positron annihilation in flight: experiment with slow and...

Positron annihilation in flight: experiment

with slow and fast positrons

J. Čížek, M. Vlček, F. Lukáč, O. Melikhova, I. Procházka

Faculty of Mathematics and Physics, Charles University Prague, Czech Republic

W. Anwand, A. Wagner, M. Butterling

Institut für Strahlenphysik, Helmholtz-Zentrum Dresden-Rossendorf, Germany

R. Krause-Rehberg

Martin-Luther University, Halle, Germany

Introduction

• positrons in solid matter are thermalized within a few ps

• non-thermalized positron annihilation in flight (AiF)

rare process (~ 1% fraction of positrons)

• thermalized positron annihilation in rest

dominating process in solids

Annihilation in flight

• single quantum annihilation in flight (SQAF)

2

0

2

02

0

2

02

0

2

052

0

2

0

54

2ln2

33

3

8

2

4cmTTcmT

cmTT

cmTcmcmTT

cmTT

rZSQAF

• cross-section (Bhabha 1934)

H.J. Bhabha, H.R. Hulme, Proc. Roy. Soc. (London) A146, 723 (1934)

• T+ - positron kinetic energy, r0 – classical electron radius, m0c2 – rest energy of electron

Z - atomic numer of target, – fine structure constant

• important only in high-Z materials and for high positron energies

Z

e e

p

Annihilation in flight

• two quantum annihilation in flight (TQAF)

• main AiF channel

e e

1

2

p

1

31ln

1

14

1

1

2

2

2

22

0

rTQAF

• cross-section (Dirac 1934)

P. A. M. Dirac, Proc. Camb. Phil. Soc. 26, 361 (1930)

• = (T+ + m0c2 ) / m0c

2, r0 – classical electron radius,

m0c2 – rest energy of electron, T+ - positron kinetic energy

positron kinetic energy (keV)

0 100 200 300 400 500cro

ss s

ection

(b

arn

)10-3

10-2

10-1

100

TQAF

SQAF

Investigations of annihilation in flight

• early measurements:

- monoenergetic positrons 1-200 MeV

- beta and gamma scintillation counters

S. A. Colgate and F.C. Gilbert, Phys. Rev. 89, 790 (1953)

H. W. Kendall and M. Deutsch, Phys. Rev. 101, 20 (1956)

- good agreement with QED theoretical prediction

• searching for resonances near W and Z0 mass and signatures of new particles

M.Z. Akrawy et al., Phys. Lett. B 257, 531 (1991)

E. Fernandez et al., Phys. Rev. D 35, 1 (1987)

S.H. Connell et al., Phys. Rev. Lett. 60, 2242 (1988)

CDB investigations of annihilation in flight

• coincidence Doppler broadening spectroscopy (CDB)

- precise coincidence measurement of energies of both annihilation quanta

- suitable tool for energy-resolved investigation of TQAF

- M. Weber and A.W. Hunt (1999)

M. Weber et al., Phys. Rev. Lett. 83, 4658 (1999)

A. W. Hunt et al., Appl. Surf. Sci. 149, 282 (1999)

- CDB studies of TQAF using mono energetic positron beam (T+ = 10-72 keV)

- thin target

- F. Bečvář (2002) CDB observation of TQAF using fast positron emitted by 22Na

F. Bečvář, talk at the workshop EPOS02 (2002) (T+,max = 545 keV)

- J. Dryzek (2007) CDB study of TQAF using fast positron emitted by 68Ge/68Ga

J. Dryzek et al., Radiation Physics and Chemistry 76, 297 (2007) (T+,max = 1897 keV)

Digital CDB spectrometer

digital CDB spectroscopy

• pulses from HPGe detetors are sampled by 12-bit digitizer (sampling period 20 ns)

J. Čížek et al., Nucl. Instrum. Methods A 623, 982 (2010)

• sampled waveforms are analyzed off-line by software

• semi-digital configuration:

- detector pulses are sharpened in spectroscopy amplifier prior to sampling

- improvement of signal-to-noise ratio (s/n)

time (s)

0 20 40 60 80 100 120 140

vo

lta

ge (

mV

)

0

20

40

60

80

100

120

rms = 0.6 mV

time (s)

0 20 40 60

voltag

e (

mV

)

0

4

8

time (s)

0 20 40 60 80 100 120 140

vo

lta

ge (

mV

)

0

20

40

60

80

100

120

rms = 0.6 mV

time (s)

0 20 40 60

voltag

e (

mV

)

0

4

8

time (s)

0 2 4 6 8 10 12 14 16 18

vo

lta

ge (

V)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

time (s)

0 1 2 3

vo

lta

ge

(V

)

0.02

0.03

0.04

rms = 1.7 mV

time (s)

0 2 4 6 8 10 12 14 16 18

vo

lta

ge (

V)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

time (s)

0 1 2 3

vo

lta

ge

(V

)

0.02

0.03

0.04

rms = 1.7 mV

detector signal: s/n = 3 104 sharpened signal: s/n = 3 106

J. Čížek et al., New. J. Phys. 14, 035005 (2012)

Digital CDB spectrometer: semi-digital setup

SA

Canberra 2020

E2

DLA

Ortec 460

CFD

Ortec 473A

SA

Canberra 2020

CFD

Ortec 473A

DLA

Ortec 460

E2

SCA

E1

Acqiris DC 440channel 1 channel 2

SSCA

ext. trigger

2. trigger level: coinc. mode

1. trigger level: single mode

E1

source & sample

E2

HPGe, detector 1

HPGe, detector 2

1 waveform = 1000 points

sampling rate = 50 MHz (sampling interval = 20 ns)

J. Čížek et al., Nucl. Instrum. Methods A 623, 982 (2010)

run 1

find maximum

read waveform

calculate background

calculate derivative

passed

apply “fixed” filters

normalize & shift

calculate height

failed

add pulse to histogram

add height to histogram

calibrate energy

spectrum

t (ns)

0 5000 10000 15000 20000 25000

U (

V)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

DU

(V

)

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

waveform

Digital CDB spectroscopy - analysis of data

run 1

find maximum

read waveform



passed


normalize & shift

calculate height

failed



calibrate energy

spectrum

t (ns)

12200 12400 12600 12800 13000

U (

V)

2.935

2.940

2.945

2.950

2.955

2.960

2.965

2.970

2.975

parabolic fitting

wmax

t


run 1

find maximum

read waveform



passed


normalize & shift

calculate height

failed



calibrate energy

spectrum

t (ns)

12200 12400 12600 12800 13000

U (

V)

2.935

2.940

2.945

2.950

2.955

2.960

2.965

2.970

2.975

parabolic fitting

wmax

t


wmax-baseline

normalized units

710 715 720 725 730 735 740

num

ber

of

wavefo

rms

0

1x106

2x106

3x106

4x106

vertical cut of 2D pulse shape histogram

lower boundary upper boundary

modus

log z-scale

Digital CDB spectroscopy – shape filters

Two-dimensional histogram of normalized waveforms

all pulses pulses accepted by shape filter

log z-scale

Digital CDB spectroscopy – shape filters

Two-dimensional histogram of normalized waveforms

semi-digital setup analogue setup

• pure Al (99.9999%)

Two-dimensional CDB spectrum sum of energies of annihilation gamma rays

plotted versus difference of these energies2

021 2 cmEE versus 21 EE

Digital CDB spectroscopy – CDB spectra

relative difference

• semi-digital setup

Digital CDB spectroscopy – CDB spectra

• pure Al (99.9999%)

Two-dimensional CDB spectrum – effect of shape filters

semi-digital setup

• monoenergetic slow positrons

TQAF investigations – positron sources

- magnetically guided slow positron beam, SPONSOR

- Helmholtz Zentrum Dresden-Rossendorf

- positron energy adjustable in the range 0.027 – 36 keV

• fast positrons with continuos energy spectrum

- 68Ge/68Ga positron generator, T+,max = 1897 keV

W. Anwand et al., Defect and Diffusion Forum 331, 25 (2012)

- pair production from bremsstrahlung radiation (GiPS), T+,max = 16 MeV

- ELBE, Helmholtz Zentrum Dresden-Rossendorf

M. Butterling et al., Nucl. Instrum. Methods B 269, 2623 (2011)

• monoenergetic slow positrons, T+ = 35 keV

CDB spectra – monoenergetic slow positrons

• thick Fe target (thickness 0.5 mm)

45 45

Detector 2 Detector 1

Ø 57.7Ø 69.2

60.837.4

e+

geometry of experiment

1 2




CDB spectrum:

sum of energies of

annihilation gamma rays 2

021 2 cmEE

21 EE

plotted versus

difference of these energies





Compton scattering of

one annihilation -ray

2 1





Random summation

in one detector

2 1

3





2’

Back-scattering of

one annihilation -ray



• thick Fe target (thickness 0.5 mm) Detector 2 Detector 1

40K (1459 keV)

scattering of 40K -ray

from background





TQAF

2 1

CDB spectra – monoenergetic slow positronsTQAF

e

e12

p

2

021

cos111

cmEE

conservation of

energy & momentum




e

e12

p

2

021

cos111

cmEE

conservation of

energy & momentum

cos1

cos2

cos1

22

2

0

22

02

21

2

021

cmcmEEcmEE


cos1

cos2

cos1

22

2

0

22

02

21

2

021

cmcmEEcmEE

TQAF

e

e

1

2

maximum energy difference

for anti-collinear -rayso180

for T+ = 35 keV

keV192keV192 21 EE


e

e

1

2

maximum energy difference

2

0

22

0

2

21

2

021 2 cmcmEEcmEE

for anti-collinear -rayso180

for T+ = 35 keV

keV192keV192 21 EE




kinematical cut-off

T+ = 35 keV

TcmEE 2

021 2

TQAF

e

e12

p




• T+ = 70 keV

• thin Al target

• thickness 0.8 m

A. W. Hunt, M.H. Weber,

J.A. Golovchenko, K.G. Lynn,

Appl. Surf. Sci. 149, 282 (1999)



T+ = 35 keV T+ = 27 eV

• TQAF disappears for slow positrons benchmark test of slow positron beams


• vertical cut integrated in the range keV192keV192 21 EE

T+ = 35 keV T+ = 27 eV



E1 + E2 - 2m0c2 (keV)

-100 -50 0 50 100

counts

101

102

103

104

105

106

107

27 eV

35 keV

35 keV




E1 + E2 - 2m0c2 (keV)

-100 -50 0 50 100

counts

101

102

103

104

105

106

107

27 eV

35 keV

35 keV

dTTS

T

A

ZNTdP

TQAFA

• probability of e+ annihilation during

slowing down from T++ dT+ to T+

R.K. Barta e al., Nucl. Phys.A 156, 314 (1970)

19.1

4.2

21

aZa

dx

dTTS

• e+ stopping power

2

0

2

0

cm

cmT

keVcmg95.5 21

1

a

keVcmg928 21

2

a




E1 + E2 - 2m0c2 (keV)

-100 -50 0 50 100

counts

101

102

103

104

105

106

107

27 eV

35 keV

35 keV

E1 + E

2 - 2m

0c

2 (keV)

0 20 40 60 80 100

counts

0

20

40

60

80

100

120

140experiment

theory

• TQAF in thick targets carries information about e+ slowing down




keV352keV5 2

021 cmEE

T+ = 35 keV T+ = 27 eV

• horizontal cut integrated in the range



E1 - E2 (keV)

-400 -200 0 200 400

counts

0

20

40

60

80

100

120

140 27 eV

35 keV

-192 keV 192 keV

keV35

21

20

220

221 cmcmEE

TQAFA dTTS

T

A

ZNEEP

• probability of TQAF creating

-rays with energy difference E1 - E2

keV352keV5 2

021 cmEE• horizontal cut integrated in the range


• total probability of TQAF in Fe

for positrons with energy of 35 keV

4109.7 TQAFP


E1 - E2 (keV)

-400 -200 0 200 400

counts

0

20

40

60

80

100

120

140 27 eV

35 keV

-192 keV 192 keV

keV352keV5 2

021 cmEE• horizontal cut integrated in the range


4109.7 TQAFP

J. Dryzek et al., Proc. PSPA-33, 33 (2001)



T+ = 35 keV T+ = 27 eV



T+ = 35 keV T+ = 27 eV

• 3- o-Ps annihilations on the surface


1

2

32

0321 2 cmEEE



• 3- o-Ps annihilations on the surface


1

2

32

0321 2 cmEEE

E (keV)

0 10 20 30

F

0.0

0.2

0.4

0.6

0.8

1.0

F parameter

E (keV)

0 10 20 30

S

0.50

0.52

0.54

0.56

0.58

0.60

0.62

S parameter

CDB spectra – fast positrons

• fast positrons, continuous energy spectrum

68Ge/68Ga, Mg target, T+ 1897 keV GiPS, W target, T+ 16 MeV

Detector 1

12

Detector 2




Detector 1

12

oo 180,177

Detector 2

• larger distance for detectors from the target

• limited range of angles



Detector 2

Detector 1

12

oo 180,177


2

0

22

0

2

21

2

021 2 cmcmEEcmEE

Detector 2




Detector 1

12

Detector 2

• higher kinematic cut-off

• GiPS: higher background due to scattering of bremsstrahlung radiation


Detector 1

12

Detector 2

inner

outer


Detector 1

12

Detector 2

• ‘inner edge’ finite size of detectors

inner


Detector 1

12

o180Detector 2

• ‘inner edge’ finite size of detectors (instrumental effect)

• ‘outer edge’ maximum Doppler shift (physical effect)

outer

• annihilation in the rest: predominantly by low momentum valence e-

• annihilation-in-flight: by all e- with equal probability

larger Doppler broadening

A.W. Hunt et al., Phys. Rev. Lett. 86, 5612 (2001)

spectroscopy of core e-


Detector 1

12

o180Detector 2

• ‘inner edge’ finite size of detectors (instrumental effect)

• ‘outer edge’ maximum Doppler shift (physical effect)

• Doppler broadening of the outer edge:

- accumulated vertical stripes shifted along the TQAF curve


• thick Mg target (thickness 10 mm)

• Doppler broadening of outer edge caused by annihilations with core e-

TQAF (T+ > 10 keV) annihilation in the rest

• fast positron from 68Ge/68Ga source

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment






E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

theory

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment

theory

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment

• Mg: 1s2 2s2 2p6 3s2

core e-






E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

theory

1s

2s

2p

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment

theory

1s

2s

2p

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

theory

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment

theory

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment

• Mg: 1s2 2s2 2p6 3s2

core e-






E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

experiment

theory

1s

2s

2p

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

0.00

0.05

0.10

0.15

0.20

0.25

experiment

theory

1s

2s

2p

• Mg: 1s2 2s2 2p6 3s2

core e-



E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

10-6

10-5

10-4

10-3

10-2

10-1

100

experiment

theory

1s

2s

2p

E1 - E

2 (keV)

0 5 10 15 20

norm

aliz

ed u

nits

10-6

10-5

10-4

10-3

10-2

10-1

100

experiment

theory

1s

2s

2p




• Mg: 1s2 2s2 2p6 3s2

core e-

Conclusions

• A novel digital CDB spectrometer enables low background measurement of TQAF

Acknowledgements

This work was supported by The Czech Science Foundation (project P108/13/09436S).

Availability of beam time at the ELBE, HZDR is gratefully acknowledged.

• Shape of TQAF contribution agrees well with theoretical prediction by QED

• TQAF was investigated using positrons from various sources

- monoenergetic positrons created in slow positron beam

- fast positrons created by b+ decay (68Ge/68Ga source)

- fast positrons created by pair production from bremsstrahlung (GiPS source)

• TQAF profile provides information about positron slowing down

• CDB study of broadening of TQAF profile: a spectroscopy of core electrons

• a signature of o-Ps 3- annihilation observed in CDB spectra of slow e+

positron annihilation in flight: experiment with slow and...

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