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Determination of the 3g fractionin positron annihilation
Bożena Jasińska
Institute of Physics, Maria Curie Sklodowska University 20-031 Lublin, Poland
Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, Kraków, June 7-12, 2015
OUTLINE:
1. Positron and positronium in the vacuum2. Positronium annihilation in the condensed matter3. ETE model4. Lifetime spectra -3g determination 5. Energetic spectrum - 3g determination
+_
511 keV
Positron annihilation
𝑒+¿+𝑒− →𝑛 𝛾 ¿
s3y = (4/9p)(p2 - 9)as2y = (l/372) s2y
511 keV
POSITRONIUM in the vacuum
t = 125 pslp-Ps = (7,98950 ± 0,00002) ns-1
t = 142 nslo-Ps = (7,03993 ± 0,00001) ms-1
P(o-Ps)/P(p-Ps) = 3/1
Experimental techniques based on positron annihilation:
- Positron Annihilation Lifetime Spectroscopy (PALS)- Doppler Broadenining of annihilation radiation (DB)- Angular Momentum Correlation (ACAR)- Age MOmentum Correlation (AMOC)- 3g measurements
2g/3g ratio determination from:- PALS measurements- Energetic spectrum
POSITRONINUMIN THE MATTER
2.6y
3.7ps
b+ 90.4%, EC 9.5%
b+ 0.006%
*2210 Ne
Ne2210
1.274
0
g
PALSPositron Annihilation Lifetime Spectroscopy
1274 keV 511 keV
Dt
22Na
POSITRONIUM in the condensed matter
Thermallization
Positronium – lifetime value shortening due to:
- ortho-para conversion- chemical and magnetic quenching- pick-off
pick-off process
Shortening of the o-Ps lifetime value 1 to 142 ns
0R R = R + RR 0 0L .O . R o e lig "P o sitro n A n n ih ila tio n " (1 9 6 7 ) 1 2 7A .P . B u c h ik h in e t a l. Z E T F 6 0 (1 9 7 1 ) 1 1 3 6
S .J . T a o , J .C h e m .P h y s . 5 6 (1 9 7 2 ) 5 4 9 9M . E ld ru p e t a l. C h e m .P h y s . 6 3 (1 9 8 1 ) 5 1
POSITRONIUM in the condensed matter
R
R
22drr)r(4P
1/ =t λpo=λbP
R
R2sin
2
1
R
R1bpo
0.0 0.2 0.4 0.6 0.8 1.0
V, nm
0
2
4
6
8
Life
time,
ns
sphe ll
cube
cuboid
3
Dependence of the mean o-Ps lifetime value on the free volume sizeand shape
POSITRONIUM in the condensed matter
tpo33 /1
,P bpo 1
t ns007.0
1tsb ns2
4
3
4
1
R
22 drrrP (For sphere)
POSITRONIUM in the condensed matter
Porous materials
POSITRONIUM in the condensed matter
1 s
1 p
1 d2 s
1 f
2 p1 g
2 d
20
2nl
Ps
2
nlR
X
m2E
EXCITED STATESSpherical potential well
Porous materials
POSITRONIUM in the condensed matter
Porous materials
POSITRONIUM in the condensed matter
Decay constant for nl-th state, spherical shape:
Decay constanst for pick-off process (averaged over all populated states) :
K. Ciesielski, A.L. Dawidowicz, T. Goworek, B. Jasińska and J. Wawryszczuk, Chem. Phys. Lett., 289, 41, (1998).
1 10 1002 3 4 5 6 7 8 9 20 30 40 50 60 70 80 900.90.80.70.60.50.40.3
R , nm
0
20
40
60
80
100
120
140
o-P
s, n
s liczba poziom ów1
5
10
20
50
100
200
500
1244
.kT
)R(Eexpg
kT)R(E
expg)R(N
1i
ii
N
1i
iiipo
drr)r(jdrr)r(j 22l
X
0
X
R/RX
22lb
nlpo
nlnl
0nl
Decay constant for nm-th state, cyllindrical shape:
drr)r(jdrr)r(j 22l
X
0
X
R/RX
22lb
nlpo
nlnl
0nl
0.1 1 10 100
0
20
40
60
80
100
120
140
160t,
ns
R, nm
3 g fraction f = to-Ps/tT.
PALS vs LN
Porous materials
POSITRONIUM in the condensed matter
3g fraction – LT spectrum
0 200 400 600 800 1000
t, ns
100
101
102
103
104
105
106
107
ZLI
CZ
EN
IA
0 0.2 0.4 0.6 0.8 1 1.2 20 40 60 80 100 120 140
, ns
0
0.1
0.2
0.3
dI/d
p-Ps e+ o-Ps
-4 0 4 8 1210
0
102
104
106
CO
UN
T N
UM
BE
R
ii T
iii
P)Pso(
4
3
372
P1
f
P=4/3I i - Ps i-th componentFormation probability (calculated from o-Ps intensity)
tT = 142 ns
Na 22 spectrum
Annihilation g spectra measured using a Ge detector at an Al(110)surface, where no positronium is formed (0% Ps) and where 100% Ps emissionoccurs at 900 K. Both curves were normalized to an equal height of the 511 keVline J. Lahtinen, A. Vehanen, H.Huomo, J. Makinen, P. IIuttunen,
K. Rytsolii, M. Bentzon and P. Hautojarvi, Nucl. Instrum.Methods Phys. Res., Sect. B, 1986, 17, 73.
6200 6240 6280 6320 6360 6400C H AN N EL N U M BE R
0
4000
8000
12000
2000
6000
10000C
OU
NT
S N
UM
BE
R
511 keV peak
Spectra normalized to the same number of emitted positrons (1274 keV peak height)
CO
UN
T N
UM
BE
RNa 22 spectrum
3g fraction f511 = Rsample - Rref
D/2/CABS/SR 1274511
Methods:- peak/peak- Peak/valley
Comparison 3g fraction from LIFETIME and Na 22 spectra
0 5 10 15 20 25
f511, %
0
10
20
30
40
f LT, %
3g fraction for Vycor glasses and MCM-41
SILICA BASED POROUS MATERIAL
Positron beam
,
R(E)=V/P
R. Ferragut et al., Jornal of Physics:Conference Series 225 (210) 012007
Summary:
- 3g fraction determined from g spectrum gives more accurate values then from lifetime values
- in hi-tech silica based porous materials 3g fraction reaches 50 % (hi porosity materials)
- in silica materials additional effects influencing o-Ps lifetime and intensity values like ortho-para spin conversion or Ps enchancement are not observed
Thank you for attention
Positronium 3γ fraction F3γ as a function of the positronimplantation energy in uncapped and capped swollen MCM-41(samples A and B,) and Davicatmeasured at room temperature and at 8 K
Positron beam
G. Consolati, R. Ferragut, A Galarneau, F Di Renzoand F Quasso, Chem. Soc. Rev., 2013,42, 3821
ii
ii
texp
ItZ
CO
UN
T N
UM
BE
R
PALS
TIME, ns
t- lifetime , I – intensity measure of cavity size measure of formation
probability