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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: g.laricchia@ucl.ac.uk (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.
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].
G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 63
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].
64 G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68
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].
G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 65
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
66 G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68
(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].
G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 67
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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