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Positronium Negative Ions
Yasuyuki NAGASHIMADepartment of Physics
Tokyo University of ScienceJAPAN 1
Our studies for Ps -
We started Ps - experiments in Tokyo Univ. of Sci. in 2005.
Observation of Ps - emission from tungsten surfaces
(Nagashima et al., New J. Phys. 8 (2006) 319; Mat. Sci. Forum 607 (2009) 161)
Efficient emission of Ps - using Cs coated tungsten surface
(Nagashima et al., New J. Phys. 10 (2008) 123029; Phys. Status Solidi C 6 (2009) 2291)
Emission of Ps - from Mo and Ta surfaces
(Michishio et al., J. Phys. Conf. Ser. 199 (2010) 012003)
Durable emission of Ps - from Na coated tungsten surface
(Terabe et al., J. Phys. Conf. Ser. 262 (2011) 012058, also in preparation)
Ps - photodetachment experiment(Michishio et al., Phys. Rev. Lett. 106 (2011) 153401)
Detection of Ps formed by the Ps - photodetachment
(Koji Michishio, O-19, on Wednesday)
2
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
3
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
4
Theoretical studies have been started.(Frolov, Phys. Lett. A 372 (2008) 6721)Nobody has produced.
Existence has been reported.(Cassidy and Mills, Nature 449 (2007) 06094)
Existence has been confirmed.
Bound states composed of e+ and e -
e+ e - Ps
e+
e -
e+ e -
e+ e -
e -
e+
Ps
Ps Ps
Ps Ps
Ps=
positronium (Ps)
positronium negative ion (Ps - )
positronium plus ion (Ps + )
positronium molecule (Ps2)
bi-positronium negative ion (Ps2e - )
bi-positronium positive ion (Ps2e + )
5
e - e+ e -
positronium negative ion (Ps- )
H - ion like state
All the constituents of Ps -
have the same mass.
The theoretical approach for H -
(Born-Oppenheimer approximation)CANNOT be used for Ps - .
Many theoretical approaches using variational principles have been performed.
positronium (Ps)
H atom like state
The theoretical approach for H atoms can be applied.
The wave function can be obtainedwithout any approximations.
6
e - e+ e -
positronium negative ion (Ps- )
e - binding energy to Ps = 0.33eV; Total binding energy (the energy required to break up Ps - into 3 isolated particles) : 0.33eV + 6.80eV = 7.13eV Mean distance e+ - e - : 5.5a0
Only one state Lifetime in vacuum : 479ps Self-annihilates into 2γ.
positronium (Ps)
Binding energy : 6.80eV
Mean distance e+ - e - : 2a0
Two eigenstates ortho-Ps (S=1, triplet) lifetime in vacuum : 142ns Self-annihilates into 3γ . para-Ps (S=0, singlet) lifetime in vacuum : 125ps Self-annihilates into 2γ .
7
History of Ps - research
1946 J.A. Wheeler predicted the existence.
e - e+ e -
positronium negative ion (Ps- )
Many theoretical researches have been performed since the prediction of Wheeler.
8
1960 Calculation of the Ps- binding energy by Kolos, Rootrhaan and Sack.1964 Calculation of the Ps- binding energy by Frost, Inokuti and Lowe.1968 Calculation of the Ps- decay rate by Ferrante.1979 Calculation of the Ps- binding energy by Ho.1983 Calculation of the Ps- binding energy and decay rate by Bhatia andDrachman.1985 Calculation of Ps- photodetachment cross sections by Bhatia and Drachman.1987 Calculation of Ps- photodetachment cross sections by Ward,
Humberston and McDowell.1990 Calculation of the Ps- decay rate by Ho.1993 Calculation of Ps- binding energy by Ho.2000 Calculation of the Ps- binding energy by Korobov.2000 Calculation of Ps- photodetachment cross sections by Igarashi, Shimamura and Toshima.2002 Calculation of Ps- binding energy by Drake, Grigorescu and Nistor. 2005 Calculation of the Ps- binding energy by Drake and Grigorescu.
EB = 0.261 998 108 122 au ~ 7.129 330 97 eV2007 Calculation of the Ps- decay rate by Puchalski and Czanecki.
Γ= 2.087 963 (12) ns-1.
Examples of theoretical investigations on Ps - :
History of Ps - research
1946 J.A. Wheeler predicted the existence. 1981 A. P. Mills, Jr. succeeded in the production. (formation efficiency=0.028%)
Ps - formation efficiency = number of formed Ps - /number of incident slow e+
e - e+ e -
positronium negative ion (Ps- )
11
• Slow positrons (470 eV) were guided to a thin carbon target.
• Ps - emitted were accelerated by the electric field and detected by their Doppler-shifted annihilation lines.
(A.P. Mills, Jr., Phys. Rev. Lett. 46 (1981) 717)
First observation of Ps - (Mills, 1981)
Ps - formation efficiency = 0.028%
θ
Ps - formation was confirmed.
12
Measurement of the Ps - decay rate
13
Γ = 2.09±0.09ns-1
A. P. Mills, Phys. Rev. Lett. 50 (1983) 671
14
Tandem acceleration method of detecting Ps -
A. P. Mills, Jr., P. G. Freeman and D. M. Zuckerman, NASA Conference Publication (1989)
Measurement of the Ps - decay rate
(Fleischer et al., Phys. Rev. Lett. 96 (2006) 063401)
1)015.0089.2( ns
Ps- fraction = 1 x 10-4
( 30eV )
Stripping-baseddetection technique
Measurement of the Ps - decay rate
History of Ps - research
1946 J.A. Wheeler predicted the existence. 1981 A. P. Mills, Jr. succeeded in the production. (formation efficiency=0.028%) Many theoretical researches have been performed.
e - e+ e -
positronium negative ion (Ps- )
Only a few experiments have been performed.
Ps - formation efficiency is too low. 16
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
17
e+ near metal surface
Diffusion length of e+ in defect free metals~ 100nm
A significant fraction of e+ incident onto surface with a few keV energy
diffuse back to the surface.
When e+ are incident onto metal surfaces, ...
annihilation cross section << collision cross section
e+ lifetime in metals ~ 100ps
18
19
: e+ work function
(The energy required to emit e+)
0
e+ are emitted from the surface.
20
eV80.6Ps
: e+ work function
: e - work function
0Ps
Ps atoms are emitted from the surface.
The energy required to emit Ps :
21
eV13.72Ps
The energy required for Ps - emission :
0Ps
Ps - might be emittedfrom the surface spontaneously.
Ps - binding energy(The energy required to break up Ps - into three isolated particles)
e - work function
e+ work function
22
Element Φ+ (eV) Φ- (eV) ΦPs- (eV)
Al (polycrystalline) -0.2 4.25 1.2
Al (1 0 0) -0.16 4.20 1.11
Al (1 1 1) 0.065 4.26 1.46
Cr (1 0 0) -1.76 4.46 0.03
Fe (polycrystalline) -1.2 4.4 0.5
Co (polycrystalline) -0.8 5.0 2.1
Ni (polycrystalline) -1.2 5.15 2.0
Ni (1 0 0) -1.0 5.22 2.3
Ni (1 1 0) -1.4 5.04 1.6
Cu (1 0 0) -0.3 5.10 2.8
Cu (1 1 0) -0.2 4.48 1.6
Cu (1 1 1) -0.4 4.94 2.4
Mo (polycrystalline) -2.2 4.6 -0.1
Mo (1 0 0) -1.7 4.53 0.2
Ta (polycrystalline) -1.2 4.25 0.2
W (polycrystalline) -2.75 4.55 -0.78
W (1 0 0) -3.0 4.63 -0.9
W (1 1 0) -3.0 5.22 0.3
W (1 1 1) -2.59 4.45 -0.82
Pt (polycrystalline) -1.8 5.64 2.4
Au (polycrystalline) 0.9 5.2 4.2
Pb (polycrystalline) 0.9 4.25 2.3
polycrystalline molybdenum tungsten (1 0 0) tungsten (1 1 1) polycrystalline tungsten
Ps - ions may be emitted.
23
polycrystalline molybdenum tungsten (1 0 0) tungsten (1 1 1) polycrystalline tungsten
Ps - ions may be emitted.
24
Element Φ+ (eV) Φ- (eV) ΦPs- (eV)
Al (polycrystalline) -0.2 4.25 1.2
Al (1 0 0) -0.16 4.20 1.11
Al (1 1 1) 0.065 4.26 1.46
Cr (1 0 0) -1.76 4.46 0.03
Fe (polycrystalline) -1.2 4.4 0.5
Co (polycrystalline) -0.8 5.0 2.1
Ni (polycrystalline) -1.2 5.15 2.0
Ni (1 0 0) -1.0 5.22 2.3
Ni (1 1 0) -1.4 5.04 1.6
Cu (1 0 0) -0.3 5.10 2.8
Cu (1 1 0) -0.2 4.48 1.6
Cu (1 1 1) -0.4 4.94 2.4
Mo (polycrystalline) -2.2 4.6 -0.1
Mo (1 0 0) -1.7 4.53 0.2
Ta (polycrystalline) -1.2 4.25 0.2
W (polycrystalline) -2.75 4.55 -0.78
W (1 0 0) -3.0 4.63 -0.9
W (1 1 0) -3.0 5.22 0.3
W (1 1 1) -2.59 4.45 -0.82
Pt (polycrystalline) -1.8 5.64 2.4
Au (polycrystalline) 0.9 5.2 4.2
Pb (polycrystalline) 0.9 4.25 2.3
NaI
GROUNDE D GRID
PM T
DI SC.
MCAAMP
TUNGSTE N TARGE T
Ps-e+
d
Pb
Ge
I NPUT
P.U.R.
SCALE:
COI NC.
0 5 10cm
W-
HAMAMATSU H6614101
103
105
Cou
nts
(d) Annealed, W=3kV
0
50
100 (c) Annealed, W=3kV
0
50
100 (b) Annealed, W=1kV
500 520 540 560 5800
50
100
Energy (keV)
(a) Unannealed, W=1kV
Ps - emission from polycrystalline tungsten surface
(Nagashima and Sakai, New J. Phys. 8 (2006) 319)
Ps - formation efficiency was only 0.007%.(1/4 of that of beam-foil method)
vacuum : 7 x 10-8 Pa (5 x 10-10 torr)
26
101
103
105
Cou
nts
(d) Annealed, W=3kV
0
50
100 (c) Annealed, W=3kV
0
50
100 (b) Annealed, W=1kV
500 520 540 560 5800
50
100
Energy (keV)
(a) Unannealed, W=1kV
(Nagashima and Sakai, New J. Phys. 8 (2006) 319)
0 10 20 30 40 50 600
2
4
6
8
10
Time after annealing (h)
( x
10-5
)Ps
- fra
ctio
n
Ps - formation efficiency decreases.
Change of the surface condition
Ps - emission from polycrystalline tungsten surface
27
e - energy level e+ energy lebel(Achcroft and Mermin) (Schultz and Lynn, Rev. Mod. Phys. 60 (1988) 701)
e - and e+ near metal surface
D
e - work function : e+ work function :D D
D
: e - chemical potential
: e+ chemical potential: effect of surface dipole
D
28
0 10 20 30 40 50 600
2
4
6
8
10
Time after annealing (h)
( x
10-5
)Ps
- fra
ctio
n
D becomes largerby the effect of oxygen, H, H2O, .....
Ps - emission from polycrystalline tungsten surface
.eV13.72Ps
D
Ps - formation efficiency decreases.
D D
eV13.72Ps
29
Ps - emission from polycrystalline tungsten surface
When the vacuum was improved, the fraction became stable.
7 x 10-8 Pa 3 x 10-8 Pa
Time dependence of Ps- formation efficiency
Ps - emission from polycrystalline tungsten surface
When the vacuum was improved, the fraction became stable.
7 x 10-8 Pa 3 x 10-8 Pa
(Nagashima and Sakai, New J. Phys. 8 (2006) 319,Nagashima, Hakodate and Sakai, Appl. Surf. Sci. 255 (2008) 217)
The dependence was due to the adsorbate coverage of the target surfaceby residual molecules in the target chamber.
Time dependence of Ps- formation efficiency
Effect of Cs coating for the Ps - emission
eV13.72Ps
D
Kiejna and Wojciechowski, Prog. in Surf. Sci. 11 (1981) 293
D decreases.
Change of for tungsten by Cs coating
Ps - formation efficiency might increase.
D decreases by Cs coating.
Ps
decreases.
32
e+ transport energy : 100eVe+ incident energy onto the target : 100eV + eW
Target W(100)
vacuum : 2×10-8Pa( 1.5×10-10torr )
Target was annealed at 1500 for 30 min.℃
target potential : -3kV
(Nagashima et al. New J. Phys. 10 (2008) 123029)
Effect of Cs coating for the Ps - emission
34
(Nagashima et al. New J. Phys. 10 (2008) 123029)
Effect of Cs coating for the Ps - emission
35
Ps - intensity is the highestat 2.2×1014cm-2 ( 0.8ML).
Kiejna and Wojciechowski, Prog. in Surf. Sci. 11 (1981) 293
Change of for tungsten by Cs coating
Effect of Cs coating for the Ps - emission
36
The highest efficiency was
1.25%,which is two orders of magnitude higherthan that obtained for uncoated surface,
and 45 times greaterthan the beam-foil method.
Effect of Cs coating for the Ps - emission
37
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
38
Element Φ+ (eV) Φ- (eV) ΦPs- (eV)
Al (polycrystalline) -0.2 4.25 1.2
Al (1 0 0) -0.16 4.20 1.11
Al (1 1 1) 0.065 4.26 1.46
Cr (1 0 0) -1.76 4.46 0.03
Fe (polycrystalline) -1.2 4.4 0.5
Co (polycrystalline) -0.8 5.0 2.1
Ni (polycrystalline) -1.2 5.15 2.0
Ni (1 0 0) -1.0 5.22 2.3
Ni (1 1 0) -1.4 5.04 1.6
Cu (1 0 0) -0.3 5.10 2.8
Cu (1 1 0) -0.2 4.48 1.6
Cu (1 1 1) -0.4 4.94 2.4
Mo (polycrystalline) -2.2 4.6 -0.1
Mo (1 0 0) -1.7 4.53 0.2
Ta (polycrystalline) -1.2 4.25 0.2
W (polycrystalline) -2.75 4.55 -0.78
W (1 0 0) -3.0 4.63 -0.9
W (1 1 0) -3.0 5.22 0.3
W (1 1 1) -2.59 4.45 -0.82
Pt (polycrystalline) -1.8 5.64 2.4
Au (polycrystalline) 0.9 5.2 4.2
Pb (polycrystalline) 0.9 4.25 2.339
Ps - emission from Cs coated Mo surfaces
Ps - ions were detected for uncoated Mo and Cs coated Mo.
2 x 1014 atoms/cm2
Ps - emission from Cs coated Mo surfaces
Ps - ions were detected for uncoated Mo and Cs coated Mo.
2 x 1014 atoms/cm2
First experimental evaluation for EB
Ps - emission from Cs coated Mo surfaces
Ps - ions were detected for uncoated Mo and Cs coated Mo.
2 x 1014 atoms/cm2
B
BPs
E
E 2
: Ps- binding energy
for the uncoated Mo surface.0Ps
eV0.72 BE
Element Φ+ (eV) Φ- (eV) ΦPs- (eV)
Al (polycrystalline) -0.2 4.25 1.2
Al (1 0 0) -0.16 4.20 1.11
Al (1 1 1) 0.065 4.26 1.46
Cr (1 0 0) -1.76 4.46 0.03
Fe (polycrystalline) -1.2 4.4 0.5
Co (polycrystalline) -0.8 5.0 2.1
Ni (polycrystalline) -1.2 5.15 2.0
Ni (1 0 0) -1.0 5.22 2.3
Ni (1 1 0) -1.4 5.04 1.6
Cu (1 0 0) -0.3 5.10 2.8
Cu (1 1 0) -0.2 4.48 1.6
Cu (1 1 1) -0.4 4.94 2.4
Mo (polycrystalline) -2.2 4.6 -0.1
Mo (1 0 0) -1.7 4.53 0.2
Ta (polycrystalline) -1.2 4.25 0.2
W (polycrystalline) -2.75 4.55 -0.78
W (1 0 0) -3.0 4.63 -0.9
W (1 1 0) -3.0 5.22 0.3
W (1 1 1) -2.59 4.45 -0.82
Pt (polycrystalline) -1.8 5.64 2.4
Au (polycrystalline) 0.9 5.2 4.2
Pb (polycrystalline) 0.9 4.25 2.343
Ps - emission from Cs deposited Ta surfaces
Ps - ions were not detected for uncoated Ta,
Ps - ions were detected for the Cs coated Ta.
The efficiency was 1.5%,which is higher than that for the Cs coated
W(100).
but
2 x 1014 atoms/cm2
Ps - emission from Cs deposited Ta surfaces
Ps - ions were not detected for uncoated Ta.
2 x 1014 atoms/cm2
B
BPs
E
E 2
: Ps - binding energy
for the uncoated Ta surface.0Ps
eV3.72 BE
Ps - emission from Cs deposited Ta surfaces
Ps - ions were not detected for uncoated Ta.
2 x 1014 atoms/cm2
B
BPs
E
E 2
: Ps - binding energy
for the uncoated Ta surface.0Ps
eV3.72 BE
eV3.7eV0.7 BE
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
48
Effect of Cs coating for the Ps - emission
Time dependence of f
carbon film
The decrease might be due tothe accumulation of residual molecules.
49
Effect of K and Na coating for the Ps - emission
Kiejna and Wojciechowski, Prog. in Surf. Sci. 11 (1981) 293
K and Na are less reactive chemically than Cs.
Ps - emission might stay longer.
The effect might be smaller.
50
Cs K Na
Effect of K and Na coating for the Ps - emission
51
Na coating is as effectiveand the effect remains LONGER!
Effect of K and Na coating for the Ps - emission
52
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
53
54
Theoretical investigations for the photodetachment of Ps - :
1985 Calculation of the photodetachment cross sections by Bhatia and Drachman
1987 Calculation of the photodetachment cross sections by Ward, Humberston and
McDowell
2000 Calculation of the photodetachment cross sections by Igarashi, Shimamura and
Toshima
( Igarashi et al, New J. Phys. 2 (2000) 17 )
55
High intensity pulsed laserPulsed e+ beam
synchronized to the laser
Ps - photodetachment experiment
56
Ps - lifetime is 479ps.
http://www-linac.kek.jp/slowpos/OVERVIEW.PDF
Pulsed e+ beam in KEK
57
Pulsed e+ beam in KEK
58
e+ beam : (from KEK Linac) pulse width 12ns repetition 50Hz
Laser : Pulsed Nd: YAG (Spectra Physics GCR290) wave length 1064nm pulse width 12ns repetition 25Hz power 10W
Ps - photodetachment experiment
(Michishio, Tachibana, Terabe, Igarashi, Wada, Hyodo, Kuga, Yagishita, Hyodo and NagashimaPhys. Rev. Lett. 106 (2011) 153401) 59
(Bhatia and Drachman, Phys. Rev. A 32 (1985) 3745,Ward, Humberston and McDowell, J. Phys. B 20 (1987) 127,Igarashi, Shimamura and Toshima, New J. Phys. 2 (2000) 17)
Ps - photodetachment experiment
1064nm
Threshold : 0.33eV
60
e+ beam : (from KEK Linac) pulse width 12ns repetition 50Hz
Laser : Pulsed Nd: YAG (Spectra Physics GCR290) wave length 1064nm pulse width 12ns repetition 25Hz power 10W
Ps - photodetachment experiment
(Michishio, Tachibana, Terabe, Igarashi, Wada, Hyodo, Kuga, Yagishita, Hyodo and NagashimaPhys. Rev. Lett. 106 (2011) 153401) 61
(Michishio, Tachibana, Terabe, Igarashi, Wada, Hyodo, Kuga, Yagishita, Hyodo and NagashimaPhys. Rev. Lett. 106 (2011) 153401)
Ps-
75% o-Ps, annihilates into 3γ.
25% p-Ps, annihilates into 2γ.
If Ps - ions are photodetached,the peak intensity will decrease.
Ps - photodetachment experiment
62
(Michishio, Tachibana, Terabe, Igarashi, Wada, Hyodo, Kuga, Yagishita, Hyodo and NagashimaPhys. Rev. Lett. 106 (2011) 153401)
Ps - photodetachment has been observed for the first time!
Ps-
75% o-Ps, annihilates into 3γ.
25% p-Ps, annihilates into 2γ.
If Ps - ions are photodetached,the peak intensity will decrease.
Ps - photodetachment experiment
63
(Michishio, Tachibana, Terabe, Igarashi, Wada, Hyodo, Kuga, Yagishita, Hyodo and NagashimaPhys. Rev. Lett. 106 (2011) 153401)
Ps - photodetachment experiment
64
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
65
OUTLINE OF THIS TALK
What is Ps - ?
Efficient emission of Ps - using Cs coated tungsten surface
Emission of Ps - from Mo and Ta surfaces
Durable emission of Ps - from Na coated tungsten surface
Ps - photodetachment experiment
Future plans
Conclusions
66
Measurement of the photodetachment cross sections
Production of energy tunable Ps beam
Precision measurement of the Ps - decay rate
67
Measurement of the Ps - photodetachment cross sections
(Michishio, Tachibana, Terabe, Igarashi, Wada, Hyodo, Kuga, Yagishita, Hyodo and NagashimaPhys. Rev. Lett. 106 (2011) 153401)
( Igarashi et al, New J. Phys. 2 (2000) 17 ) 68
Measurement of the Ps - photodetachment cross sections
resonances
Production of energy tunable Ps beam using Ps - photodetachment technique and its applications
69
“Production of an energy tunable positronium beamby the photodetachment of positronium negative ions”
by Koji Michishio on Wednesday
Measurement of the Ps - decay rate
70
Γ = 2.09±0.09ns-1
A. P. Mills, Phys. Rev. Lett. 50 (1983) 671
(Fleischer et al., Phys. Rev. Lett. 96 (2006) 063401)
1)015.0089.2( ns
Ps- fraction = 1 x 10-4
( 30eV )
Stripping-baseddetection technique
Measurement of the Ps - decay rate
By changing the distance and voltage between the target and the earthed grid, we aim high precision measurement with the error ~ 0.1%
Ne dispenser
Precision measurement of the Ps - decay rate
(1) We have succeeded in the efficient formation Ps - .
(2) We have succeeded in the first estimation of the binding energy of Ps - .
(3) We have succeeded in first observation of the photodetachment of Ps - .
(4) We have started the next experiments for Ps - .
CONCLUSIONS
73
Member of our group
Tokyo University of Science
Koji Michishio, Takayuki TachibanaHiroki Terabe, Ryohei Suzuki
Ayaka Miyamoto, Toshihide HakodateTakahiko Sakai
Akira Yagishita (KEK)Toshio Hyodo (KEK)
Ken Wada (KEK)Akinori Igarashi (Miyazaki Univ.)Takahiro Kuga (Univ. of Tokyo)
74
Thank you very much for your attention !
75
76
Why Ps- fraction increased dramatically?
021 BE holds for the Ps- emission,
If we assume that the Ps- is formed from positrons in the bottom of the positron band,
where and are the energy levels of two electrons measured from the vacuum level.1 2
22111
dDdDf
BB EE
Ps- fraction :
D : electron density of states
VA C U U M L E V E L
VA C U U M L E V E L
φ - E ( = - 1 0 .1 e V )
- ( = - 4 .6 e V )φ
- ' ( = - 1 .5 e V )φ
φ ' - E ( = - 7 .0 e V )
+
-
-
+
B
B
φ - E + B φ ' - E + B -φ - - 'φ -
ε1
ε2.21
)(
)(
uncoatedf
depositionCswithf
This is too low to explain the experimental results.
If is constant below the top of the conduction band,
D
77
The Ps- formation depends on the overlap of a e+ wave functionand two e- wave functions just outside of the surface,which depend on their corresponding work functions.
surfacebulk vacuum
e+
e
e
-
-
e+ and e- wave functions
Cs deposited
uncoated
The Ps- formation mechanism should be affected
by the Cs deposition.
Why Ps- fraction increased dramatically?
78
MMe Ps
PsIePs EETT ./eV8.6 2nEPs
(Brown, Positron Annihilation (1985) 328)
Ps 生成の微分断面積は前方にピークを持つ
, where
エネルギー可変 Ps ビーム
e+ ビームと気体分子との電荷交換反応
79
(Weber et al., Phys. Rev. Lett. 61 (1988) 2542)
応用例: LiF 表面での Ps の鏡面反射
エネルギー可変 Ps ビーム
80
(Mills and Crane, Phys. Rev. A 31 (1985) 593)
ddEEdN 2/32/13 )eV10(
Ps energy distribution:
エネルギー可変 Ps ビーム
81