LEP5.2.24

-15Energy loss of aa-particles in gases with MCA

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P2522415 1

Related topicsRange, mean ionization energy of gas atoms, mean energyloss of a-particles per collision, differential energy loss, Betheformula, electron concentration in gases.

PrincipleThe energy sensitivity of the detector is calibrated with anuncovered 241Am-source in vacuum.The dependence of the energy loss of a-particles on the con-centration of air particles between source and detector ismeasured. The dependence of energy loss of the a-particles on the sortof gas particles between source and detector is determinedand compared to the electron density in that sort of gas.

MaterialMulti Channel Analyzer 13727.99 1MCA Software 14524.61 1Alpha and Photo detector * 09099.00 1Americium-241 source, 370 kBq 09090.11 1Americium-241 source, 3.7 kBq 09090.03 1Container f. nuclear phys. experiments. 09103.00 1Pre-amplifier f. alpha detector 09100.10 1Vacuum gauge

DVR 2, 1…1000 hPa, 1 hPa resol. 34171.00 1Diaphragm pump, two stage ** 08163.93 1Fine control valve for pressure bottles 33499.00 1Compressed gas, helium, 12 l 41772.03 1Compressed gas, nitrogen, 12 l 41772.04 1Compressed gas, CO2, 12 l 41772.06 1Vacuum tube, NBR, 6/15 mm 39289.00 3Hose clamp for 10-17 mm diameter 40998.00 9Tubing connect., Y–shape 47518.03 2

Pinchcock, width 20 mm 43631.20 2Screened cable, BNC, l = 750 mm 07542.11 1Screened cable, BNC, l = 300 mm 07542.10 1PC, Windows® 95 or higher* AlternativelyAlpha detector 09100.00 1

** AlternativelyRotary vane vacuum pump, one-stage 02750.93 1Oil mist filter 02752.00 1

Tasks1. The pulse height spectrum resulting from a-particles com-

ing from an uncovered 241Am emitter is recorded with theMCA. The a-particle energy of the principal peak,5.486 MeV, is used for calibration.

2. The spectrum of a-particles reaching the detector from acovered 241Am source in 10 cm distance from the detectoris recorded in dependence on air pressure. The rate of ener-gy loss in dependence on particle energy is evaluated andcompared to predictions by the Bethe-formula.

3. The spectrum of a-particles reaching the detector from asource at 10 cm distance in helium, carbon dioxide andnitrogen with 100 hPa pressure is recorded. The energy lossin dependence on electron density is compared to predic-tions by the Bethe-formula.

Set–upFig. 1 shows the experimental set-up. In the beginning no gasbottle is connected to the fine control valve and the pinchcock on the tube leading to the fine control valve is closed.

Fig. 1: Experimental set-up.

LEP5.2.24

-15Energy loss of aa-particles in gases with MCA

P2522415 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen2

The black shielding is mounted on the detector and the detec-tor is attached to the flange cover. The uncovered 3.7 kBq241Am source is put into the black detector shielding up to thebed stop so the source is as near to the detector as possible.The sliding rod is retracted and secured with the milled screw.The flange cover is always mounted to the experimental con-tainer without use of the fixing nuts - the ambient pressure willhold the flange of the experimental vessel when the vessel isevacuated and pressurizing the vessel with a gas bottle bymistake is made impossible this way.The upper two preamplifier switches have to be set to "a" and"Inv.". The "Bias" switch has to be set to "Int." and the polar-ity switch for the internal bias must be kept to "–" to avoidaccidental wrong polarisation of the detector diode.The short BNC cable is used to connect the experimental ves-sel to the "Detector" socket of the a-preamplifier. The otherBNC cable connects the "Output" socket of the a-preamplifi-er with the "Input" socket of the MCA. The 5-pole cable con-nects the "+/- 12 V" jack of the MCA with the correspondingsocket of the a-preamplifier. Turn MCA and preamplifier on right at the beginning so theyhave time to thermalise before starting the measurement.Complete the electrical connections and the preamplifier set-tings prior to turning on the MCA. The MCA is connected by USB to a computer with "measure"-software installed on it. It may be necessary to remove a USBdriver that was installed by "Windows" automatically and toinstall the correct USB driver for the MCA manually if the MCAis used with the computer the first time.

ProcedureTask 1:Close the venting screw of the flange cover and evacuate theexperimental vessel. When the final pressure achievable withthe pump is reached, close the pinch cock on the tube to thepump and then turn off the vacuum pump. Start the "mea-sure" program, select "Gauge" > "Multi Channel Analyser".Select "Spectra recording" and use the "Continue" button(Fig. 2).

Set "Gain" to "Level 2" and "Offset [%]" to 1. The countingrate should be between 50 and 60 per second.Select "Channel number" as "X-Data" and "1" as "Intervalwidth [channels]" (Fig. 3).Stop the measurement with the "Accept data" button, whenthe position of the main 241Am-peak is clearly visible for eval-uation. 5000 impulses should be sufficient for this purpose.The recorded data appear now in a window in the "measure"main program. Denote the measurement parameters using the"Display options" dialog and save the measurement data.

Task 2:Fully vent the experimental vessel, open it and remove the cal-ibration source.Mount the covered 370 kBq 241Am source to the end of thesliding rod. Position the source such that the distancebetween source and detector diode is 10 cm. The position ofthe detector diode can be seen with the black light shieldingremoved. Fix the sliding rod with the milled screw so it can notmove into the vessel when the pressure is reduced.Evacuate the vessel, record a spectrum with the settings asbefore. The counting rate is between 40 and 50 per secondagain though the distance to the source is much greaterbecause the source's activity is that much higher.Record for the lowest achievable pressure at least 10000 inci-dents and for the other pressure values at least 5000 inci-dents. Save the spectra denoting the pressure.Increase the pressure in steps of 20 hPa each time recordinga spectrum. Use the fine control valve to control the pressure:open the pinch cock in the tube leading to the fine controlvalve, adjust the pressure with the fine control valve and closethe pinch cock again. The fine control valve is not completelygas tight from handle to outlet - the pinch cock prevents thusthe pressure to rise during measurement.When the counting rate has dropped with rising pressure tohalf the initial value, there is no more peak visible and the mea-surement can be terminated.

Fig. 2: Start window for the MCA. Fig. 3: Spectra recording window.

LEP5.2.24

-15Energy loss of aa-particles in gases with MCA

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P2522415 3

A background spectrum can be recorded with the vessel fullyvented, but above 400 hPa there should be no recordable inci-dents except from ambient radon (above channel # 2800). Ifyou measure some background, check presence of light at thedetector - darken the room or use cardboard to shield the ves-sel, presence of nearby mobile phones or nuclear contamina-tion of the vessel.

Task 3:Connect a compressed gas bottle to the fine control valve andevacuate the vessel again now with the pinch cock open onthe tube leading to the fine control valve. Close the pinch cock on the tubing of the pump when finalpressure is reached and turn off the pump. Then release somegas from the compressed gas bottle into the vessel with thefine control valve until the pressure is about 100 hPa. Closethe pinch cock on the tubing of the fine control valve.Record a spectrum collecting at least 10000 incidents andsave it denoting pressure and sort of gas.Vent the vessel with air before changing the gas type. Doingso you assure the composition of the rest gas to be the samethroughout your measurements. For example if you use thetwo stage diaphragm pump, the final pressure may be 22 hPa.Then you know if you have vented the vessel before evacuat-ing it, that the rest gas is always air. If you have filled the ves-sel up to 100 hPa with a specific sort of gas, the compositionof gases will be 22 hPa air and 78 hPa of the specific gas. Youcan then assume that the constant intermixture of air affectseach spectrum in the same manner and does not matter in theevaluation.Resume with the other available types of gas.

TheoryFor a short sketch of a-decay theory refer to LEP 5.2.20-15.a-particles interact strongly with matter because of their elec-tric charge and are stopped by some cm of air or some tensof µm of condensed matter.The main deceleration process is scattering at electrons.Scattering at atomic nuclei can be neglected here.Because a-particles are much heavier than electrons thea-particles lose only a small fraction of their energy in eachimpact on an electron. The direction of the a-particle'simpulse is only slightly changed and it needs hundreds ofinteractions with electrons until they are stopped.

A model describing the electronic deceleration process is theBethe formula (1). It applies for a-particle energies that arehigh compared to electronic binding energies and assumesthe electrons to be free above an electron binding energythreshold equal to the ionisation energy I. The type of interac-tion is assumed to be Coulomb-like, the electron binding Ilimiting the interaction for high impact parameters, that iselectrons far away from the path of the a-particle. Includingelectron spin and relativistic calculation yields for the differen-tial energy change dE in a layer dx in a medium with electrondensity n

(1)

where e = 1.602 · 10-19 denotes the elementary charge,Ze the charge of the a-particle,me = 511 keV/c2 the electron rest mass, e0 = 8.854 · 10-12 (As)/(Vm) the electric constant,c = speed of light,b = n/c with a-particle speed n andE = the relativistic a-particle energy.

The negative of (1), the energy loss, is minimal for the energyE approximately three times the a-particle rest mass (4 u =4 · 931.5 MeV/c2 ≈ 4 GeV). The differential energy loss risesfor high energies with the logarithm of the energy but rises atlow energies with the square of the inverse energy – before itdrops to very low energies where the model does not applyany more.When trying to plot this equation, remember E = (g - 1) m0 c2

with

Non-relativistic approximation, b << 1, yields

(2)

(2) is a first-order differential equation with separated vari-ables, but the integral has no elementary solution but may bepresented as a series. With E = 1/2 mHe n

2 , mHe the a-particle mass, Z = 2,µ = me/mHe (2) becomes

Fig. 4 shows a plot of the logarithm of the stopping powerover the logarithm of the a-particle energy for dry air.Presented are the data from the Bethe formula both relativis-tic and non-relativistic assuming I = 100 eV and the semi-empiric ASTAR-data on electronic stopping power of air fora-particles from the US-American NIST (National Institute ofStandards and Technology). The ASTAR-data account for thenecessary modifications of the stopping power data at lowenergies where the Bethe formula is incorrect. It can be seenthat the Bethe formula is applicable for energies above 1 MeV.The non-relativistic calculus begins to loose its accuracyabove 100 MeV which is far above the energies available inthis experiment.

�dE

dx�

n 2p m E

1e2>e0 22 ln 14m E>I 2

�dE

dx�

4p n Z2

men2 a e2

4p e0b 2

ln a 2men2

I b

g �121 � b2

thus b2 �E2 � 2mHec

2

1E � mHec2 22 .

�dE

dx�

4p n Z2

mec2 b2 a e2

4p e0b 2

ln a 2mec2 b2

I 11 � b2 2 � b2 b

Fig. 4: Stopping power in dependence on a-particle energy,bilogarithmic plot.

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-15Energy loss of aa-particles in gases with MCA

P2522415 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen4

The energy loss is not dependent on the density and pathlength but on the total amount of matter penetrated by theparticles. A long path in low density material is assumed tohave the same effect as a short path in high density material.So the stopping power is often specified as energy loss persurface mass density MeV · cm2 / g. The electron density nthat is responsible for the stopping power can be determinedfor a given substance of atomic mass A, k electrons per par-ticle and density r as

with atomic mass unit u = 1.6605 · 10-31 kg. So for dry airassumed to consist of 79% nitrogen (N2) and 21% oxygen(O2) with molar volume Vm = 22.7 l/mol (at 0° C = 273 K and1000 hPa) and Avogadro-number NA = 6.022·1023 mol-1 it isk = 0.79·2·7 + 0.21·2·8 = 14.4,A = 0.79·2·14 + 0.21·2·16 = 28.8,and the density r depending on pressure p and temperature Tis

= 1.269 kg/m3· (p/1000 hPa) / (T/273 K) and

= 3.825·1026 m-3 · (p/1000 hPa) / (T/273 K).

It is of significance that the stopping power is proportional tothe energy per unit length deposited by a beam of a-particles.This energy is proportional to the number of ion pairs pro-duced which is a measure for the dose of ionizing radiationabsorbed. When a beam of monoenergetic a-particles isstopped within matter, the graph plotting the dose depositedalong it's path is called Bragg curve and it is governed by theBethe formula. Since the stopping power is low at high ener-gies, the beam deposits a low dose when entering a body buta high dose at the end of it's trajectory. This can be employedin radiation therapy for example against brain tumours. Inmedicine use is made of protons from an accelerator withstorage ring which show a similar Bragg curve but have ahigher penetration depth. The Bragg curve is an integral of theBethe function plotted over path length.

In this experiment not the x-dependence, but the pressuredependence of the energy loss is measured for a fixed dis-tance x = 10 cm.The electron density per area N is for a gas layer thickness of10 cm passed by the a-particles at 293 K then

(3)� k · p · 2.47 · 1019 l�1 hPa�1 .

n � k · NA

Vm ·

p

1000 hPa ·

273 K293 K

n1p,T 2 �p

T ·

k · NA · 273 K

Vm · 1000 hPa

r1p,T 2 �p · A · u · NA · 273 K

T · V m · 1000 hPa

n �k · r

A · u

Fig. 5: Bragg curve plotted with help of spread sheet calculation from the ASTAR-data for an a-particle starting with 7 MeV inair.

LEP5.2.24

-15Energy loss of aa-particles in gases with MCA

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P2522415 5

(2) becomes withµ = me/mHe = 511 keV / 3.727 GeV = 1.371·10-4 and Z = 2

or

(4)

241Am decays to 100% to stable 237Np and in 85% of thedecays an a-particle of 5486 keV is emitted which contributesto the main peak.Fig. 6 shows a decay scheme. The 5.486 MeV line is used herefor calibrating the set-up.The main peak a-particles are of interest here.

EvaluationTask 1:

For details of the a-particle energy detection refer to LEP5.2.23-15.Use the "Survey" function (-button) to determine the positionof the main peak. In the measurement example the peak wasfound at ch. # 2454. For calculating the energy sensitivity s,that is particle energy per channel, the offset has to beaccounted for. With an offset of 1% of 4000 cannels, that is40 channels, it is s = (2454 + 40) channels / 5486 keV =0.4546 channels/keV or one channel corresponds to 2.2 keV.So in the following ∆E = ∆ch./s.

Task 2:Use the "smooth" function on the recorded curves (" " but-ton or "Analysis" > "Smooth…"). Select "strong" smoothing. Itmay be useful to select "Measurement" > "Display options…"> "Interpolation: straight lines" for displaying the curves. Fig. 8shows an example with and without smoothing.

Use the "survey" tool (" " button) to determine the channelnumber of the peak position. If you merge all the curves into one diagram with"Measurement" > "Adopt channel…" and scale them with the" " button using "fit individually" you may obtain a diagramas Fig. 9.

�dE

dp� k ·

1E

· 940 keV2>hPa ·ln15.848·10�4·E>I 2

�dE

dp� k ·

1E

· 2.41 · 10�29J2>hPa ·ln15.848·10�4·E>I 2

�dE

dx�

2p Z2

mE ·

N1p 2p

· a e2

4p e0b 2

ln am 4E

I b

�dE

dx�

2p n Z2

mE a e2

4p e0b 2

ln am 4E

I b

Fig. 7: Number of incidents per channel for the calibrationsource.

Fig. 6: 241Am decay scheme.

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P2522415 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen6

Fig. 10 is a plot of the last two columns of Table 1 over theaverage energy. The data show a good agreement.There is a statistical error due to the uncertainty of the peakposition of a peak with noise and a systematic error due to thefact, that the a-particles from the covered source are notstrictly monoenergetic but show an energy distribution. Sincethe deceleration behaviour is not linear, the peak getsdeformed and displaced which falsifies the values mainly foralmost stopped particles or relatively high pressure.

Table 1: Example of measurement results for retarding ofa-particles in dependency on air pressure

Fig. 9: Smoothed a-energy spectra after passing 10 cm of air of different pressure.

Fig. 8: Example of a-energy spectrum.

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-15Energy loss of aa-particles in gases with MCA

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Fig. 11 plots a Bragg curve using first and third column ofTable 1. The differential energy loss is derived using "Analysis"> "Channel modification…" > "differentiate".

Task 3:In the measurement example the total pressure was 105 hPa,of which 11 hPa were air, so 94 hPa of the specific gas wasrelevant for the peak energy loss. The spectra were smoothedas above and the peak positions were evaluated using the"survey" function of "measure". The peak displacement withrespect to the reference peak of air at lowest attainable pres-sure was calculated. Table 2 shows the experimental data.The reference peak corresponds to an energy of E = 4025 keV.Assuming the energy loss linear, that is -dE/dp = -∆E/∆p, (4)yields with ∆p = 94 hPa:

-∆E/k = 94 hPa / 4025 keV·940 keV2/hPa) · ln(23.54)= 69 keV

The deviation of about 15% may be assigned to the in facthigher energy loss due to lower a-particle energy and in caseof He the uncertainty of the peak position. Fig. 12 plots theresults.

sort of gas k -∆E/ch. # -∆E/keV -∆E/k/keV

He 2 77 169 85

N2 14 478 1057 75

O2 22 781 1717 78

average 79

Table 2: Example of measurement results for retarding ofa-particles in dependency on sort of gas, k the num-ber of electrons per gas particle

Fig. 12: Different spectra for different retarding gases at samepressure.

Fig. 11: Bragg plot, a-energy and differential energy loss overpressure in hPa.

Fig. 10.

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Fig. 13: Energy loss over number of electrons per gas particle.In ideal gases the particle density is independent onthe sort of gas at the same pressure and temperature.So k is proportional to electron density.