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