣: To be continued (٦/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٣٨Ba ٠ ٨٢ ٥٦
(٢)٠٠٤٥ (٢٤)٠٠٥٨ (١٦)٠٠٤٨ (١٨)٠٠٣٦ (٢٢)٠٠٤٨ (١١)٠٣٨ (٤)١٦٥
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٧]
٠٣٦٩٥ ٠٣٦٨٠ SU(٥)-O(٦)
١٤٠Ce ٠ ٨٢ ٥٨
(١)٠٠٥٩ (٢٢)٠٠٥٦ (١٤)٠٠٤٤ (٣)٠٠٣٩ (٢)٠٠٣٤ (٥)٠٣٦ (٥)٠٢٧
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٣]
٠٣٨٩٤ ٠٣٧٨٥ SU(٥)-O(٦)
١٤٢Nd ٠ ٨٢ ٦٠
(٢)٠٠٥٤ (٢٤)٠٠٦٠ (١٦)٠٠٤٨ (٦)٠١٠١ (٥)٠٠٧٩
٠٣٤7.1
4.3
−+
[١٨] [١٩] [٢٠] [٢١] [٢٢]
[٢٣]
٠٣٨٥٢ ٠٣٨٠٧ SU(٥)-O(٦)
١٤٤Sm ٠ ٨٢ ٦٢ (٥٤)٠١٣٢ (٣٤)٠١٠٤ (٣٥)٠٠٢٩
[١٩] [٢٠] [٢٥]
٠١٥٥٢ ٠١٥٠٧ SU(٥)-O(٦)
١٤٦Gd ٠ ٨٢ ٦٤ (٢٢)٠٠٥٤ (١٤)٠٠٤٢
[١٩] [٢٠]
٠٠٧١٣ ٠٠٦٧٨ SU(٥)-O(٦)
١٣٨Xe ٢ ٨٤ ٥٤ (١)٠٠٠٥ (٥٤)٠١٣٢ (٣٦)٠١٠٦
[١٨] [١٩] [٢٠]
٠١٢٤٨ ٠١١٣٦ O(٦)
١٤٠Ba ٣ ٨٤ ٥٦
(٥٦)٠١٣٨ (٣٦)٠١١٠ (١)٠٠٠٧ (٣)٠٠٧٤
[١٨] [١٩] [٢٠] [٢١]
٠١٥١٠ ٠١٤٧٣ SU(٥)-O(٦)
١٤٢Ce ٠٠٨٨٢ ٠٠٩١٣ [١٨] (٢)٠٠٩٠ ٤ ٨٤ ٥٨ SU(٥)-O(٦)
.................................................................... .............. ٧١٠
NO. 33 33 ………..….… JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
EDUCATIO
NEDUCATIO
NEDUCATIO
NEDUCATIO
N2008
2008
2008
2008
(٥٦)٠١٣٨ (٣٦)٠١١ (٩)٠١٣١ (٨)٠١١٥
٠٠٥٩30.0
059.0
−+
(٨)٠٤١ (٥)٠١٠١
[١٩] [٢٠] [٢١] [٢٢]
[٢٣]
[٢٣] [٢٧]
Table-٣: To be continued (٧/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٤٤Nd ٥ ٨٤ ٦٠
(٦)٠١١٠ (٥٦)٠١٣٦ (٣٦)٠١٠٨ (٣)٠٠٧٨ (٤)٠٠٨٥ (٥)٠٢٣
٠٤٤22.0
44.0
−+
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣]
[٢٣]
٠٤٤٠١ ٠٤٤٠٠ SU(٥)-O(٦)
١٤٦Sm ٦ ٨٤ ٦٢ (٢)٠٠٥٣ (٢٤)٠٠٦٠ (١٦)٠٠٤٨
[١٨] [١٩] [٢٠]
٠٠٤٣٧ ٠٠٤٥٩ SU(٥)-O(٦)
١٤٨Gd ٧ ٨٤ ٦٤ (٥٦)٠١٣٦ (٣٤)٠١٠٦
[١٩] [٢٠]
٠١٤٣٧ ٠١٣٥٩ SU(٥)-O(٦)
١٤٠Xe ٤ ٨٦ ٥٤ (٣)٠٠٦٤ (٨٤)٠٢٠٤ (٥٤)٠١٦٤
[١٨] [١٩] [٢٠]
٠١٧٣٥ ٠١٨٠٤ O(٦)
١٤٢Ba ٦ ٨٦ ٥٦
(١٢)٠١٣٦ (٩٤)٠٢٣٠ (٦٠)٠١٨٤ ٠٦٠٢x٤-١٠
[١٨] [١٩] [٢٠] [٢٥]
٠٢٦٠٣ ٠٢٦٠٢ SU(٥)-O(٦)
١٤٤Ce ٨ ٨٦ ٥٨
(٩٠)٠٢٢٢ (٥٨)٠١٧٦ (٦)٠١٢٩ (٨)٠١٢٥
[١٨] [١٩] [٢٠] [٢١]
٠١٤١١ ٠١٣٠١ SU(٥)-O(٦)
١٤٦Nd ١٠ ٨٦ ٦٠
(٦)٠١٥٢ (٨٤)٠٢٠٨ (٥٤)٠١٦٢ (٨)٠١٦٣ (٨)٠١٥٠ (٢٥)٠٨٥
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣]
٠٢١٤٦ ٠٢٣١١ SU(٥)-O(٦)
١٤٨Sm ١٢ ٨٦ ٦٢
(٥٦)٠١٣٤ (٣٤)٠١٠٤ (٦)٠١١ (٥)٠١٠٧
[١٩] [٢٠] [٢١] [٢٢]
٠١٧٦٣ ٠١٦٨٨ SU(٥)-O(٦)
.......................................... .......................................... ٧١١
NO. 33 33 ………..….… JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
JOURNAL O
F COLLEGE O
F
EDUCATIO
NEDUCATIO
NEDUCATIO
NEDUCATIO
N2008
2008
2008
2008
[٢٣] (١٠)٠٨٩
١٥٠Gd ١٤ ٨٦ ٦٤
(٦٨)٠١٦٦ (٤٢)٠١٢٨ (١٤)٠١٦٠ (٣٢)٠٢٢٦
[١٩] [٢٠] [٢١] [٢٢]
٠١٦٨٣ ٠١٦٢٨ SU(٥)-O(٦)
١٤٢Xe ٦ ٨٨ ٥٤
(١٦)٠٣٨ (١٠٠)٠٢٩٨ (٧)٠١٠٩ (١٨)٠١٣٦
[١٩] [٢٠] [٢١] [٢٢]
٠٢٨١١ ٠٢٦٥٦ O(٦)
Table-٣: To be continued (٨/٨).
B(E٢; +12 - +
10 ) (eb)٢ Isotopes Z N Nπ.Nυ Exp. Ref. IBM-١(pw) IBM-٢(pw)
Behaviour (pw)
١٤٤Ba ٩ ٨٨ ٥٦
(١٢)٠٢٠٨ (١٦)٠٤٢٠ (١٠٠)٠٣٢٠ (٣٦)٠٢٠٤ (١٤)٠١٥٤ ٠١٢٧x٣-١٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٥]
٠٣٢٨٠ ٠٣٢٧٣ O(٦)-SU(٥)
١٤٦Ce ١٢ ٨٨ ٥٨
(٢٦)٠١٨٦ (١٤)٠٣٤ (٨٨)٠٢٦٦ (٢٤)٠٢٢٢ (٢٢)٠٢١٠
[١٨] [١٩] [٢٠] [٢١] [٢٢]
٠١٧٦٠ ٠١٧٣٤ O(٦)-SU(٥)
١٤٨Nd ١٥ ٨٨ ٦٠
(٦)٠٢٧٦ (١٢)٠٣٢ (٨)٠٢٤ (٢٢)٠٢٢٤ (٢٦)٠٢٥٦ (٤٧)١٥٨ (٢٠)٠٦٠
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣] [٢٣]
٠٣٣٢٦ ٠٣١١٤ O(٦)-SU(٥)
١٥٠Sm ١٨ ٨٨ ٦٢
(٦)٠١٤٤ (٧٤)٠١٨٢ (٤٦)٠١٤٠ (٧)٠١٣٤ (٧)٠١٤٦ (٦)١٣٢
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣]
٠١٩٤٥ ٠١٩٨٥ O(٦)-SU(٥)
١٥٢Gd ٢١ ٨٨ ٦٤
(٣٠)٠٣٥٢ (١٢)٠٣٠ (٧٨)٠٢٣٤ (١٤)٠٣٤٨ (١٨)٠٤٢٨ (١٨)١٠٧
[١٨] [١٩] [٢٠] [٢١] [٢٢] [٢٣]
٠٣٤٥٦ ٠٣٣٤٨ O(٦)-SU(٥)
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
E(4
1+ ) / E
(21+
)
N=70N=72N=74N=76N=78N=80N=82N=84
N=70N=72
N=74N=76
N=78
N=80
N=82
N=84
Exp.
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Figure (١): Systematic of the experimental energy ratio E(+14 )/E( +
12 ) for the A=١٥٢-١٢٠ region, against Z.
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1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
48 50 52 54 56 58 60 62 64 66 68 70 72
ATOMIC NUMBER Z
E(6
1+ ) / E
(21+ ) N=70
N=72
N=74
N=76
N=78
N=80
N=82
N=84
N=86
N=88
N=70
N=72N=74N=76
N=78
N=80
N=82
N=84
N=86
N=88
Exp.
0
1
2
3
4
5
6
48 50 52 54 56 58 60 62 64 66 68 70 72
ATOMIC NUMBER Z
E(6
1+)/
E(2
1+)
N=70N=72N=74N=76N=78N=80N=82N=84N=86N=88
(a)IBM-1 (PW)
N=70
N=72N=74
N=76
N=78
N=80
N=82
N=84
N=86
N=88
0
1
2
3
4
5
6
48 50 52 54 56 58 60 62 64 66 68 70 72
ATOMIC NUMBER Z
E(6
1+)/
E(2
1+) N=70
N=72N=74
N=76
N=78
N=80N=82
N=84
N=86
N=88
(b)IBM-2 (PW)
N=70
N=72N=74
N=76
N=78
N=80
N=82
N=84
N=86
N=88
Figure (٣): Systematic of the experimental energy ratio E(+16 )/E( +
12 ) for the A=١٥٢-١٢٠ region, against Z.
Figure (٤): Systematic of the theoretical energy ratio E(+16 )/E( +
12 ) for the A=١٥٢-١٢٠ region, against Z. (a) IBM-١; (b) IBM- ٢
0
0.5
1
1.5
2
2.5
3
3.5
48 50 52 54 56 58 60 62 64 66 68 70 72
ATOMIC NUMBER Z
E(4
1+ )/E
(21+ )
N=70
N=72
N=74
N=76
N=78
N=80
N=82
N=84
N=86N=88
N=70
N=72 N=74
N=76 N=78N=80
N=82
N=84
N=86
N=88
(b)IBM-2 (PW)
0
0.5
1
1.5
2
2.5
3
3.5
48 50 52 54 56 58 60 62 64 66 68 70 72
ATOMIC NUMBER Z
E(4
1+ )/E
(21+ ) N=70
N=72
N=74
N=76
N=78
N=80
N=82
N=84
N=86
N=88
(a)IBM-1 (PW)
N=70N=72
N=74
N=88
N=76 N=78N=80
N=82
N=84N=86
Figure (٢): Systematic of the theoretical energy ratio E( +14 )/E( +
12 ) for the A=١٥٢-١٢٠ region, against Z. (a) IBM-١; (b) IBM- ٢
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Figures ٥ and ٦ show a systematics of the energy ratio E(+14 )/E( +
12 ) and E( +
16 )/E( +12 ) respectively for the A=١٥٢-١٢٠ regions, plotted against
Nπ.Nυ in the present work for theoretical IBM calculations besides the experimental results to give a degree of simplification with the comparison of figures (٤→١).
Figure (٥): Systematic of the theoretical and experimental energy ratio E( +
14 )/E( +12 ) for various Nπ.Nυ for Z≤٥٦ and Z>٥٦ for the
A=١٥٢-١٢٠ region.
Figure (٦): Systematic of the theoretical and experimental energy ratio E( +
16 )/E( +12 ) for various Nπ.Nυ for Z≤٥٦ and Z>٥٦ for the
A=١٥٢-١٢٠ region.
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The data points shown in both figures fall on a single smooth universal curve, instead of being widely dispersed, except for a few N=٨٦ and ٨٨ points. These points in the E(+
14 )/E( +12 ) and E( +
16 )/E( +12 ) plots are of
a proton gap as discussed above and the gap is partially intact at N=٨٦. The smoothness of the curve for the other points can be used to study the subshell structure of Z=٥٦ near N=٨٦. The N=٨٦ and ٨٨ points defines an effective valence proton number, where it is shown that Np=٥٦ (Te, Xe, Ba, Ce, Nd N=٨٦) is intermediate between the values obtained from the Z=٥٠-٦٤, and Z=٨٢-٥٠ shell definitions.
Figures (٩→٧) show a similar comparison for the B(E٢; +12 → +
10 ) values. The B(E٢) values confirm the evidence from the energies that the calculations give the correct trends in the data. The only notable discrepancy is B(E٢; +
12 → +10 ) values that are too low for N=٨٨-٨٤ for the
mid-Z nuclei near Z=٥٦. This would seen the gamma soft structure – O(٦) is a predicted structure for nuclei with Z<٥٦. However, the experimental and the theoretical of IBM calculations of transition rates for these nuclei with relatively small B(E٢; +
12 → +10 ) values result from a coherent quasi
vibrational gamma soft, O(٦)-SU(٥), collective structure. The experimental and calculated B(E٢) plot (figure ٧ and ٨) for this
region also reflects the empirical results although with some discrepancies in detail (Z-dependence for low N-values, Z-independence for large N-values). From the two figures, could enhance the experimental results over the purely collective contribution and lead to the observed discrepancy. At the largest neutron numbers, especially for Ce, Nd, Sm, and Gd the calculated B(E٢) values continue to increase while the data show a saturation in collectivity. Figure ٨ exhibits again the same flaring out as in the E( +
14 )/E( +12 ) and E( +
16 )/E( +12 ) ratios and as in the data. Hence, in figure ٩
the B(E٢; +12 - +
10 ) calculations (IBM-١ and ٢) and the experimental values show a minimum at Nπ.Nυ=١٠ for Z=٥٦ and N=٨٨-٧٢, with, now, a maximum at Nπ.Nυ =١٠ near Z=٥٤ and N=٧٢-٧٠ and a bunching for N≥٨٦. Moreover, the N=٨٦-٨٤ gap is progressively smaller for higher and lower Nπ.Nυ values.
Figure ١٠ shows Nπ.Nυ plot for E( +12 ) in the A=١٥٢-١٢٠ regions. The
curves are obtained by experimental and theoretical calculated IBM results for each Nπ.Nυ value, which shown a demonstrate a rather accurate reproduction of the gap for the complex behaviour between Z≤٥٤ and Z≥٥٦ region.
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
48 50 52 54 56 58 60 62 64 66 68 70
ATOMIC NUMBER Z
B(E
2;2 1
+ - 0
1+) (
eb)
2 N=70N=72N=74N=76N=78N=80N=82N=84N=86N=88Poly. (N=72)
N=72
N=70
N=74
N=76
N=82 N=84 N=78
N=8 N=86
N=88
Exp.
Figure (٧): Systematic of the experimental B(E٢; ++ − 11 02 ) values for the A=١٥٢-١٢٠ region, against Z.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
48 50 52 54 56 58 60 62 64 66 68 70
ATOMIC NUMBER Z
B(E
2;2 1
+ -
01+ )
(eb
)2
N=70
N=72
N=74
N=76
N=78
N=70
N=72
N=74
N=76
N=80
N=82
N=84
N=78
N=88
N=86
(B) IBM-2 (PW)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
48 50 52 54 56 58 60 62 64 66 68 70
ATOMIC NUMBER Z
B(E
2;2 1
+ - 0
1+ ) (
eb)2
N=70
N=72
N=74
N=76
N=78
N=70
N=72
N=74
N=76
N=78
N=80
N=82
N=84
N=86
N=88
(a) IBM-1 (PW)
Figure (٨): Systematic of the theoretical B(E٢; ++ − 11 02 ) values for the A=١٥٢-١٢٠ region, against Z. (a) IBM-١, (b) IBM-٢.
.......................................... .......................................... ٧١٧
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2008
Figure (٩): Systematic of the theoretical and experimental B(E٢; ++ − 11 02 ) values against Nπ.Nυ for the mass region ١٥٢-١٢٠ . for Z≤٥٤ and Z≥٥٦..
Figure (١٠): Systematic of the theoretical and experimental E(+12 ) energy values
against Nπ.Nυ for A= ١٥٢-١٢٠ region. for Z≤٥٤ and Z≥٥٦.
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N2008
2008
2008
2008
1.125
1.13
1.135
1.14
1.145
1.15
1.155
1.16
1.165
1.17
1.175
68 70 72 74 76 78
NEUTRON NUMBER N
E(2
1+ ) (
MeV
)
Exp.IBM-1IBM-2
50Sn(A=120-126)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
68 70 72 74 76 78 80 82 84
NEUTRON NUMBER N
E(2
1+ ) (
MeV
)
Exp.IBM-1IBM-2
52Te(A=122-134)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
68 70 72 74 76 78 80 82 84 86 88
NEUTRON NUMBER N
E(2
1+ ) (
MeV
)
Exp.IBM-1IBM-2
54Xe(A=124-140)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(2
1+)
(M
eV)
Exp.IBM-1IBM-2
56Ba(A=126-144)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(2
1+ ) (
MeV
)
Exp.IBM-1IBM-2
58Ce(A=128-146)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(2
1+ ) (
MeV
)
Exp.IBM-1IBM-2
60Nd(A=134-148)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
82 84 86 88 90
NEUTRON NUMBER N
E(2
1+)
(M
eV)
Exp.IBM-1IBM-2
64Gd(A=148-152)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(2
1+)
(M
eV)
Exp.IBM-1IBM-2
62Sm(A=140-150)
Figure (١١): Theoretical and experimental E( +12 ) energy values against neutrons
number for A= ١٥٢-١٢٠ region.
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2008
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
68 70 72 74 76 78
NEUTRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
50Sn(A=120-126)
1
1.2
1.4
1.6
1.8
2
2.2
2.4
68 70 72 74 76 78 80 82 84
NEUTRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
52Te(A=122-134)
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
68 70 72 74 76 78 80 82 84 86 88
NEUTRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
54Xe(A=124-140)
1
1.5
2
2.5
3
3.5
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
56Ba(A=126-144)
1
1.5
2
2.5
3
3.5
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
58Ce(A=128-146)
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
60Nd(A=134-148)
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(4
1+)
/ E(2
1+)
Exp.IBM-1IBM-2
62Sm(A=140-150)
1
1.2
1.4
1.6
1.8
2
2.2
2.4
82 84 86 88 90
NUETRON NUMBER N
E(4
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
64Gd(A=148-152)
Figure (١٢): Theoretical and experimental energy ratio E )4( 1+ /E )2( 1
+ against neutrons number for A= ١٥٢-١٢٠ region.
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N2008
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2008
2008
1
1.5
2
2.5
3
3.5
68 70 72 74 76 78
NEUTRON NUMBER N
E(6
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
50Sn(A=120-126)
1
1.5
2
2.5
3
3.5
68 70 72 74 76 78 80 82 84
NEUTRON NUMBER N
E(6
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
52Te(A=122-134)
1
1.5
2
2.5
3
3.5
4
4.5
5
68 70 72 74 76 78 80 82 84 86 88
NEUTRON NUMBER N
E(6
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
54Xe(A=124-140)
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(6
1+ ) / E
(21+
)
Exp.IBM-1IBM-2
56Ba(A=126-144)
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(6
1+)
/ E(2
1+ )
Exp.IBM-1IBM-2
58Ce(A=128-146)
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(6
1+)
/ E(2
1+ )
Exp.IBM-1IBM-2
60Nd(A=134-148)
1
1.5
2
2.5
3
3.5
4
4.5
76 78 80 82 84 86 88 90
NEUTRON NUMBER N
E(6
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
62Sm(A=140-150)
1
1.5
2
2.5
3
3.5
4
82 84 86 88 90
NEUTRON NUMBER N
E(6
1+ ) / E
(21+ )
Exp.IBM-1IBM-2
64Gd(A=148-152)
Figure (١٣): Theoretical and experimental energy ratio E )6( 1+ /E )2( 1
+ against neutrons number for A= ١٥٢-١٢٠ region.
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2008
2008
50Sn(A=120-132)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
68 70 72 74 76 78 80 82 84
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+)
(eb
)2
Exp.IBM-1IBM-2
52Te(A=122-134)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
68 70 72 74 76 78 80 82 84
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+ ) (
eb)2
Exp.IBM-1IBM-2
54Xe(A=124-142)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+)
(eb
)2
Exp.IBM-1IBM-2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+)
(eb
)2
Exp.IBM-1IBM-2
56Ba(A=126-144)
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
4.00E-01
4.50E-01
68 70 72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+ ) (
eb)2
Exp.IBM-1IBM-2
58Ce(A=128-146)
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
4.00E-01
4.50E-01
5.00E-01
72 74 76 78 80 82 84 86 88 90
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+)
(eb
)2
Exp.IBM-1IBM-2
60Nd(A=134-148)
62Sm(A=140-150)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
76 78 80 82 84 86 88 90
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+ ) (
eb)2
Exp.IBM-1IBM-2
64Gd(A=142-152)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
76 78 80 82 84 86 88 90
NEUTRON NUMBER N
B(E
2;2 1
+ - 0
1+ ) (
eb)2
Exp.IBM-1IBM-2
Figure (١٤): Theoretical and experimental B(E٢; ++ − 11 02 ) values against neutrons number for A= ١٥٢-١٢٠ region.
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Detailed comparisons can be expressed in more informative terms to carry out nucleus by nucleus. It is useful to show these results as shown in figures (١٤→١١) for E( +
12 ) , E( +14 )/E( +
12 ) , E( +16 )/E( +
12 ), and B(E٢; +12 - +
10 ) respectively. The overview of these figures show a good agreement in which the widely different behaviour of different elements are reflected in the calculations. Each region will now be discussed as follows:
In the mass number A=١٥٢-١٢٠ region, the deformation becomes more and more rapid as Z increases from ٦٤-٥٤ and decreases as Z decreases from ٥٠-٥٤ and decreases as Z increases from ٨٢-٦٤ and decreasing after that. The changes in the structure of the nuclei of each region that for closed shell neutron numbers the nuclei are spherical.
This is clearly evident in the slopes of figures (١٤→١١) and the theoretical IBM calculations reproduce the same onset.
In figure ١١ for the +12 energies, the agreement is again good except
for E( +12 ) values for Sn that are too high for N=٧٠. In addition, the overall
+12 energies for Sn for N≤٧٦ are to be considered in IBM calculations to be
higher than predicted. In figure ١٢ and ١٣ the experimental and calculated (IBM-١ and ٢)
values for the E(+14 )/E( +
12 ) and E( +16 )/E( +
12 ) ratios respectively are usually too high for (N=٨٨ ,٨٦), particularly for Ba, since the Z=٥٦ gap is considered to be effective once protons begin filling the ١g٧/٢ orbit as they must for Z>٥٦. The calculations were carried out assuming that the gap is still operative and the proton shell splits into two parts, Z=٥٦-٥٠ and ٦٤-٥٦. In the first part, Ce has Nπ=٤ and a rather O(٦)-SU(٥) transitional structure as occurs for low values of Nπ.Nυ. In the second part, Nπ=٠ and a more vibrational pattern result, with lower E(+
14 )/E( +12 ), E( +
16 )/E( +12 ) and higher
E( +12 ) values.
An interesting test would be B(E٢) values. Since the B(E٢; +12 - +
10 ) values give the evidence that the calculations give the correct trends in the data. Figure ١٤ shows the comparisons between the calculated (IBM-١ and ٢) values and the available experimental values. These comparisons demonstrate the validity not only of the overall approbations that we have employed but also of the specific uncertainties that we have assigned to the experimental values. The uncertainties quoted in the current experimental B(E٢) values are based on the considerations described in the next paragraph.
Most of the experimental results are for nuclei; with B(E٢) values, far off the stability line; they are intrinsically difficult, and the results are often discordant. When there is only one reported value we have no choice, but
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when two or more values are listed in table ٣ for a particular nucleus, we select for the sake of this test, the theoretical calculated (IBM-١ and ٢) values that agree with one of reported values depending on the dynamical symmetry of the nucleus with which the calculated B(E٢) values choice with the best fit from the energy levels correctly reproduces the current eigenvectors of the states.
Here, this is clearly evident in the slopes in figure ١٤ and the calculations reproduce this behaviour nicely. The only discrepancies in details are: ١. The B(E٢; +
12 - +10 ) of 74,70
124,12050Sn ; the agreement is between the calculated
(IBM-١ and ٢) results. Both are slightly higher than the experimental values. ٢. The B(E٢; +
12 - +10 ) of 80,78,76
130,128,12650Te ; both calculated (IBM-١ and ٢) results
are in good agreement and they are slightly lower than the experimental values. ٣. The B(E٢; +
12 - +10 ) of 74
12652Te ; the agreement is between the calculated
(IBM-١) value with experiment. While in (IBM-٢) the result is higher. ٤. The B(E٢; +
12 - +10 ) of 76
12852Te ; both (IBM-١ and ٢) results are higher than
the experimental value. ٥. The B(E٢; +
12 - +10 ) of 82
14260 Nd ; the (IBM-٢) results are slightly higher than
(IBM-١). Both results are too high than the experimental value. ٦. The B(E٢; +
12 - +10 ) of 88,86
150,14862Sn ; both (IBM-١ and ٢) results are in good
agreement and slightly higher than experimental values. Once again, an overview of these nuclei in figure ١٤ discloses a
remarkable agreement in which different behaviour of different nuclei is closely reflected in the calculations.
The structure of the wave function in the O(٦) limit is determined by the PP ˆ.ˆ † term, which is the only non diagonal one in a SU(٥) basis.
The O(٦) and SU(٥) limits may appear similar. Many of the same level groupings with each spin occur in both, the E٢ selection rule ∆τ=±١ for the O(٦) limit is similar to the ∆nd=±١ rule for SU(٥), and the branching ratios for allowed transitions are the same in both limits.
There are an important differences as follows: ١. The level groupings are not similar (a) The ٠+ level of the two-phonon triplet does not occur in the O(٦) limit in which the σ=σmax, τ=٢ group has only ٢+ and ٤+ members. (b) The ٢+ state of the three-phonon quintuplet in SU(٥) is absent in O(٦) limit.
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(c) If the σ=N-٢, τ=٠, the ٠+ state were associated with the missing members of the two-phonon triplet. (d) The ٢+ state above, it cannot be the missing ٢+ of the three-phonon, since the latter state decays in SU(٥) to all three two-phonon triplet states. (e) In O(٦) this ٢+ level decays only to the ٠+ state below it. (f) The O(٦) states with σ<N do not occur in SU(٥) limit. ٢. The differences may be discussed by considering certain features of the actual wave functions. Since the present scheme is carried out in the IBM-١ formalism which closely related to the IBM-٢ as follows: (a) The Hamiltonian, of equation (١), is identical in form to that used in the IBM-٢ with the absent of LL ˆ.ˆ† term, which appears not to be needed in large-scale global calculations, such as presented in this work. (b) The one parameter that varies with the nucleus, ε, varies as a function of Nπ.Nυ parameterization, in the framework of the IBM-٢, using the concept of F-spin, which projects states of maximum F-spin in the IBM-٢ onto states of the IBM-١. Where the proton bosons have a Z-projection FZ=+١/٢ and the neutron boson have FZ=-١/٢. CONCLUSIONS ١. The detailed behaviour of each chain of isotopes is reproduced. Here, the main structural change is from O(٦) toward SU(٥). Which proof a new gap at mid-Z of A=١٥٢-١٢٠ region. ٢. The ultimate result of this work is a set of IBM calculations that reproduce the structure systematics of spherical –gamma soft transition regions in simple approach. These calculations providing a global phenomenological scheme and a unique characteristics of medium and heavy nuclei ranging from A=١٥٢-١٢٠. ٣. The present approach may be useful in calculations with other collective models as well as IBM. REFERENCES [١] Arima A., and Fachello F.: Phys. Rev. Lett., Vol.٤٠, P.(١٩٧٨)٣٨٥. [٢] Iachello F., and Arima A.: Interacting boson model. Published. by Cambridge, Engalnd. PP. (١٩٨٧) ١٨٦-١٢. [٣] Pfeifer W.: An introduction to the Interacting Boson Model of the Atomic Nucleus: Part ١. Published by Switzerland. PP. (١٩٩٨) .١٠٦-١. [٤] Dioszegi I., Maraczy Cs., and Veres A.: Nucl. Phys. A., Vol. ٤٣٨, P.٣٩٥. (١٩٨٥). [٥] Iachello F.: Phys. Rev. Lett., Vol. ٨٧٠٥, P. (٢٠٠١) .٢٥٠٢. [٦] Gade A., Wiedenhover I., Meise H., Gelberg A., and Vonbrentano P.: Nucl. Phys. A, Vol. ٦٩٧, P. (٢٠٠٢) ٧٥.
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[٧] Hagino K., Bertsch G.F., and Reinhard P.G.: Phys. Rev. C, Vol.٦٨, P. (٢٠٠٣) ٠٢٤٣٠٦. [٨] Tajima N. : arxiv nucl-th/٩٣٠٩٠٠٧ VI. P.(٢٠٠٤) ١. [٩] Ogawa M., Broda R., Zell K., Daly P.J., and Kleinheinz P.: Phys. Rev. Lett., Vol.٤١, P.(١٩٧٨) ٢٨٩. [١٠] Casten R.F., Warner D.D., Brenner D.S., and Gill R.L.: Phys. Rev. Lett., Vol. ٤٧, P.(١٩٨١) ١٤٣٣. [١١] Gill R.L., Casten R.F., Warner D.D., Brenner D.S., and Walters W.B.: Phys. Lett. B, Vol.١١٨, P.(١٩٨٢) .٢٥١. [١٢] Zemel A.: The effect of the Z=٦٤ subshell on IBA calculations: Phys. Lett.B., Vol.١٢٦, P.(١٩٨٣) .١٤٥. [١٣] Ibrahim N., and Stewart N.M.: Retarded Dissipation of the Z=٦٤ Shell Gap in 94
16066 Dy :J.Phys.G.: Nucl. Phys., Vol.٩, P.(١٩٨٣) ١٩٥.
[١٤] Lipas P.O., Toivonen P., and Warner D.D.: Phys. Lett. B., Vol.١٥٥, P.٢٩٥. (١٩٨٥). [١٥] Van Isacker P., Heyde K., Jolie J., and Sevrin A.: Ann. Phys., (N.Y.). Vol. ١٧١, P. (١٩٨٦) ٥٢٣. [١٦] Otsuka F., and Yoshida N.: Jap. At. En. Res. Ins. Report, PP. ٠٩٤-٨٥ (١٩٨٥); User's Manual of the NPBOS and NPBTRN cods, New version, University of Tokyo, B٣٤٠٦E, PH٢١٩A (١٩٨٥). [١٧] Lederer C.M., and Shirley V.S.: Table of isotopes ٧th Edn. (New York: Wiley), (١٩٧٨). [١٨] Raman S., Nestor W., Kahane S., and Bhatt K.H.: Atomic Data and Nuclear Data Tables. Vol.٤٢, P.(١٩٨٩) ١. [١٩] Bohr A., and Mottelson B.R.: Mat. Fys. Medd. Dan. Vidensk. Selsk. Vol.٢٧, No.(١٩٥٣) ١٦. [٢٠] Grodzins L.: Phys. Lett., Vol.٢, P.(١٩٦٢) ٨٨. [٢١] Ross C.K., and Bhaduri R.K.: Nucl. Phys. A, Vol.١٩٦, P.(١٩٧٢) ٣٦٩. [٢٢] Patnaik R., Patra R., and Satpathy L.: Phys. Rev. C, Vol.١٢, P. ٢٠٣B(١٩٧٥). [٢٣] Stelson P.H., and Grodzins L.: Nuclear Data Section A, Vol.١, P.(١٩٦٥) ٦١. [٢٤] Raman S., Malarkey C.H., Milner W.T, Nestor O.W., and Stelson P.H.: Atomic Data and Nuclear Data Tables. Vol.٣٦, No.(١٩٨٧) ١. [٢٥] Endt P.M.: Atomic Data and Nuclear Data Tables. Vol.٢٥, No. (١٩٨١) ٦-١. [٢٦] Subber A.R., Park P., Hamilton W.D., Kumar K., Schreckenbach K., and Colven G.: J. Phys. G. Nucl. Phys., Vol.١٢, P.(١٩٨٦) ٨٥. [٢٧] Christy A., and Hausser O.,: Atomic Data and Nuclear Data Sheet A. Vol.١١, No.(١٩٧٢) ٤-١.
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Single Layer Anti-Reflection
Coating for near Infrared Region
A.K.Iltaif, S.S.Thieban and A.I.Khudiar.
Ministry of Science and Technology
Abstract: Thermal evaporation method was employed to deposit silicon monoxide
(SiO) as a single layer anti-reflection coating (ARC's) in the near IR region (٣ -١) µm.SiO deposited on both sides with two types of Si substrates intrinsic and extrinsic. The film thickness was ٢٣٣٦ nm and the deposition rate ٠٥ nm/s. The maximum transmittance at ١٧ µm for the intrinsic type increase to ٨٢٪, while for extrinsic Si substrate with thickness (٠٥،١،١٥) mm increase to (٥٠،٪٥٦،٪٦١٪) respectively. The toleration of the prepared films was studies using Nd-glass laser system output energy ١٠J, pulse duration nearly ٣٠٠ µs using different tests. In the first test, different energy density for a single shot was used to determine the damage threshold which was ٧٣٤ J/cm٢. In the second test ,the same energy was used (less than the damage threshold) but with different number of shots until the damage threshold was reached . The time interval between shoots was ٥ Sec .
<1 : +( ( + R @0 H 0 1 !
I =I +I5 U I(3 5 ?0( L +( + >)6F8 ( 0 - ( G88,; *3 9,D /@ . IO (
*0 6,A ( EGp LI +(I +( ( +(D9p, D;p, ;6p) - (9,D, 6, 6,D) > . * -(
O 1 ! R – ) S ) 69 * ( 5I QI 899 )3 1 .( . )I 5I I1 0 )L 1 * 1 !
) 0 H ? L% K ( A,87 * /². U 1 . 1 ! 3 0 K > *< > 5 + K1 . I5 + < +
1=D . .
١.Introduction: Anti-reflection phenomenon was first recognized by Raleigh and Fraunhofer in the ١٩th century as a spontaneous process on atmospherically tarnished lenses [١]. Knittl studied the anti-reflection coating phenomena by the deposition of more than one of thin film layers in series [٢]. Grebenshchikov et. al. [٣] has published in ١٩٤٦ the first book in anti-reflection coating of optical surfaces including the multilayer coating. ARC's enter new stage when characteristic matrix theory is submitted and
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discussed by Abeles [٤] in ١٩٥٠. Herpin [٥] and Epstein [٦] introduce the mathematical bases for designing and manufacturing optical filters. In ١٩٨١ Nagendra [٧] used BiF٢, ZnSe, and MgF٢ as ARC's materials deposited on Ge substrate for IR applications. In ١٩٩٧ Gaullant et.al. [٨] got excellent results by using semiconductor laser to deposit single layer (Zr- Si) film at wavelength (٠٩٩ µm).In (٢٠٠٠) Quesnel [٩] submitted a comparative study of YF٣ thin film deposited either by conventional e-beam evaporation or ion beam sputtering process. Anti-reflection films on alkali-borosilicate glasses produced by chemical treatments were studied by [١١ ,١٠]. In ١٩٩٢ Monga [١٢] used TiO٢ as ARC to get high transmission window. Lee et.al. [١٣] have designed a special type of double layer ARC's (SiO٢ /TiO٢). Useful applications of such coatings in the lenses of optical instruments and windows, multi purpose broad and narrow band pass filters. Moreover , ARC's are used with all optical instruments that usually used to generate lasers of different wavelengths. The aim of this work is to manufacture near infrared optical window using single layer (SiO) ARC's deposited on different types of silicon substrates. Also, studying the effect of high power Nd-glass laser on the toleration of the manufactured ARC's.
٢.Experimental Techniques Si (extrinsic and intrinsic) materials have been used as substrates after
cutting, grinding, polishing and cleaning them with special chemical materials (٢٥٪ HF then rinsed with deionized water and immersed in methanol). The transmission spectrum of these substrates has been measured using Fourier transform infrared (FT-IR) spectrophotometer. These materials distributed according to priority inside evaporation boats in coating chamber (model A٧٠٠ Q from LEYBOLD HERAEUSE ) , and deposited SiO on both sides of Si substrate with deposition rate ٠٥ nm/s and pressure of ٢x٥-١٠ mbar,but during evaporated process a decrease in pressure to ٥x٦-١٠ mbar observed because SiO is an absorber to oxygen. The temperature of the substrate should be kept below ١٠٠ °C in order to improve the oxidation during the film deposition. The amount of oxygen that absorbed during film deposition and that leads to oxidation decreases with increase in substrate temperature to ١٨٠ °C .Thus, increasing the absorption and the refractive index of evaporated SiO film according to the following equation:
nt = λ/(١) ٤ Where (n) is the refractive index (n=١٩ for SiO film [١٤]), t: is the
film thickness and λ: is the designed wavelength at ١٧ µm .The calculated film optical thickness was ٢٢٣٦ nm.
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The toleration of the prepared films was studied using Nd-glass laser system with ١٠٦ µm. Since, such laser have wavelength suitable with band wavelength that transmitted through the film (١٧ µm), furthermore this type of laser have high energy (١٠ J and pulse duration ٣٠٠ µs) density for measuring damage threshold. The experimental setup used in laser damage testing, and the shape of laser pulse are shown in figures (١ and ٢) respectively.
٣. Results and discussion: The transmittance of the extrinsic Si substrate with different
thicknesses were ٢٩ ,٪٢٣٪ and ٣٥٪ at ١ ,١٥ and ٠٥ mm, respectively as shown in figure (٣).The transmittance for intrinsic Si substrate of thickness ٠٥ mm was ٥٠٪ as shown in figure (٤). Results show the importance of using intrinsic Si substrate with ARC's film due to high transmission compared with the extrinsic Si substrate for the same thickness. Figures (٥) and (٦) show the transmission spectrum for SiO film deposited on silicon substrates in the range of (٥-١٤) µm. It is clear from figure (٥) that the maximum transmittance is ٥٠٪ and ٥٦٪ for extrinsic Si substrate with thickness ١٥, and ١ mm respectively at ١٧ µm. While figure (٦) shows that the maximum transmittance for extrinsic Si substrate with thickness ٠٥ mm is ٦١٪. Also, shows that the maximum transmittance for intrinsic Si substrate with thickness ٠٥ % at ١٧ µm is increased to ٨٢ %.The experimental results for coated and uncoated substrates give agreement with the theoretical studies by[١٥]figure (٧).
From results it may be conclude that, the possibility of using single layer ARC's for manufacturing infrared window with high transmission ٨٢٪.
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The damage threshold of SiO deposited on intrinsic Si substrate as function of energy density of Nd-glass laser is given in table (١). Damage occurs at energy density lies between (٧٣-٦٦) J/cm² .Figure (٨) Shows the damage in whole ARC's. It is clear from this figure, that the manufactured window can be used safely without damage using energy density of ٦٦ J/cm².
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Table (١): Damage threshold of SiO deposited on intrinsic Si substrate. In the second test the damage threshold was measured as a function of
number of laser shots with same energy. The damage threshold for SiO deposited on intrinsic Si substrate is shown in figure (٩).
It is clear from this figure that, as the laser energy increases the damage threshold rapidly occur with low number of shots and when laser energy decrease the number of shots to reach damage threshold must be high. ٤. Conclusion: Results shows the advantage of using intrinsic substrate in manufacturing the infrared window due to its high transmission (٨٢٪) comparing with low transmission (٦١٪) in using extrinsic substrate at wavelength of ١٧ µm. Further, the damage threshold depends strongly on the thickness of film such that it increases as the thickness decreases (i.e. we need high energy density or high number of shots to cause damage for thinner films).
Energy Density (J/cm² ) Damage Threshold
١ ٨ No damage
٢ ٨ No damage
٦ ٦ No damage
٧ ٣ damage occurs
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References:
١) H.A.Macleod," Thin Film Optical Filters",McGraw-Hill Co.,N.Y., (١٩٨٦).
٢) Z.Knittl, "Optics of Thin Films",Wiely,N.Y.,(١٩٧٦).
٣) I.V.Grebenshchikov, L.g.Vlasov,B.S. Neporent and N.V.Suikovskaya, prosvtleniye Optiki ,Anti-reflection coating of optical surfaces, state publishers of Technical and Theoretical Litreture , Moscow-Leningrad (١٩٤٦).
٤) F. Abeles, " multilayer anti-reflection coating", Ann. De Physique ,(١٩٥٠) ٥،٥٩٦.
٥) J. D. Herpin," Optical Thin Film" User Hand Book", MacMillan, N.Y., (١٩٨٧)
٦) L.I .Epstein,"The design of optical filters ",J. Opt.Soc.Am.,(١٩٥٢) ٤٢،٨٠٦.
٧) C.L. Nagendra and G.K, M. Thutupalli," Single and double layer anti -flection coatings for application in the infrared region", Vacuum, (١٩٨١) ١٣٧ ,٣١. ٨) D.J. Gallant, M.I.Tilton and G.C. Dente,"Optimized single-layer anti-reflection coatings for semiconductor laser", IEEE Photon Techno. Lett., (١٩٩٧)٩،٣٠٠.
٩) E.Quesnel ,"Near-Uv to IR optical characterization of YF٣ thin films deposition by evaporated and ion beam processes ",SPIE Proceedings, ٢٧٧٦, (٢٠٠٠) ٣٦٦. ١٠) F. H.Elmer and F.W.Martin ,"Anti-reflection Films on Alkali-Borosilicate Glasses", Am.Ceramic Society Bulletin, (١٩٨٩),٥٨،١٠٩٢.
١١) Mussaet and A.Thelen," Multilayer anti-reflection coatings in progress in optics", E.Wolf,ed., North-Holland, Amsterdam, (١٩٧٠) ١٨،٢٠١.
١٢) J. C. Mongo," Double-layer broadband anti- reflection coatings for grazing incidence angle", Appl. Opt., (١٩٩٢) ,٥٤٦ ,٣١. ١٣) J.Lee, and T.Kamaiya, "Broad band double layer anti- reflection coatings", Jap. J. App. Phys., ٣٦, part (١٩٩٧) ,٢. ١٤) J. F. Hall and W.F.C.Ferguson," Single layer anti-reflection coating in semiconductors"J.Opt.Soc. Am.,(١٩٦٥) ٤٥،٧١٤.
١٥) J. T. Cox, and G. Hass,"Anti- reflection coatings for germanium and silicon in the infrared , J.Opt.Soc.Am., (١٩٨٨) ٤٨،٦٧٧.
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Induced Attenuation by exposing optical fiber
to ionizing radiations Haider Abdullah kadhum Al-Mustansiriyah University
College of Sciences- Department of Physics ABSTRACT:- An experimental study has been made on the effect of different low dose rates of gamma ray on PMMA optical fiber using (Bi-٢٠٧) of ٤٢٠KBq activity source. The results indicated that more dose rates caused more attenuation in the power of the He:Ne laser that used in this work.
:-
! .[ 3LB ( *3 X ,0 1 .3 + < 3LN (BiFG9A) ! 3LP 7G9 *(( .[ > ) ) *1 K H< X< + 5 4, <1 + +P ) *3
,0 HW >P ) + 3LB He:Ne ! 1. Introduction
Great influence of the ionizing radiations on the laser beam transmitted through optical fiber due to the effect of these radiations on the optical fiber’s material. Thus, the fiber will be suffered from considerable changes in its structure as a consequence of the occurrence of cross-linking and degradation processes as well as color-center formations that caused the attenuation in optical fiber[١]. One of the famous rays that affect strongly on the optical fiber is gamma rays. Gamma rays are photons of high energy typically on the order of MeV. Each interaction with matter effectively removes gamma photons from the beam either by scattering it out of the beam or by absorbing it so that it disappears [٢]. Nuclear irradiation of optical fibers gives rise to transmission losses which increase with the observed dose and changes in the dimensions of the fiber [١]. In each case exposure to gamma, neutron or other forms of nuclear radiation, optical fibers can suffer from the direct effects of ionizing radiation, specifically; it will induce the transmission loss in the fiber. The initial losses usually anneal but some fibers are permanently affected. Theoretical part: Interaction of radiation with polymers: The primary interaction between the bombarding radiations (gamma ray) and the absorbing material results in the ejection of the energetic secondary electrons, which are themselves capable of ionizing many
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molecules[٣]. These secondary electrons, lost their energy and its velocity become decreases so that the free electrons which are produced can not escape from the columbic field of the parent positive ion and geminate recombination. An excited molecule is produced if the energies of the bombarding particles are transferred to an orbital electron which may not have suffice energy to produce an ionization. The energy of excitation may fairly rapidly become localized in some particular bond of a molecule resulting in hemolytic bond scission[٤]:
AB* A+B AB*: the excitation state The reactions introduced by high energy radiation can be specified at most chemical reactions because the initial energy is rapidly degraded in matter, and much of the chemical changes produced by radiation are the consequence of the action of electrons of energy less than about ١٠٠eV[٥]. Furthermore, the transit species produced by such electrons do not give final product immediately but take part in various transfer process in such a way that the molecules finally altered are not necessarily the only molecules which are affected, in the first instance one of the commonest reactions is called cross–linking. A cross – linking is the formation of the new band between adjacent high polymer molecules, resulting in increasing of the molecular weight of the polymer. It can occur in solutions, although there are quantitative differences when both hydrogen atoms are formed from the same molecule, an instauration double bound can be formed instead of cross – linking [٦].
Instauration and cross–linking are often formed together, another important reaction is degradation. Degradation is the breaking of the primary polymer linkage, which is the opposite of cross – linking, e.g., C-C scission. This is especially important with certain polymers, e.g. PMMA, cellulose acetate, and in fact many of the physical and chemical effects on such substance as polymers can be explained in terms of two reactions cross – linking and degradation [٨ ,٧].
One of the most important characteristic of a polymer is its molecular weight. Radiation can affect the molecular weight in two ways. It can increase it, by linking molecules together (cross–linking) or it can decrease it, by inducing main–chain degradation. Scission might in the main chain of a polymer, and at least one of the fragments might link to the main chain of a neighboring molecule to give a branch molecule of higher molecular weight [٩].
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Subsequently rapture of chemical bonds, resulting in this producing of free radicals, which their amount is proportional to the increase in the irradiation dose. The produced free radicals may cross link or degrade to change the structure of the polymer and alter the physical properties of the materials [١٠]. The interaction between gamma ray and optical fiber material depend on the distance between irradiation source and optical fiber, i.e. interactions depend on the dose and dose rate(dose rate is the dose at limit time). Dose is proportional inversely with distance between optical fiber and irradiation source according to inverse square law[١٠]. ٢-١ Attenuation and Attenuation Units: Signal attenuation is a major factor in the design of any communication system, since optical fibers are not loss-less media .The basic attenuation mechanisms in a fiber are absorption, scattering and radiative losses of optical energy by bending [١٢]. Absorption is related to the fiber material, while scattering is associated both with the fiber material and with structural imperfections in the optical wave-guide [١٣]. Signal attenuation (or fiber loss) is defined as the ratio of optical output power outP from a fiber of length L to the optical input powerinP .
In optical fiber communication the attenuation α is usually expressed in decibels per meter (dB /m) where [١٣]:
out
in
P
P
Llog
10=α …………………………………….(١)
Rayleigh scattering characterizes the inhomogeneous core density due to the polymerization techniques. An equation for the loss caused by the Rayleigh diffusion is[١٤]:
4
121075.2)(
λλ ×=RA ………………………………….. (٢)
Where )(λRA is the Rayleigh scattering (dB / km) and λ is the wavelengths (nm).
PMMA fibers are available which have a normal transmission loss
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١٦٠ dB / km or less near ٦٥٠ nm as illustrated in figure(١) [١٥].
Figure (١): The total loss versus wavelength[١٥].
EXPERIMENTAL PART :
PMMA optical fiber of ٥m length was exposed to gamma ray (from Bi-٢٠٧ of ٤٢٠kBq activity). The dose rates were ٠٠١ ,٠٠٢٥ and ٠٠٠٤mGy/h as shown in Figure(٢).
Figure (٢): A block diagram of the irradiation chamber for exposure to gamma photons.
Radioactive Source
Bundle Of Optical Fiber
٥ cm thick lead
Optical power meter
Wavelength (nm)
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The PMMA optical fiber was irradiated with gamma photons for time intervals up to ١٢٠ min. The attenuation in laser power as a function of time have been monitored during the irradiation.
The radioactive source was employed in this research that emits γ photons like (Bi-٢٠٧) with radioactivity ٤٢٠kBq. The half-life of this isotope is ٣٨ years and gamma photons were emitted from it by maximum energy of ١٧٧،٠٥٦٩ and ١،٠٦٣ MeV. The optical fiber that used was made from polymer, multimode graded index of ٥m length.
A helium-neon (He-Ne) laser was used as a source. The source emits ٣mW laser beam at ٦٣٢٨ nm wavelength. The spot size was ٢mm at ١٠cm distance. The Chopper was used to convert the continuous wave to pulsed wave.
The experimental setup designed and constructed for this work are presented in figure (٣).This includes a brief description of laser source, optical fibers, radioactive source, photo detector and optical power meter. All of these were used for measurements power.
Figure(٣): Experiment setup.
Results and Discussion
Dose is proportional inversely with distance between optical fiber and irradiation source according to inverse square law. Figure ٤ shows the relation between attenuation in the power of the laser beam with irradiation time at low dose rate (٠٠٠٤mGy/h), this curve predict that; at time zero (before irradiation) there is no attenuation, by increasing the dose a simple increasing in attenuation was appeared and stable the value of the
Optical power meter
He-Ne Laser
Choppe Convex Lens
Optical fiber fiber
Radioactive source sorSource
٥cm lead chamber leadchamber
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attenuation along the time of irradiation and reach the maximum value about ٠٠٥ dB/m. Figure ٥ shows more attenuation in the laser power at dose rate ٠٠١ mGy/h this can interpreted as follows: the irradiation source is becoming nearest to optical fiber and causing more interactions with fiber jacket and attenuated the laser power, the maximum value that reached was ٠٣ dB/m. Figure ٦ shows a large increasing in attenuation occurred after ٦٠ minutes of irradiation at ٠٠٢٥ mGy/h dose rate, this increasing happened because of the damage in optical fiber material, the maximum value that reached was ٥٧ dB/m.
CONCLUSIONS: The above results show the responsivity of optical fiber to radiation depending on dose rate of gamma photons. It was high at high dose rate and vice versa (i.e. more dose rates caused more attenuation in laser power).
Figure(٤): variation of attenuation with irradiation time for ٠ ٠٠٤ mGy/h dose rate.
Figure (٥): variation of attenuation with irradiation time for ٠ ٠١ mGy/h dose rate.
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Figure (٦):variation of attenuation with irradiation time for ٠ ٠٢٥ mGy/h dose rate.
References: ١. Dakin, J., “Optical Fiber Sensors: Principles and Applications” ,SPIE Proceeding, ١٩٩٢ ,٤٢٩ ,٣٦٩. ٢. Cember, H., "Introduction to Health Physics " , Pergamon Press, N.Y., ١٩٨٣. ٣. Tsoulfanidis, N., “Measurement and Detection of Radiation " , McGraw-Hill. N.Y., ١٩٨٣. ٤. Kaplan, I., "Nuclear Physics", Addison Wesley, London, ١٩٨٤. ٥. Swallow, A.S., “Radiation Chemistry of Organic Compounds", Pergamon Press, N.Y., ١٩٦٠. ٦. Dienes , G. J., Vineyard, G.H., "Radiation Effects in Solids", Willey interscience, N.Y., ١٩٨٧. ٧. Jaffar H.I., "The effect of gamma- rays radiation on the mechanical properties of polymer matrix composites", Iraqi J. Sci, ٤٢C, ٢٠٠١ ,١٤. ٨. Moschem E., Ding H., Desters A., and Attal, G., "Influence of LED optical characteristic on performance of plastic optical fiber transmission link", SPIE Proceeding, ١٩٩٧ ,١١٠ ,٨٦٧. ٩. West R.H., "Choosing a Fiber for Use in a Nuclear Radiation Environment", SPIE Proceeding, ١٩٨٣ ,٩ ,٤٠٤. ١٠. MoschemAs E., “AlxGa١-x LED Optimum Spectral Characteristics for Applications using Plastic Optical fibers”, SPIE Proceeding, ٢٢٠،١٩٨٩ ,١١٧٤. ١١. Kaino ,T., Fujiki , M., and Jinguiniji, K.,"Preparation of plastic optical fiber", ECL Review ١٩٨٤ ,٣٢،٤٧٨. ١٢. Palais, J.C., "Fiber Optic communication", Prentice-Hall, London , ١٩٨٤. ١٣. Senior , J.M., "Optical fiber communications: Principle and Practice", Printice –Hall international Inc, London , ١٩٩٢. ١٤. liu , Max Ming-Kang., "Principles and Applications of optical fiber communication"., McGraw-Hill, N.Y., ١٩٩٦. ١٥. Bolt, R.O., Carrol, J.G., "Radiation effects on organic material", Eds. Academic Press, ١٩٦٣.
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Structural characterization of Magnetron
Sputtered ZnO thin films
Najiba Abdulla Hassan. Mustafa Shakir Hashim. Reem Saadi Khaleel.
Physics Department , Education College, Al-Mustansirya University, Baghdad. Iraq.
Abstract The effects of increasing Magnetic Field on the structure of ZnO films, during its’ preparing by Magnetron sputtering method, is studied using XRD. Three peaks of (١٠٠), (٠٠٢) and (١٠١) orientations are appeared in X ray chart indicating the polycrystalline nature of the films, from this chart it is seen that, the dominant orientation of ZnO films is (٠٠٢). All the peaks have large broadening due to relatively small values of Grain size (١٧٨٥(Ǻ) ±٣٨٥) and the strains inside films. The results of increasing Magnetic Field between ٢٢٠ and ٥٧٠ Gauss are: Increasing the intensities of all peaks and Fluctuations in values of Grain size, Stress, Energy gaps and Strain. Introduction:- Zinc oxide (ZnO) is an interesting wide-band-gap semiconductor material with a direct band gap of ٣٣٦ eV at room temperature. It has crystalline structure of the wurtzite type and the unit cell with the constants a = ٣٢٤ Å and c = ٥٢٠٤(Ǻ). ZnO can be found easily as n-type because of Zn interstitials and oxygen vacancies.[١] Thin films of undoped and doped ZnO are utilized for a wide variety of electronic and opto-electronic applications, such as surface acoustic wave devices, transparent conducting electrodes, heat mirrors, nanoscale porous structures of ZnO with a high surface area find their application in chemical sensors, and dye-sensitised solar cells [٦-٢]. Various techniques have been used to deposit undoped and doped ZnO films on different substrates, including spray pyrolysis, organometallic chemical vapor deposition, pulsed laser deposition, sputtering, and sol-gel process [١١-٧]. Magnetron sputtering is a high rate vacuum coating technique for depositing metal, alloys and compound onto a wide range of materials with thickness up to about ٥ µm. Magnetron sputtering reliability is over other vacuum coating technique and this has led to the development of a number of commercial applications ranging from microelectronics fabrication through to simple decorative coatings. The advantages for using magnetron sputtering are: [١٥-١٢] High deposition rate, Ease of sputtering any metal, alloy or compound, High-purity films, Extremely high adhesion films, Excellent coverage of steps and small features,
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Ability to coat heat-sensitive substrates, Ease of automation, Excellent uniformity on large-area substrates, for example: architectural glass. High density of the films, Good controllability and long-term stability of the process. The purpose of this work is studying the effect of increasing the magnetic field (٥٧٠-٢٢٠)Gauss on the structure of ZnO films, during its’ preparing by Magnetron sputtering method . EXPEREMANTAL PART:- Sputtering Device which is used in this work was constructed in Batan physical laboratory by P٣TM-BATAN .The Sputtering Conditions are : Target( ZnO plate (purity ٩٩٩٪)) , Sputtering atmosphere (Ar ١٠٠٪) , Sputtering gas pressure (٦x٢-١٠ Torr) , Target-anode distance (٣٠ mm) , Substrate type(glass) , Substrate temperature (ambient), Magnetic field (٥٧٠-٢٢٠) G , DC power (٥٠ W) . Magnetron sputtering involves placing magnets behind the sputtering target as shown in Figure (١).
Figure (١) Side view schematic of a magnetron-assisted sputterer. The magnetron
locally traps the electrons close to the substrate causing increased ionization The data of the experiment and the specifications for X-ray test were as follows: • X-ray tube (Target- Co), (Voltage-٣٠ kV), (Current-٣٠ mA). • Slits (Divergence slit-١ deg),(Scatter slit-١deg),(Receiving slit-٠٦٠ mm). • Scanning (Scan mode- step), (Sampling pitch-٠٠٢٠ deg), (Preset time-١٠ sec), (Full scale-١٠ kcps). RESULTS AND DISCUSSION:-
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XRD analysis (Figure٢) reveals that all films exhibit none strong preferred orientation, however there is dominant orientation of the (٠٠٢) direction for all films,
Figure(٢) XRD patterns of ZnO films ,as a function of Magnetic Field. and other peaks corresponding to (١٠٠) and (١٠١) are indicating the polycrystalline nature of the films. The increasing of Magnetic Field results in increasing of the intensities of all peaks, but its increasing relatively larger for (١٠٠) and (١٠١) compared with that for (٠٠٢).This can be explained by the nucleation kinetics and the film growth which are influenced by the interactions between the substrate and the incoming energetic atoms.[١٦]
The energy of Argon ions increased due to increase magnetic field so, under energetic Argon bombardment , the(٠٠٢) plane ,which, being the most closely packed and having the lowest free surface energy , is more damaged than loosely packed planes such as (١٠٠) and (١٠١).Therefore crystallites along (١٠٠) and (١٠١) may grow undisturbed and serve as seeds for further growth . The tendency for the crystallite orientation change to a more loosely packed plane under high energetic ion bombardment has been observed by many researchers. [١٧]
In many papers…[٢٠-١٨] when the growth temperature increases, the (٠٠٢) diffraction peak becomes progressively more dominant and at temperatures
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near ٣٥٢ ºC the films are strongly textured with preferential orientation along the (٠٠٢) axis. Even though the films were deposited at room temperature in this work, they show some crystalline quality. In general, ZnO thin films grown by other techniques show crystallinity only above a substrate temperature of ٢٠٠ ºC while most films prepared at room temperature (R.T.) show an amorphous phase. [٢١]
The effect of increasing Magnetic Field on the orientation of the polycrystalline films are investigated also by evaluating the texture coefficient Tc (hkl) using the following relation [٢٢]
where Tc(hkl) is the texture coefficient of the (hkl) plane, I is the measured intensity, Io is the JCPDS standard intensity and N is the number of diffraction peaks. From the above equation, it is seen that, the texture coefficient approaches unity for a randomly distributed powder sample, while Tc is larger than unity when the (hkl) plane is preferentially oriented [٢٣].
Figure (٣) Texture coefficient of ZnO films at various Mag.Field. It is seen from Fig. (٣) that, the preferred orientation of ZnO films is (٠٠٢) plane, but it’s Tc(hkl) decreases with increasing of magnetic field and the Tc(hkl) of the (١٠٠) & (١٠١) planes becomes bigger. The increase in Tc(hkl) is attributed with the increased number of grains along the plane.[٢٤] In order to investigate the effect of the magnetic field on the average grain size, the full width at half maximum (FWHM) is calculated from the XRD spectra, and the average grain size can be deduced by the Scherrer formula :[٢٥]
t=٠ ٩٦ λ/B cosθ - - - - - - - - - - - (٢)
- - - - - - - - - (١)
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where t is the grain size, B is the FWHM, and θ is the Bragg angle. The values of Grain size are relatively small (١٧٨٥(Aº) ±٣٨٥), it responsible (among other things) on the broadening of XRD profile in figure (٢). The fluctuation of grain size with magnetic field as shown in Fig. (٤), may be due to the competition between the following factors:
Figure(٤) Variation of grain size with magnetic field
١- The increasing of magnetic field produces increasing of speed deposition which increases film thickness , according to(Y. Qu,et.al) [٢٦] the grain sizes are increased with the increase of film thickness,٢- Subsurface recrystallization ,which reduces disorder within the grain, and therefore is expected to decrease grain size.[١٥] Generally, all of the films deposited by sputtering are in state of stress due to the ionic bombarding during film deformation. [١٣] The difference in c-axis lattice constants has to be attributed to the occurrence of stresses in the films, all of them having the c- axis perpendicular to substrate surface, because crystalline ZnO exhibits a strong tendency to grow with its c- axis perpendicular to the substrate [٢٧].Under compression (parallel to the surface), the c- axis lattice constant will increase, leading to a somewhat larger interplanar distance for the (٠٠٢) planes. Under tension the reverse occurs.[٢٨]
The following equation is used to calculate the stress σ inside films [١٣]
σfilm= - ٢٣٢ ٧٥[(cfilm- cbulk) / cbulk] GPa
C-axis lattice parameters were calculated using the following equation [٢٩]...
dhkl = a / ( h٢ + k٢ + (a/c)٢ l٢ )١/٢
- - - - - - - - - - - (٣)
- - - - - - - - - - (٤)
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Where ,c/a=١٦٣٣ for ZnO ,cbulk(٠٠٢) = ٥٢٠٤(Ǻ). [٣٠] The result of stress calculation is drown as a function of Magnetic Field in Figure (٥).
Fig(٤) The Stress as a function of Magnetic Field.
Fig(٥) The Stress as a Function of Magnetic Field The shift of the diffraction peaks’ positions from its normal value - see Table (١) below - is mainly associated with residual stress in the film [٣١]. In this work, the compressive stresses found in all films were due to increment of the c-axis value in comparison at the C (ASTM) Ǻ.
Table (١) Peak position and calculated lattice parameters at different Mag.Field.
Where [٢θ (°) JCPDS] in Table (١) are the peaks positions for crystal planes of reference data for Wurtzite ZnO.[١٥] When the deposition is performed at low temperature, defects can not be annealed out. A high dislocation density and the generation of compressive stress are typical effects. Therefore, with increasing ion energies (as a result of increasing Magnetic Field), defects become larger, and more defects are
Mag Field Orientation ٢θ(°) ٢θ (°) [JCPDS] Interplanar spacing d,(Ǻ)
Lattice constant c,(Ǻ)
٢٤٧٦ ٣٦٢٥٣ ٣٦٢٥ (١٠١) ٢٢٠ -
(٠٠٢) ٥٢١٧ ٢٦٠٨٥ ٣٤٤٢٢ ٣٤٣٥
(١٠٠) ٢٨٢٠٢ ٣١٧٧ ٣١٧ -
٢٤٩٢٦ ٣٦٢٥٣ ٣٦ (١٠١) ٣٧٠ -
(٠٠٢) ٥٢٣١٨ ٢٦١٥٩ ٣٤٤٢٢ ٣٤٢٥
(١٠٠) ٢٨٣٣٣ ٣١٧٧ ٣١٥٥ -
٢٤٨٩٣ ٣٦٢٥٣ ٣٦٠٥ (١٠١) ٤٧٠ -
(٠٠٢) ٥٢٢٤٤ ٢٦١٢٢ ٣٤٤٢٢ ٣٤٣
(١٠٠) ٢٨٢٤٦ ٣١٧٧ ٣١٦٥ -
٢٤٨٩٣ ٣٦٢٥٣ ٣٦٠٥ (١٠١) ٥٧٠ -
(٠٠٢) ٥٢٢٤٤ ٢٦١٢٢ ٣٤٤٢٢ ٣٤٣
(١٠٠) ٢٨٢٤٦ ٣١٧٧ ٣١٦٥ -
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trapped in the film.[٢٤] This defects participate with other reasons in producing the broadening of XRD profile which is clear in Figure (٢).
In order to investigate the action of magnetic field on nanocrystal band gap E (gap,nanocrystal) , equation(٥) is used to calculate it [٣٢] ,and the result is drown in Fig(٦), E(gap,nanocrystal)=E(gap,bulk)+(π٢ħ٢/٢t٢)((١/me
*)+(١/mh*))− ٠ ٢٤٨ E *Ry.
The bulk band gap E(gap,bulk) for ZnO is taken as ٣٢ eV. [٣٣] and the bulk exciton binding energy E *Ry can be taken as ٦٠ meV. [٣٤] The electron and hole effective masses are taken as me
*= ٠٢٤m٠ and mh* =٢٣١m٠,
respectively. Additionally, h is Planck’s constant and t is grain size (Ǻ) of ZnO (its values change with magnetic field). From Fig. (٦) It is noticed that the band gap does not show much variation with the grain size, this is mainly because the grain size is not small enough to show a distinct variation of the band gap. This behavior has good agreement with that observed by (S. T. Tan et.al) [٣٢].
Figure (٦ ) E(gap,nanocrystal)as a function of grain size(Ǻ)
The band gap have approximate relation with film stress, this can be noticed by comparing the behavior of stress in Fig (٥) with the behavior of energy gap in Fig.(٧).The same behavior is observed by (Luis Manuel ) [١٣].
- - - - - - - - (٥)
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Figure (٧) E(gap,nanocrystal)as a function of Magnetic Field
Another factor responsible on broadening in XRD profile is non-uniform strains in the films, which are caused during the growth of thin films [٣٥]. From the shift in the peak positions the strain (ε١) in the c- direction and from it, the strain in the plane of the film (ε٢) can be estimated [٣٦] (Eq. ٨-٦) ε١ = (d(٠٠٢)film – d(٠٠٢)powder) / d(٠٠٢)powder x (٦)- - - - - - - - - - - ,١٠٠ c (٠٠٢) film = ٢ x d(٠٠٢)film , - - - - - - - - - - -(٧) ε٢ = - ε١ / v. - - - - - - - - - - - (٨) d(٠٠٢)powder = ٢٦٠٢ Ǻ , Poisson’s ratio (v) of ZnO is taken as [٣٦] ٠٣٦.
Fig(٨) ε١(%) and ε٢(%) as a function of Magnetic Field .
By comparing the curve of ε٢ (%) with that of stress in Figure (٥) ,we observe the same behavior, because the stress(σ) relates with strain in following equation [٣٧]
Y= σ/ ε - - - - - - - - - - - - - - - - - - - - - (٩) Where Y is young’s modulus of ZnO. Also from Figure (٨), it is clear that the tensile strain ε١ (in magnitude) is less than compressive strain ε٢ which generates it; because Poisson’s ratio for ZnO is ٠٣٦. Another mechanism which participates in generation of strains inside films is thermal expansion mismatch between the films and substrate (glass in this work).
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Conclusions:- The increasing of Magnetic Field results in increasing of the intensities of all XRD peaks, and the shift of the diffraction peaks’ positions from its normal value is mainly associated with residual stress in the film.The compressive stresses found in all films were due to increment of the c-axis value in comparison at the C (ASTM) Ǻ. It is noticed that the band gap of ZnO films does not show much variation with the grain sizes.
References:- ١- Jeung Hun Park J. of the Korean Physical Society, Vol. ٤٩, December ٢٠٠٦, pp. S٥٨٤_S٥٨٨ ٢- Li B.S., Chu Y.S., Shen D.Z., Lu Y.M., Zhang J.Y., Fan X.W., J. Appl. Phys., ٥٠١ ,(٢٠٠٢) ٩١. ٣- Srikant V., Clarke D.R., J. Appl. Phys., ٦٣٥٧ ,(١٩٩٧) ٨١. ٤- Minami T., Nato H., Takata S., Thin Solid Films, ٤٣ ,(١٩٨٥) ١٢٤. ٥- Weibenrieder K.S., Muller J., Thin Solid Films, ٣٠ ,(١٩٩٧) ٣٠٠. ٦- Seok-Soon Kim, Jun-Ho Yum, Yung-Eun Sung, Solar Energy Mat. Solar Cells, ٤٩٥ ,(٢٠٠٣) ٧٩. ٧- Nunes P., Fortun Adeo E., Martins R., Thin Solid Films, ٢٧٧ ,(٢٠٠١) ٣٨٣. ٨- Roth A.P., Williams D.F., J. Appl. Phys., ٦٦٨٥ ,(١٩٨١) ٥٢. ٩- J. Lu Y.F., Ni H.Q., Mai Z.H., Ren Z.M., J. Appl. Phys., ٤٩٨ ,(٢٠٠٠) ٨٨. ١٠- Jiang X.,Wong F.L.,Fung M.K., Lee S.T., Appl. Phys. Lett., (٢٠٠٣) ٨٣, ١٨٧٥. ١١- Jimenez-Gonzalez A.E., Urueta J.A.S., Suarez-Parra R., J. Crystal Growth, ٤٣٠ ,(١٩٩٨) ١٩٢. ١٢- S. Swann. Phys.Technol.(١٩٨٨)١٩. ١٣- Luis Manuel Angelats Silva , thesis , University of Puerto Rico,٢٠٠٦. ١٤- K. Ellmer, J. Phys D: Appl. Phys, (٢٠٠٠) ٣٣ R١٧-R٣٢. Printed in the UK. ١٥- Loren Wellington Rieth, Dissertation, University of Florida٢٠٠١. ١٦- W. Ensinger,Nucl. Instr. Meth. B(١٩٩٧) ٧٩٦ ,١٢٧/١٢٨. ١٧-TadatsuguMinami,ToshikazuKakumu,and ShinzoTakata.J.Vac.Sci.Technol.A.Vol.١٤,No.٣,May/Jun ١٩٩٦. ١٨- Malle Krunks,Enn Mellikov.Thin Solid Films ٣٦-٣٣(١٩٩٥)٢٧٠. ١٩- F.Caillaud,A.Smith and J.F.Baumard,J.Eur.Ceram..Soc.٣١٣(١٩٩٠)٦. ٢٠-D. J. Goyal, C. Agashe, M. G. Takwale, B. R. Marathe and V.G.Bhide,J.Mater.Sc.٤٧٠٧(١٩٩٢)٢٧. ٢١ - Zhao Dachun, Qu Zhougkai, Pan Xiaoren, Dai Muji and Sun Minggen, J. Vac. Sci. Technol. B(١٩٩٧) ٨٠٥ ,١٥. ٢٢- P. SAGAR, M. KUMAR, R.M. MEHRA Materials Science-Poland, Vol. ٢٣, No. ٢٠٠٥ ,٣. ٢٣- T. Mahalingam, V. S. John and L. S. Hsu J. New Mat. Electrochem. Systems (٢٠٠٧) ١٤-٩ ,١٠.
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٢٤- SangWoo Whangbo, HongKyu Jang, SangGon Kim, ManHo Cho, Kwangho Jeong and ChungNam Whang J. of the Korean Physical Society, Vol. ٣٧, No. ٤, October ٢٠٠٠, pp. ٤٦٠_٤٥٦. ٢٥- Scherrer P. Goettinger Nachr ٢:٩٨;١٩١٨. ٢٦- Y. Qu, T.A. Gessert, K. Ramanathan, R,.G. Dhere, R. Noufi, T.J. Coutts.J. Vac. Sci. Technol. ١٩٩٣, A, Vol.(٤)١١, p. ١٠٠٠-٩٩٦ . ٢٧- T.L.Tansley,D.F.Neely and C.P.Foley,Thin Solid Films ١٩(١٩٨٤)١١٧. ٢٨- R.G.Heideman,P.V.Lambeck,J.G.E.Gardeniers .٠ptical Materials٤ (١٩٩٥)٧٥٥-٧٤١. ٢٩- B.D. Cullity and S.R. Stock, Elements of X-ray diffraction, third edition, Prentice Hall, New Jersey (٢٠٠١) ٩-٤. ٣٠- Ali Jasim AL-Jabiry , thesis , University of Technology,Baghdad,٢٠٠٧. ٣١- V. Gupta and A. Mansingh, J. Appl. Phys. ١٥ ,(٢)٨٠ July ١٩٩٦. ٣٢- S. T. Tan, B. J. Chen, X. W. Sun,a_ and W. J. Fan. J. Appl. Phys. ٩٨, (٢٠٠٥) ٠١٣٥٠٥. ٣٣- S. J. Pearton, D. P. Norton, K. Ip, Y. W. Heo, T. Steiner, Prog. Mater. Sci. (٢٠٠٥) ٢٩٣ ,٥٠. ٣٤- X. W. Sun and H. S. Kwok, J. Appl. Phys. (١٩٩٩) ٤٠٨ ,٨٦.
٣٥- J. G. Van Berkum , J. G. M. , A. C. Varmcuch , R. Delhen , Th. H. Dinkeijser , and E. J. Hemeijer , J. Appl. Crys. , ٣٥٧-٣٤٥ , (١٩٩٤) , ٢٧ .
٣٦- I. Özen, M. A. Gülgün and Meriç Özcan Key Engineering Materials Vols. (٢٠٠٤) ٢٦٨-٢٦٤ pp.١٢٢٨-١٢٢٥. ٣٧- Mathematical and Physical Data, Equations, and Rules of Thumb,Stan Gibilisco, McGraw-Hil, ٢٠٠١.
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The Electric Field effects on the charge state
and the Potential Energy Surfaces of the system
Na/Ni (--I)
Haider Q. Al-Edany and Majid M. Al-Samer
Physics department – college of education- University of Basra-Basra – Iraq.
Abstract: Distance and screening effects on the adatom’s effective charge are studied within the framework of the time – dependent Anderson – Newns model throughout the chemisorption theory. An analytical formula for the effective charges is used and developed where the repulsion of the two electrons of opposite spins in the adatom is taken into account by means of the correlation energy.
An analytical formulation for the metallic chemisorption energy [١] is also used and developed while the ionic contribution to the chemisorption energy is solved numerically. The chemisorption energies are calculated as a function of distance, screening length and applied electric field. The comparison with the behavior of the experimental data gives good agreement.
G :
< ) ).W L > ! . + S– , I( $ <I O *1 + + > 3 . I
%< *3 1 I( ! I I O 1 ).W L 0 0 M 1 < ) ( 3 (.
$ <I I 0 I3 ? %< *3 1 e 5 , ([6] $ < 0 ? M * e I eI , I( .
0I , M( * *0 ! ( , ( $ < 0 . / *3 4, 3 K< *1 + > *<
)! 3. Introduction : The study of the interaction between adatoms and surface is considered as one of the most important subjects in surface physics, since it looks for calculating the adatom’s binding energy and the potential energy
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dependence on the distance normal to the surface [١] during the adsorption and desorption processes.
As the atom approaches the surface, its atomic levels (Ionization level Vi and affinity level VA) will be shifted due to image forces and broadened due to their interaction with the solid band levels.
It is well known that as the atom chemisorbed on the surface, chemical bond is formed between the adatom and the surface will be compensating by redistribution and rearranging in the electronic surface density. The nature of this bond is restricted between the ionic bond and the covalent bond. It is possible to compute the chemisorption energy and study the factors that affect the chemisorption process throughout calculation potential energy curves or what is called “Potential Energy Surfaces” PES. These calculations are considered as a very important step in the chemisorption theory.
The researchers offered many theoretical studies on chemisorption and one of the most important studies was awarded by Rasser and Remy [٢] to explain the dependence of the charge exchange process on the normal distance to the surface and surface temperature, taking into account the image shift and the correlation effects.
Gadzuk and others [٣] offered a theory of chemisorption concern with the adsorption of alkali atoms on metal surfaces. The alkali chemisorption energy is proposed to consist of two parts, the metallic and the ionic parts. They concluded that the ionic bond is prevailing as the alkali ion chemisorbed on the transitional metal surface.
Researchers like Brivio [٤] and others assured the importance of taking lattice structure into account in their studies to chemisorption using “Local Density Functional Approximation” and they discussed the effect of the bandwidth on adatom levels. Recently, analytical consequences of chemisorption theory are derived and discussed in part (٢) of ref. [٥]. Their realistic treatment was extended to large atom surface separation and the temperature effect was also introduced. Including the Coulomb repulsion between opposite spin electrons provided us with a qualitatively correct physical description to the atom – metal interaction. Calculations of the atomic level’s position, half width and occupation as well as the effective Coulomb term were used to calculate the binding energies for different alkali types and substrates crystallography which give good quantitative agreement with experimental data (see also ref. [٧]). Alkali atom is chemisorbed on the surface of transitional metal as a positive ion [٦].
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As the practical studies of the phenomena which occur on the surface (such as Diffusion, Crystal growth, Field Ion Microscope, Field Emission, Field Evaporation, field Desorption and others) are originally focusing on the binding energy and dependence of potential energy on the distance, this research will concentrate on the interaction between the adatom and the surface, where the calculations of the chemisorption energy (binding energy) as a function of distance which means to find the potential energy surfaces (PES), which is considered a very important step in those calculations, furthermore, the most important matter is that represents the charge state on the surface during the adsorption process.
In this work, a complete treatment was used to calculate the occupation numbers for the system Na/Ni(١١٠) taking into account the effects of distance, applied electrical field, screening length, image effects and correlation effects. Then the results of these calculations have been used to calculate the energies that are mentioned above.
Theoretical considerations: In regard to subject of this work, an analytical formula was derived
for the occupation numbers of the adatom’s levels (valance level with spin +σ and affinity level with spin –σ) is given at any temperature by the following [٦ ,١]:
Γ−
+
Γ−−
+
Γ++Γ+−
Γ+
Γ−
−Γ=
−−
−
σσ
σσ
σ
σσ
σσπ
aBaB
aB
aBa
aBa
ETkB
ETkB
ETk
ETkEa
EuTkan
12
11
22
22
201
2
tantan
)(
)(lntan2
------------(6)
where
22
2202
21
)(
1
Γ++=
=+
aEaaB
BB
aσσ
σσ
21, aandaao are constants, kB is the Boltezman constant, T is the temperature of the surface, uo is the band with of conduction band and Γ represents the half width (the broadening) of the adatom energy level.
Taking into account the image shift )(SE∆ and correlation effects effU the corresponding energy levels positions are given by [١،٦]:
σσ φ +± +∆+−= aeffioa nUEVE ------------(٢)
where oφ is surface work function. Equation (١) and (٢) are solved consistently getting two types of solutions, magnetic )( σσ −≠ aa nn and non-magnetic )( σσ −= aa nn . The naming magnetic or non-magnetic refers to the net spin on the adatom whereas the
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occupation numbers σ±an , the positions of the atomic levels σ+
aE and the
atomic half width σ±Γ are functions of spin. When the adatom approaches to the surface, a strong coupling occur which leads to charge transfer from the adatom to the surface. That mean the non-magnetic solutions )( σσ −= aa nn appear on the surface. Where the occupation numbers )( σ±
an represents a standard to the charge state on the adatom. The density of electronic states of the adatom ))(( Ea
σρ ± given by [٢]:
22 ))(())((
)(1)(
SSEE
SE
a
a σσ
σσ
πρ ±±
±±
Γ+−Γ= -----------(8)
Whereas )(Sσ±Γ is the half width of the adatom energy level which is given by[٧]:
σ
σσ
σσ ±−
±±
±±
++−
+=Γ aqS
ai
aoio
a eqrS
qVrSV
qS 22
2
)(2
11)(2
)(16
)()( -----------(7)
ri represents the ionic radius and Vo=Ø + |uo| , whereas |uo| is the metal band width and σ±
aq is given b: σσ ±± = aa Eq 2 ----------(D)
An analytical formula was also derived for the metallic binding energy that is given by the following:
∑∑=
−−=σ
σσσσ
π
5
1
1)(
iaaeffiiM nnUgCSE -----------(;)
Whereas the functions Ci and gi are well known in the reference [6]. However, the ionic energy part is given by the following relation [٣] that has been solved numerically:
∫∞
+−=
S o
leff
ISS
dSSZeSE
2/
/22
)(4
)()( -----------(A)
So represents the screening length and Zeff(S) is the effective charge that concentrated on the adatom. Accordingly, the total chemisorption energy is given by:
)()()( SESESE IMCH += -----------(E)
From equation (E), it would be possible to find the potential energy surfaces PES that represents the system energy states whether it is in the magnetic state (atomic) or in the non-magnetic state (ionic) especially near the surface. And the binding energy was calculated as follows:
)()0( ∞=−== SESEE CHCHB -----------(C)
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By applying external electrical field of strength F on the system of adatom – surface, thus its affect is added to the surface of the adatom
energy level that will be shifted by ( eFSo )[E], whereas So represents the screening length. Then, the chemisorption energy of the non-magnetic state
as a function of distance(S) and the applied field (F) given by [C]:
2
2
1),(),(),(),( FFSEFSEFSEFSE iIFIMCH α−++= -----------(69)
Where Em(S,F) and EI(S,F) are calculated according to eq.s(;A) with the
applied field. The third term of eq.(69) amount of the energy which
associated with the brings of the effective charge |e|Zeff(S,F) from S=9 to the applied field zone at the distance S from the surface and it is given by
[C]:
∫+
′′=0
),(),(oSS
effIF SdFSZFeFSE -----------(66)
The fourth term of eq.(69) represents the ion polarization energy and αi is a polarization factor of the electric dipole of ion. The chemisorption energy of the magnetic state as a function of
distance(S) and the applied field (F) is given by a similar formula to eq.(69) but by changing αA instead of αi (whereas αA is a polarization factor of the electric dipole of atom). Results and discussion:
In the chemisorption model; the band width( uo ) and the work
function (which was included in σ+aE formula) are the surface discriminated
factor and the discriminated factors of the adatom are represented by the ionization level (Vi and affinity level VA ) and the atomic radius (ri) which
is included into the correlation energy formula (effU ) and the half width
( σ±Γ ) consequently. All correlation interactions have been neglected except those that occur on
the adatom, effU , which include the image shift effects. Worth mentioning, the screening effects influence clearly near the surface and determine the atomic level positions and ionic binding energy. Firstly, the system Na/Ni (١١٠) has been studied because it is one of the practically used system and it also represents the state between oφ > Vi
and oφ < Vi states, i.e. one can get the two types of solutions (magnetic
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)( σσ −≠ aa nn and non-magnetic )( σσ −= aa nn ). The occupation numbers σ±
an calculation was done and the corresponding energy levels σ+aE with the
screening length So=٠٩٨٧٢ Ao for various values of applied electric field, for purpose to assure its general behavior as a function of distance and applied external field. Table(١) shows the following:
١. The occupation numbers σ±an (the position of adatom energy level
σmaE ) decrease (increase) for all distance values, especially at the
surface, as the applied field increases. ٢. The point (Sch) explains the region in which the solution changes
from magnetic into non-magnetic solution whereas (Sch) varies with the applied field.
The importance of this point is to limit the distance at which the solutions are non-magnetic, therefore limiting the system charge state as a function of distance.
٣. The adatom energy levels are sited above the Fermi energy level, as shown in figure (١). However, the value of density of states on adatom decrease with the applied field increases at the surface where the solutions are non-magnetic )( σσ −= aa nn either the filed was existed or not existed.
While figure (٢) shows the density of states calculations at distance S=٣٠ Ao from the surface, to compare it with those at the surface (S=٠). The
σ−aE site above ( σ+
aE nearly fitting at) Fermi level (EF=٠) either the filed was
existed or not existed. Where σσ −+ Γ>>Γ and σσ −+ >> aa nn , so, the solutions are magnetic state because the acting of correlation effects and image force effects. ٤. Chemisorption energy calculation was also done to the two solutions, the
magnetic and non-magnetic one, for the system Na/Ni(669) as a function of distance and applied field where the results of occupation numbers calculations were used as input data to calculate chemisorption energy, see figure (٣).
For the case oφ < Vi, two states appear: the ionic (connected line) and the atomic (dashed line) which intersect in the point (SC), this point has an importance in the desorption process because it assures that the ground state of the system is atomic state (EM>EI) when the atom is faraway from the surface while the ionic state is (EM<EI) as the atom approach to the surface.
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These calculations shown in table (٢), from which one can conclude that the ionic participation in the chemisorption energy ECH (in the binding energy) is prevailing to all values of the applied field and this participation increases with the applied field increases, on the contrary of the metallic participation. The theoretical and experimental values of the binding energies mentioned in table (٢) which where taken from the references [٣،١٠] are measured with respect to the ionic state, so it must be compared with ECH value. The results that were obtained give a good agreement with experimental data. ٥. To study the external electric field effect, the calculation of PES was
done on the Na/Ni (١١٠) system as a function of applied field. By applying an external electrical field F , which should be greater than the local field causes by the induced image at the surface on the ion that is wanted to be desorbed. The adatom energy level will shift up to Fermi level by( |e|FSo). As a result, the local electronic charge near the adatom will be greatly decreased (especially to the stronger fields), because the trails of the adatom Lorentizian shape will be intersected with levels of the metal energy band. Then, the increases of the broadening Γ of the adatom energy level that leads to decreasing of the electronic charge na which was localized near the adatom.
Figure(٤) shows the magnetic solution (dashed line) is not affected by the weak applied field but the effect of the applied field is added of this kind of
solutions as a shifting with amount 2
2
1FAα matching with the case of F=٠.
While for the stronger applied field there is no magnetic state, because the adatom energy level will shifted up to Fermi level then, the non-magnetic state was dominated starting from the effective charges (occupation numbers) and ending with the chemisorption energy.
The non-magnetic solution (connecting line) is being curved with respect to strength of the applied field F, comparing with the case of F=٠ which was shown in the previous figure (٣). The intersect of these curves (magnetic and non-magnetic curves) depend on the strength of applied field. Figure(٤) shows the mechanism of desorption process, where adatom is been desorbed as a positive ion through the ground state G.S. of the system, which is an ionic state without intersecting with the magnetic state (atom) curve, i.e. the crossing point SC is vanish. Conclusion: A model derived from the chemisorption theory, which determines the effective charges of an alkali atom adsorbed on a metallic surface. It has explained that the effective charge and the chemisorption energy are very
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Figure (١): The density of states on the adatom at the surface (S=٠).
sensitive to the atom – surface distance and strength of the applied electric field, especially at the distances larger than ٥ao . This is of a great interest for various atoms –surface interaction processes involving external electric field. By applying an external electrical field F , the adatom energy level will shift up to Fermi level by( |e|FSo). As a result, the local electronic charge near the adatom will be greatly decreased especially to the stronger fields.
The magnetic solution is not affected by the weak applied field but the effect of the applied field is added of this kind of solutions as a shifting
with amount 2
2
1FAα and for the stronger applied field there is no magnetic
state. The non-magnetic state was dominated starting from the effective charges (occupation numbers) and ending with the chemisorption energy. The non-magnetic solution is being curved with respect to strength of the applied field F, while the intersecting of the magnetic and non-magnetic curves depends on the strength of applied field.
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Figure (٢): The density of states on the adatom at distance (S=٣٠ Ao) from the surface.
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Figure (٣):The PES for the system Na/Ni(١١٠).
Figure (٤): The PES for the system Na/Ni(١١٠) with applying an electrical field.
References: ١- H. Q. Al-Edany, M. Sc. Thesis, University of Basra, Basra, Iraq, (٢٠٠٢).
٢- B. Rassar and M .Remy, Sur. Sci.,( ١٩٨٠), P.٢٢٣. ٣- J. W. Gadzuk, J. K. Hartman and T. N. Rhodin, Phy. Rev. B, Vol.٤, No.٢,( ١٩٧١), P.٢٤١. ٤- M. I. Trioni, G. P. Brivio, S. Crampin and Iaglesfield, Phy. Rev., Vol.B(١٩٩٦),٥٣, P.٨٠٥٢. ٥- J. M. Al-Mukh, Ph. D. Thesis, University of Basra, Basra, Iraq, ١٩٩٧. ٦- H. Q. Al-Edany and J. M. Al-Mukh, J. Basra Researches, Vol. ٢٨,Part ٣, (٢٠٠٢) P. ١٤٥-١٣٦. ٧- K. Murray, K. Boyd and Y. Naite, International union of pure and applied chemistry (٢٠٠٦) P. ٤٨-١.
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٨- M. A. Ibraheem, M. Sc. Thesis, University of Basra, Basra, Iraq, (١٩٩٠). ٩- J. M. Al-Mukh and S. I. Essa, Basra J. Science, C, Vol. ١٨, No. (٢٠٠٠) ,٢ p. ١٥٨-١٤٥. ١٠- T. T. Tsong, Report on Progress in Physics, Vol. ٥١, Part (١٩٨٨) ٢.
