Positronium induced collisions

Nuclear Instruments and Methods in Physics Research B 221 (2004) 60–68

www.elsevier.com/locate/nimb

Positronium induced collisions

G. Laricchia *, S. Armitage, D.E. Leslie

Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

Abstract

Progress in the production of a monoenergetic Ps beam and in the experimental investigation of its interactions with

simple atoms and molecules is reviewed. The current status on measurements of total and positronium fragmentation

cross-sections, as well as their comparison with theories, is summarised.

� 2004 Elsevier B.V. All rights reserved.

PACS: 34.00; 34.80; 36.00; 36.90

Keywords: Positron; Positronium beams; Differential positronium formation cross-section; Positronium total cross-section;

Positronium fragmentation

1. Introduction

Positronium (Ps) is the bound state of an elec-

tron (e�) and its antiparticle, the positron (eþ).Since the centres of charge and mass coincide in

Ps, its static interaction with an atom is zero and,

since it is itself neutral, there is no first order

polarization. As a result, theorists have empha-

sized the importance of treating the exchange

interaction fully since it plays a comparatively

larger role in Ps-atom collisions than in the case of

electrons (e.g. [1] and references therein). Theearliest experimental information on Ps scattering

was extracted from measurements of its lifetime

in a host gas (e.g. [2]). In high density/low tem-

perature gases, Ps was found to annihilate from a

region of lower-than-average density (i.e. a ‘‘bub-

ble’’) due to exchange repulsion with the gas

* Corresponding author. Tel.: +44-207-679-3470; fax: +44-

207-679-2564.

E-mail address: [email protected] (G. Laricchia).

0168-583X/$ - see front matter � 2004 Elsevier B.V. All rights reser

doi:10.1016/j.nimb.2004.03.032

electrons. From the depth of the potential ascribed

to the ‘‘bubble’’, zero-energy elastic-scattering

cross-sections, relð0Þ, were extracted (e.g. [3,4]).

Additionally, momentum-transfer cross-sections(rm) may be evaluated using methods such as

angular correlation (ACAR) (e.g. [5]) or time-re-

solved Doppler broadening (TR-DB) (e.g. [6]) of

the annihilation radiation. These methodologies

restrict measurements to low energies. More con-

trolled investigations have been enabled by the

production of Ps beams (e.g. [7,8]). The efficiency

for the production of collimated Ps, a quantityrelated to the differential Ps formation cross-sec-

tion (drPs=dX), has been investigated for H2, He

and Ar [9] and more recently for N2 [10] and Xe

[11]. By means of an attenuation method, total

cross-sections (rT) for Ps scattering from simple

atoms and molecules (i.e. He, Ar, H2 and O2) have

also been measured [9,12–14].

It was pointed out long ago [15] that, due to thelight mass of Ps, recoil should be significant in its

scattering from atomic and molecular targets, as is

ved.

mail to: [email protected]

G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 61

the case for e� and eþ. Indeed, such manifestations

have been discerned from striking differences in the

ionisation cross-sections by the lighter eþ and e� in

comparison to protons and antiprotons (e.g. [16–18]). Recently, the clearest experimental evidence

for recoil effects in Ps scattering has been gained

from measurements of the longitudinal energy

distribution of the remnant positrons arising from

Ps fragmentation in collisions with He [19]. In the

present paper, we review some of these develop-

ments.

2. Experimental arrangement

Fig. 1 shows a schematic diagram of the Ps

beamline at UCL. A radioisotope of sodium

(22Na) provides the source of bþ particles, which

are moderated by a solid argon film [20] and

accelerated to the required beam energy. The sloweþ are then guided by a magnetic field produced by

11 Helmholtz coils. A Wien filter is used to sepa-

rate the slow eþ beam from the flux of fast parti-

cles emanating from the source. Ps is generated in

the ‘‘production cell’’ via charge-exchange [9,10].

A retarding arrangement after the production cell

serves to remove transmitted eþ from the beam.

The second cell contains the gas under investiga-tion by Ps impact. Two detection methods are

currently used. A time-of-flight (ToF) method,

incorporating a remoderation stage, involves two

electron-multiplier-arrays (CEMA1 and CEMA2)

[21]. The second detection method utilizes a gam-

ma-ray detector (NaI or CsI) in coincidence with

CEMA2 [9,14]. When this latter system is em-

Axial Magnetic Field

Na

Incident

PrimaryPositrons

PrimaryPositrons

Wien Filter

RGS Moderator

Pro

22

Na

Fig. 1. Schematic diagram of th

ployed, CEMA1 is removed from the beamline

and the full intensity eþ beam used. In both cases,

the detector signals are recorded using two multi-

channel scalars and the coincidences using a multi-channel analyser.

3. Ps beam production

Providing there are no other inelastic processes

simultaneous with Ps formation, the kinetic energy

of the Ps beam (EPs) is tuneable via that of the eþ

(Eþ) through

EPs ¼ Eþ � I þ 6:8 eV=n2; ð1Þ

where 6.8 eV/n2 gives the Ps binding energy in a

state of principal quantum number n and I is the

ionization potential of the production gas. Mea-

surements with the ToF system enable the energy

and dominant quantum state of the Ps atoms to be

monitored [13,22].

The Ps beam production efficiency, ePs, is de-fined as the number of Ps atoms produced per

incident eþ per steradian in accordance with

ePs ¼NPs

XNþD; ð2Þ

where NPs and Nþ are the number of Ps atoms and

incident eþ respectively, D corrects for the in-flight

decay of Ps and X takes into account the detection

solid angle. Studies into the Ps beam production

efficiency have found, as shown in Fig. 2, molec-

ular hydrogen to be the best converter at lowenergies [9] whilst N2 is better above 90 eV and

useable up to 250 eV [10]. Recently, investigations

Gas In

duction Cell

RetardingArrangement Gas In

Scattering Cell

o-Ps

CEMA2

RetardingArrangement

NaI-Photomultiplier

e Ps beam at UCL [9–14].

EPs=41.5eV

0 2 4 6 8 10 12 14 16

0.0

0.1

0.2

0.3

0.4

0.5

0.6

EPs=30eV

0 2 4 6 8 10 12 14 16 18

Ps

Pro

duct

ion

Eff

icie

ncy

(Ps

e+-1

sr-1

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

EPs=120eV

0 2 4 6 8 10 12 14 16

0.00

0.02

0.04

0.06

0.08

EPs=90eV

0 2 4 6 8 10 12 14 16

0.00

0.02

0.04

0.06

0.08

0.10

0.12

EPs=65eV

0 2 4 6 8 10 12 14 16 18

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

EPs=250eV

0 5 10 15 20 25

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

Gas Pressure (µmHg) Gas Pressure (µmHg)Gas Pressure (µmHg)

Fig. 2. Beam production efficiencies of Ps at the energies shown on each plot: H2 (circles) and N2 (triangles) [10]. Lines: H2 (light grey

dashed), He (dark grey dashed), Ar (dash-dot) [9].

62 G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68

have been extended to Xe [11] following an anal-

ysis that implied that the fraction of Ps in excited

states formed in eþ-Xe collisions might be as high

as 50–100% above �35 eV [23]. In contrast to these

expectations, as can be seen in Fig. 3, both the

position of the peak and the consistency of the Ps

energy distributions with target pressure indicate

Ps Energy (eV)

10 20 30 40 50

coun

ts p

er s

ec p

ere+

-0.001

0.000

0.001

0.002

0.003

(n=1)

Fig. 3. Comparison of the energy distribution of 30 eV Ps

formed from Xe and H2: (full circles) H2; (grey circles) Xe at 5

lmHg and (hollow circles) Xe at 2 lmHg [11].

that the main beam component arises from

ground-state Ps. However, the collimated-Ps yields

for Xe, as shown in Fig. 4, appear surprisingly low

given its relatively large integrated Ps formation

cross-section. This might arise from a broad

drPsðn ¼ 1Þ=dX [24] (possibly due to its large static

interaction or to the non-zero angular momentumof the captured e�), or from some quenching

mechanism by the production gas itself (e.g. [25]

and references therein), or indeed Ps might be

formed dominantly in a state n > 1 but very little

of it is detected near 0� due to an even broader

drPsðn > 1Þ=dX and/or higher rT for excited

states.

4. Differential Ps formation cross-sections

The Ps beam production efficiency [9] can be

expressed as

ePs / f1� expð�qlþrTþÞg1

rTþ

Z h0

0

drPs

dXsin hdh

( )

� expð�qlPsrTPsÞ; ð3Þ

Pspe

rpo

sitr

onpe

rst

erad

ian

per

µ mH

g*

(ε+/ε

Ps )

0.0

0.2

0.4

0.6

Ps Energy (eV)

0 20 40 60 80 100 120 140

0.0

0.2

0.4

0.6

0.0

0.1

0.2

0.3

0.4

0.5

He Ar

Xe

Ps Energy (eV)

0 20 40 60 80 100 120 140

0.0

0.2

0.4

0.6

0.8

H2, N2

Fig. 5. Comparison of the energy dependence of ePs per unit pressure with those of theoretical differential Ps formation cross-sections

at 0�. In all cases, the absolute magnitude of the theoretical data (in a20) may be regained by dividing by 0.019. He: experimental data

[9]; dot-dash line [26]; dotted line [27], Ar: experimental data [9]; solid line [24], H2: experimental data (black squares) [9], (hollow

circles) [10]; theory [28], N2: experimental data (hollow triangles) [10], Xe: solid circles [11]; theory [24].

EPs=30eV

Gas Pressure (µmHg)

0 2 4 6 8 10 12 14 16 18 20Psat

oms

per

inci

dent

posi

tron

per

ster

adia

n(1

0-3Ps

e+-1

sr-1

)

0

20

40

60

80

100

120

EPs=50eV

Gas Pressure (µmHg)

0 2 4 6 8 10 12 14 16 180

20

40

60

80

100

Fig. 4. Variation of the beam production efficiency with gas pressure at the Ps energies shown on the plots: Xe (circles) [11]; H2 (light

grey dashed line); He (dark grey dashed line) and Ar (black dash-dot) [9].


where the first term corresponds to the fraction of

scattered eþ, the second to the probability of

forming Ps within the angular range 0–h0 and the

third to the transmission probability of Ps througha gas of number density q and length lPs. At low

pressures, if Ps scattering may be assumed to be

negligible, ePs is then directly proportional to

drPs=dX. In Fig. 5, a comparison is made between

the energy dependence of available theoretical

data for drPs=dX at 0� and that of the experi-

mental ePs per unit pressure and corrected for the

ratio of the energy-dependent detection-efficiencies

of positrons and positronium [29].

5. Total cross-sections

Under the assumption that at low pressures the

third term in Eq. (3) may be neglected, an indirect

determination of the Ps total cross-section can be

Energy (eV)

0 50 100 150 200 250 300

Cro

ssSe

ctio

n(1

0-20 m

2 )

0

5

10

15

20

25

30

35

Energy (eV)0 10 20 30 40 50 60

0

10

20

30

40

50

60

N2 Xe

Fig. 6. Indirect estimates of Ps total cross-sections for: N2 (hollow circles) [10], (full circles) [6]; Xe (hollow circles) [11], (full circle) [30],

(line) [31].


made by extrapolating the low pressure values of

ePs [22]. The results are shown in Fig. 6 along with

other available data. The N2 data show an average

value of �21 · 10�20 m2 up to an energy of �60 eV

and then a decrease to a value of �3 · 10�20 m2 at

250 eV. The data point of Skalsey et al. [6] is forthe momentum-transfer cross-section. The values

determined for Xe at 30 and 50 eV are constant

within errors. The zero-energy theoretical value of

[30] is considerably smaller than the corresponding

result of [31] which indicates a rapid decrease with

increasing energy.

In the case of H2, Ar and He, the total cross-

section measurements performed with the Ps beam[9,12,14] are compared in Fig. 7 with recent cal-

culations and indirect experimental estimates [3–

6,32–46]. The beam data have been determined by

measuring the attenuation of the Ps flux through a

target of known areal density using the Beer–

Lambert law

rT ¼ kTpL

lnI0I

� �; ð4Þ

where I0ðIÞ is the net incident (transmitted) flux, kis the Boltzmann constant, p the target pressure

and T is its temperature. The effective cell length,

L, is determined for each target gas by measuring

corresponding positron total cross-sections and

normalising them to known values [47]. The three

sets of beam measurements shown correspond to

various detector angular acceptances as given in

the figure caption, h ¼ 0� being the extrapolated

value as discussed in Section 6 below.

In the case of H2, the results of a coupled

channel model [44], with and without excitation of

the first two higher states of the target, are lower

and peak earlier than the beam data. At lowenergies, there is a considerable discrepancy be-

tween the two rm values [6,45].

In the case of Ar, the results of coupled-

pseudostate (no exchange) approach of McAlin-

den et al. [38] converges with the beam data at the

highest energies. At intermediate energies, the

more recent data of Blackwood et al. [31], which

treat exchange fully, display a small broad peak atan energy close to that in the experimental results,

albeit of a magnitude �60% lower. The rm values

of [6,32] are much lower than the theoretical rel of

[31] but agree with that of [46]. However, Black-

wood et al. [1] have found drel=dX to become

anisotropic (thus inferring a divergence of rm from

rel) within the first few eV above zero. This finding

is qualitatively consistent with the considerableforward-scattering effects observed with the Ps

beam as discussed in the next section.

In the case of He, the elaborate theory [34]

undercuts the beam data above �20 eV, however

the inclusion of target excitation in a close cou-

pling calculation [37] reduces this discrepancy. At

low energies, significant disagreement remains

among theories and among experiments, althougha degree of convergence is beginning to emerge. It

0 10 20 30 40 50 60 70 80 90 100 110 120

Tota

l-C

ross

-Sec

tion

(10-2

0m

2

0

5

10

15

20

25

30

Ps Energy (eV)0 10 20 30 40 50 60 70 80 90 100 110 120

Tota

l-C

ross

-Sec

tion

(10-2

0m

2 )

0

2

4

6

8

10

12

14

16

18

20

Ps Energy (eV)

0 10 20 30 40 50 60 70 80 90 100 110 120

Tota

l-cr

oss-

sect

ion

(10-2

0m

2 )

0

2

4

6

8

10

12

14

ArH2

He

Ps Energy (eV)

)

Fig. 7. Total Ps cross-sections. H2. Experiment: (hollow circles) h � 0�, Garner et al. [14]; (full circles) h � 1:5�, Garner

et al. [9]; (full triangle) hm, Skalsey et al. [6]; (hollow triangle) rm, Nagashima et al. [45]. Theory: (full line) Biswas and

Adhikari [44]; (dashed line) Biswas and Adhikari [44]. Ar. Experiment: (hollow circles) h � 0�, Garner et al. [14]; (full circles)

h � 1:5�, Garner et al. [9]; (full squares) h � 6�, Zafar et al. [12]. rm: (hollow triangle) Skalsey et al. [6]; (full triangle) Coleman

et al. [32]. Theory: (solid line) Blackwood et al. [31]; (dashed line) Biswas and Adhikari [46]; (dash-dot line) McAlinden et al.

[38]. He. Experiment: (hollow circles) h � 0�, Garner et al. [14]; (full circles) h � 1:5�, Garner et al. [9]. rel(0): (hollow trian-

gle) Canter et al. [3]; (full upside-down triangle) Ryts€ol€a et al. [4]. rm: (full square) Skalsey et al. [6]; (hollow square) Nagashima

et al. [5]; (full triangle) Coleman et al. [32]. Theory: (full hexagon) Chiesa et al. [41]; (full diamond) Ivanov et al. [33]; (hollow

diamond) Drachman and Houston [40]; (hollow upside-down triangle) Adhikari [42]; (full line) Blackwood et al. [34]; (long-

dashed line) Biswas and Adhikari [35]; (short-dashed line) Basu et al. [37]; (dash-dot line) Sarker et al. [36]; (dotted line) Mc-

Alinden et al. [38].


is hoped that measurements currently in progress

with the Ps beam will help in resolving some of the

current uncertainties.

6. Ps differential elastic cross-sections

It was observed by Garner et al. [14] that themeasured total cross-section, ðrTÞm, increased for

decreasing detection solid angle due to forward

scattering according to

ðrTÞm ¼ rT �drdX

� �DX; ð5Þ

where rT is the ‘true’ total cross-section, hdr=dXiis an average differential scattering cross-section

and DX is the detection solid angle. By performing

measurements in the angular range (±1.5� to

±6.4�), Garner et al. estimated, at each incident

energy, values for hdr=dXi which averaged over

the range 15–100 eV yielded (34± 12) · 10�20

m2 sr�1 for He, (46± 11) · 10�20 m2 sr�1 for H2 and


(114± 11) · 10�20 m2 sr�1 for Ar. The latter value is

approximately a factor of ten higher that calcu-

lated by Blackwood et al. [1] at 5 eV.

7. Integrated cross-section for Ps fragmentation

The absolute cross-section for the fragmenta-

tion of Ps in collision with He, rf , has been

determined by detecting the remnant positrons [19]

and is given by

rfðEÞ ¼Nþ

ðNPsÞscattrTðEÞSG

ePs

eþ

� �; ð6Þ

where Nþ is the number of residual eþ; ðNPsÞscatt isthe number of scattered Ps atoms, rTðEÞ is the

corresponding total-cross-section, S and G are

corrections respectively for in-flight annihilation of

Ps and the ratio of the solid angles for detection

of the residual positrons and Ps. The numbers of

residual positrons and Ps atoms were corrected for

the ratio (eþ=ePs) of their respective detection effi-

ciencies measured explicitly in a separate study[29]. The results for rf in Ps–He collisions are

shown in Fig. 8, where they are compared with

available theories. The three experimental deter-

minations shown in the figure arise from the sys-

tematic uncertainty in the determination of the

positron- and Ps-detection efficiencies [29]. It can

Ps incident energy (eV)

0 5 10 15 20 25 30 35 40

frag

men

tatio

ncr

oss-

sect

ion

(10-2

0m

2 )

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Fig. 8. Absolute cross-section for the fragmentation of Ps in

collision with He: (symbols) Armitage et al. [19]; (solid line)

Blackwood et al. [34]; (long-dashed line) Biswas and Adhikari

[35], (short-dashed line) Ray [48].

be noted that the theoretical determination of

Biswas and Adhikari [35] overestimates the

measurements by approximately a factor of two. Agood agreement is found between the experiment

and the theory of Blackwood et al. [34] whilst the

Coulomb–Born approximation (no exchange) of

Ray [48] underestimates the measurements by

approximately 40%.

8. Longitudinal energy distributions of residualpositrons

Since the fragmentation study has been under-

taken using the time-of-flight detection system, the

energy distributions of the residual positrons have

been determined at the same time. Fig. 9 shows the

results corresponding to the four incident Ps

energies investigated. A peak just below 50% ofthe residual energy (Er ¼ EPs � 6:8 eV) becomes

increasingly apparent in the spectra with increas-

ing Ps incident energy. This structure implies that

the light final state particles travel in the forward

direction with a similar velocity, signalling the

occurrence of electron loss to the continuum [49].

As the positrons released through Ps fragmenta-

tion are confined by the axial magnetic field, theenergy shift of the peak from Er=2 suggests that

the residual positrons are emitted within a small

angle (6 20� at the higher energies) with respect to

the beam axis. Recently, the shape of the energy

distributions has been reproduced using a classi-

cal-trajectory-Monte Carlo simulation [50]. Here

an asymmetry has been found between the energy

spreads for the two residual particles. This pre-diction awaits experimental investigation.

9. Outlook

Measurements of the total cross-section for Ps

in collision with N2 and Xe are currently underway

in order to shed further light on their efficiencyfor collimated Ps production. Following the Ps

detection efficiency study [29], new low energy

(<10 eV) Ps–He total cross-sections are also in

progress. Measurements of the residual e� energy

distributions are also planned. It is hoped that

Energy (eV)

0 5 10 15 20 25

Arb

. Uni

ts.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Energy (eV)

0 5 10 15 20 25 30

Arb

. Uni

ts.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Energy (eV)0 2 4 6 8 10 12 14

Arb

. Uni

ts.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Energy (eV)0 5 10 15 20

Arb

. Uni

ts.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Er/2Er/2

Er/2 Er /2

E=25eV E=33eV

E=18eVE=13eV

Fig. 9. Longitudinal-energy-distributions of residual positron from Ps break-up. The incident Ps energy is shown on each plot. The

arrows indicate position of half of the residual energy [19].


through these measurements, target ionisation

may be distinguished by a comparison with those

for the residual positrons.

Acknowledgements

The Engineering and Physical Sciences Re-

search Council is gratefully acknowledged for

supporting this work under grant no. GR/S16041/

01 and for providing D.E. Leslie with a student-ship.

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Positronium induced collisions