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Radiation Physics and Chemistry 68 (2003) 21–31
Positron and positronium interactions with atomsand molecules
G. Laricchia*, S. Armitage, D.E. Leslie, M. Sz"ui !nska, P. Van Reeth
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
Abstract
Recent advances in the field of positron-induced ionization and positronium collisions are reviewed. Major
outstanding problems are highlighted.
r 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Positron; Positronium; Annihilation; Positron impact excitation; Positron impact ionization; Positronium formation;
Positronium total cross-sections; Positronium fragmentation
1. Introduction
One hundred years since the birth of Dirac and 70
years since his prediction of antimatter, positrons and
positronium (Ps, the bound state of an electron and its
antimatter counterpart, the positron) are widely em-
ployed, e.g. from the exploration of fundamental
phenomena in atomic (e.g. Andersen et al., 1998, 2000,
2002) and condensed matter physics (e.g. Schultz and
Lynn, 1988) to the diagnostics of electronic and
structural properties of materials (e.g. Triftsh.auser
et al., 2001) and of living biological systems (e.g.
Sharma and Piwnica-Worms, 2002). Among the first
experiments to be carried out in atomic physics with
monoenergetic positron beams were measurements of
total cross-sections from room temperature gases.
Increasing intensities of positron beams, achieved with
better sources and especially better moderators, have
permitted the study of dilute targets (e.g. H and the
alkali atoms) which allow more stringent comparisons
with theory. Investigations now encompass measure-
ments of partial and differential cross-sections, near-
threshold behaviour and molecular excitations, the latter
(e.g. Sullivan et al., 2001, 2002) performed with a beam
possessing room-temperature energy resolution (Gilbert
et al., 1997). In this brief overview, we shall concentrate
on positron-induced ionization processes and positro-
nium collisions. The interested reader is referred to
e.g. Laricchia (2002), Charlton and Humberston (2001),
and Andersen et al. (1998, 2000, 2002) for further
information.
2. Positron collisions
2.1. Ps formation
Due to the partial cancellation at low energies of the
static and polarization interactions in positron–atom/
molecule scattering, a pronounced minimum arises in
the total cross-sections (Qt) of many gaseous targets just
below the threshold for positronium formation, EPs: Amarked increase of Qt is thus evident in most cases near
EPs; as a result of the importance of this channel. Thereaction may be represented by e++A-Ps+A+ with
threshold EPs ¼ Ei2B; where Ei is the target ionization
energy and B the Ps binding energy (6.8 eV/n2), n being
the principal quantum number.
The Ps formation cross-sections, QPs; integrated overall quantum states of Ps and the ion, have been
measured for all the inert atoms (Moxom et al., 1993,
1994; Overton et al., 1993), some molecules (Moxom
et al., 1993; Laricchia andMoxom, 1993; Laricchia et al.,
1993), atomic hydrogen (Zhou et al., 1997 and references
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*Corresponding author. Tel.: +44-20-7679-7809; fax: +44-
20-7679-2564.
E-mail address: [email protected] (G. Laricchia).
0969-806X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0969-806X(03)00248-2
therein), alkali atoms (Zhou et al., 1994; Surdutovich
et al., 1996, 2002) and Mg (Stein et al., 1996, 1998).
Good convergence exists among recent theories and
the experimental QPs in the case of atomic hydrogen
(Zhou et al., 1997). For He, good agreement between
experiment (Overton et al., 1993) and theory (Campbell
et al., 1998) exists at the intermediate energy range,
however discrepancies still remain both near threshold
(Van Reeth and Humberston, 1999) and at high energies
(Campbell et al., 1998). In the case of He, the coupled-
pseudostate calculation of Campbell et al. (1998)
suggests that the ground state Ps formation dominates
the cross-section, with only B20% of Ps formed in the
excited state. In the case of the alkali atoms, Ps
formation is an exothermic process, so it is expected
that QPs-N as E-0: Calculations of Walters et al.(1995) have predicted a collapse of ground-state Ps
formation in going from Li to Cs with a simultaneous
increase in the excited state Ps formation. This predic-
tion awaits experimental confirmation. As shown in
Fig. 1, the recent measurements for Li (Surdutovich
et al., 2002) agree reasonably well with the calculation of
McAlinden et al. (1997), however those obtained for Na
(Surdutovich et al., 2002) remain significantly higher
than the theoretical ones (Campbell et al., 1998) below
B2 eV.
In Fig. 2, the various QPs for the heavier noble gases
are shown. Among them, the recent QPs extracted from
total ionization cross-sections (Laricchia et al., 2002)
and direct ionization cross-sections (Moxom et al., 1996;
Kara et al., 1997) are also included. There are many
discrepancies among all available data, however the
agreement of the data of Laricchia et al. with the results
of Jin et al. (1994) for Ne and Ar, which were measured
and normalized with different methods, is encouraging.
The very recent measurements for Ar by Sullivan et al.
(2002), performed with the room-temperature energy
resolution beam, also agree very well both on the energy
dependence and the magnitude of the first peak.
As shown in Fig. 2, QPs of Laricchia et al. (2002)
develop a double-peak structure for Ar, Kr and Xe. The
first peaks, approximately at twice EPsðn ¼ 1Þ; have beenattributed to the Ps formation in the ground state,
whereas the second peaks, located at approximately
twice EPsðn ¼ 2Þ; might be a manifestation of Ps
formation in excited states. Theoretical and direct
experimental investigations of this hypothesis are
awaited. The theory of McAlinden and Walters (1992),
depicted in the figure, includes Ps formation in the
ground state only.
2.2. Scaling formula for ionization
An empirical scaling formula has recently been found
by Sz"ui !nska et al. (2002) which factors out the targetdependence of the shape and magnitude of positron-and
electron-impact cross-sections. Cross-sections for Ps
formation or direct single ionization fall broadly on a
common curve, QxðE=EthÞ; when scaled in terms of theircorresponding threshold energy ðEthÞ; i.e. QA
x ðE=EAthÞ=
ðQAx Þmax ¼ QB
x ðE=EBthÞ=ðQ
Bx Þmax; where x refers to a
particular process for a given projectile and A, B refer
to any two atoms. E is the incident projectile energy and
ðQAx Þmax the maximum value of QA
x : This parametriza-tion of ionization cross-sections depends on two
parameters Eth and ðQxÞmax but it may be further
reduced to depend only on one parameter, since ðQxÞmax(for atoms belonging to the same column of the periodic
table) is found to correlate well with Eth: This, as shownin Fig. 3, could be approximated by ðQxÞmax ¼a expð�bEthÞ; where a; b are constants which are the
same for atoms belonging to the given column of the
periodic table. From the above, a simple scaling formula
was obtained, QAx ðE=EA
thÞ ¼ QxðE=EthÞexp½�bðEBth �
ECth�; which can be used to estimate a cross-section for
any atom (A) if the ðQxÞmax values for any two atoms,belonging to the same column, are available for the
determination of b: Further analysis of data is in
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Fig. 1. Positronium formation cross-sections for positron–Li and positron–Na scattering (Surdutovich et al., 2002).
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–3122
progress for these and other combinations of projectiles
and targets with an investigation of possible mechanisms
underlying these factorisations. (Note also the recent
progress in semi-empirical models for electron-projectile
ionization (e.g. Kim et al., 1998; Deutsch et al., 1997).
2.3. Direct ionization
Using different techniques, several measurements of
the single direct ionization cross-sections by positron-
impact have been made for various targets, including H
(Jones et al., 1993) and reasonable agreement on both
the magnitude and energy dependence has been found.
The energy loss experiments (e.g. Mori and Sueoka,
1994) do not extend to very high energies and the cross-
sections were normalized using the values of the total
scattering cross-section obtained in other experiments.
The coincidence method, relying on detecting correlated
ions and scattered positrons (Knudsen et al., 1990;
Jacobsen et al., 1995; Moxom et al., 1996; Kara et al.,
1997), can be extended to higher energies, typically
1000 eV, where normalization is performed to known
electron impact ionization data. This normalization
procedure is based on the fact that at sufficiently high
energy the first Born approximation predicts that each
individual ionization cross-section for positron-impact
and for electron-impact should merge. A recent inves-
tigation (Van Reeth et al., 2002) has shown that a source
of uncertainties in the magnitude of the positron data
was due to differences between the various electron-
impact ionization cross-sections for a given atom.
In Fig. 4, the renormalized experimental data from
Moxom et al. (1996) and Kara et al. (1997) for the other
noble gases are presented together with the results of
Jacobsen et al. (1995) and Mori and Sueoka (1994).
Once again, the agreement in the case of Ne and Ar
between the data of Mori and Sueoka and Kara et al.
normalized by two very different methods is encoura-
ging. Also shown in Fig. 4 are the theoretical results of
Moores (1998) which are found to peak at an energy
close to the peak in the experimental results but are up
to 60% larger. Those of Campeanu et al. (2001) are in
broad agreement for both shape and magnitude in the
common energy range, except in the case of Ne.
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10 1000.0
0.2
0.4
0.6
0.8
10 1000
2
4
6
810 100
0
1
2
3
4
5
10 1000
2
4
6
8
10
12
14
16
Pos
itron
ium
form
atio
n cr
oss-
sect
ion
(10-1
6 cm2 )
Incident energy (eV)
Ne Ar
Kr Xe
Fig. 2. Comparison of the experimental and theoretical QPs: solid curves—Laricchia et al. (2002); hollow diamonds—Charlton et al.
(1983); hollow circles—Jin et al. (1994); hollow squares—Diana et al. (1985, 1986, 1987, 1989); crosses—Fornari et al. (1983); down
hollow triangles—Stein et al. (1998) upper limit; up hollow triangles—Stein et al. (1998) lower limit; full diamonds—Sullivan et al.
(2002); dashed curves-theory of McAlinden and Walters (1992).
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–31 23
In the case of He and H2, high-resolution data exist
close to the ionization threshold (Ashley et al., 1996)
which reveal interesting differences with their electron-
impact counterpart. For these, the Wannier theory
predicts Qþi ðe
-ÞpE01:27 where E0 is the excess energy,
i.e. the difference between the incoming energy and the
threshold energy. In the case of positron-impact ioniza-
tion, there is no exchange between the projectile and the
ejected electron and positronium formation may com-
pete with the direct ionization channel. Consequently,
the same form for Qþi ðe
þÞ is predicted but with E02:65
(Klar, 1981). However, the energy dependence of
experimental Qþi ðe
þÞ (Ashley et al., 1996), was foundto be proportional to E01:9970:19 in the energy range
1–3 eV. A recent theory (Ihra et al., 1997) has found that
inclusion of anharmonic terms in the three-particle
potential around the Wannier configuration reproduces
the experimental data. An even more recent quantal-
semiclassical calculation of Deb and Crothers (2002),
which includes values of up to 11 for the total angular
momentum azimuthal quantum number, has also been
found to be in good agreement with the experimental
data over a wide energy range 3–10 eV. Very close to the
threshold, however, significant differences are found.
The comparison of the single ionization cross section
by e�, e+, p and p� impact reveals interesting trends as
can be seen in Fig. 5, where the single ionization cross-
sections for He by all four projectiles are plotted at equi-
velocity (note that an energy of 100 eV for the light
projectiles corresponds to approximately 0.2MeV/amu).
At the high velocity, all cross-sections are seen to merge
in accordance with the first Born approximation. At
medium velocity, close to the position of the respective
peak, the cross-sections for the heavier particles are seen
to be larger while, within each particle/antiparticle pairs,
those with the positive charge have the largest cross-
sections. This charge dependence is inverted at lower
energies, supposedly because of competition from the
electron capture channel in the case of positively charged
particles. For the heavier noble gases, similar trends are
observed but due to the increased static interaction,
trajectory effects for the light particles become more
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e+ e+
e-
e+
e-
e+
Eth
4 6 8 10 12 14 16 18 200.1
1
10
Eth
10 12 14 16 18 20 22 24 26
Max
imum
val
ue o
f Q
i
Max
imum
val
ue o
f Q
i
Max
imum
val
ue o
f Q
Ps
0.1
1
10
Eth
5 10 15 20 25 30
1
10
ArKr
Ne
Xe
Ne
KrXe
(c)
(a)
Noble GasesHalogenscolumn VIcolumn Vcolumn IV
(b)
Ar
HeHe
e+ e+
e-
Fig. 3. Maximum value of the cross-section plotted versus relevant threshold energy, Eth: (a) direct ionization of the inert gases by
positron impact; (b) Ps formation for the inert gases; (c) single ionization by electron impact for the inert gases, halogens and atoms
belonging to the IV, V and VI columns.
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–3124
important, leading to an earlier merging of the electron
and anti-proton cross-sections than that of the positron
and proton (Paludan et al., 1997 and references therein).
The first triple-differential measurements of positron-
impact ionization have recently become available for a
H2 target (K .ov!er and Laricchia, 1998; K .ov!er et al.,
2001). At 100 eV incident energy, a small broad peak has
been observed in the spectrum of electrons ejected at 0
in coincidence with positrons scattered into the same
direction, indicating the occurrence of electron-capture-
to-the-continuum, a phenomenon first predicted for
positron impact by Brauner and Briggs (1986). At 50 eV
impact energy, a shift of around 1.6 eV has been
observed in comparison with a theory (Fiol et al.,
2001). Since this calculation does not include the
molecular degrees of freedom of the target, it has been
conjectured that the shift might be an indication of
molecular excitation/dissociation (K .ov!er et al., 2001).
2.4. Annihilation
Very recently, measurements of the energy depen-
dence of the annihilation cross-section have been
reported for a number of molecules (Gilbert et al.,
2002). The data are shown in Fig. 6. In some cases,
peaks are observed at energies lower than the thresholds
for vibrational excitation. The energy downshifts of
these peaks have been interpreted as being consistent
with the presence of long-lived vibrational Feshbach
resonances (Gribakin, 2000). However, it remains
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100 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
10 100 10000
1
2
3
4
5
6
KrX Data
10 100 10000
1
2
3
4 Ar
10 100 10000
2
4
6
8
10
Xe
positron incident energy (eV)
cros
s-se
ctio
n (1
0-16 c
m2 )
Ne
Fig. 4. Comparison of the renormalized direct ionization cross-sections: full circles—Kara et al. (1997) and Moxom et al. (1996);
hollow circles—Jacobsen et al. (1995); hollow triangles—-Mori and Sueoka (1994); dashes curve—Moores (1998); solid curve—
Campeanu et al. (2001).
MeV/amu0.01 0.1 1
σ i+(1
0-16
cm2 )
0.0
0.2
0.4
0.6
0.8
Fig. 5. The direct ionization cross-section with equivelocity
projectiles on He (Knudsen and Reading, 1992): solid line—e+;
dashed line—e�; chain—p+; symbols—p�.
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–31 25
unclear whether the existence of such resonances is
necessary to explain the very large annihilation rates
from molecules with a high density of molecular and
electronic excitation thresholds. This is because an
increased annihilation probability near threshold en-
ergies might arise from the temporary ‘‘trapping’’ of the
e+ near the target-electron(s) for the duration of virtual
processes (Laricchia and Wikin, 1997; Van Reeth and
Humberston, 1998). Future investigations of the energy
dependence of the annihilation probability from simple
atomic targets should help in resolving current
controversies.
3. Ps collisions
3.1. Introduction and experimental arrangement
Theoretically, Ps-atom scattering is a difficult problem
to treat due to the fact that both the projectile and target
are composite objects with internal structure. Experi-
mentally, information on Ps collisions near thermal
energies have been obtained indirectly using methods
such as angular correlation of annihilation radiation
(ACAR) (Coleman et al., 1994; Nagashima et al., 1998)
and Doppler broadening (Skalsey et al., 1998). The first
measures the angular deviation from co-linearity of the
two annihilation quanta predominantly emitted in
positron annihilation, whereas the second uses the shift
in energy of the gammas due to the momentum of the
e+–e� pair. At higher energies, cross-sections have
been measured directly using a Ps beam, produced by
neutralizing a positron beam in a gaseous target via the
charge exchange reaction (e++A-Ps+A+) (Laricchia
et al., 1987). Due to the finite lifetime of Ps, the beam at
atomic velocities is composed of the longer lived o-Ps.
To a first approximation, the kinetic energy of the Ps
beam, TPs; is tuneable via, TPs ¼ Eþ2EPs; where Eþ is
the positron kinetic energy and EPs; the Ps formationthreshold energy.
Using a time-of-flight method, Zafar et al. (1991)
identified ground- and excited-state atoms in the Ps
beam formed from He and Ar. The same method has
been used to measure Ps total-and projectile-ionization
cross-sections. In the latter case, the longitudinal energy
distributions of the residual positrons have, very
recently, also been extracted, as discussed below.
3.2. Ps beam production
The Ps beam production efficiency depends on the
differential Ps formation cross-section, dsPs=dO; and thetotal cross-section, sT; for both e+ and Ps scattering
according to the equation:
ePsp f1� expð�rlþsTþÞg1
sTþ
Z y0
0
dsPsdO
sin y dy
( )
� expð�rlPssTPsÞ;
where the first term corresponds to the fraction of
scattered e+, the second to the probability of forming Ps
within the angular range 02y0 and the third to the
transmission probability of Ps through a gas of number
density r and length lPs: Garner et al. (1996) investigatedthe conversion of a positron- into a Ps-beam via charge
exchange in H2, He and Ar at Ps kinetic energy in the
range 30–120 eV at gas pressures up to 14mTorr.
Recently, Leslie et al. (2002) have found that the range
of Ps kinetic energy attainable can be extended at least
up to 250 eV by using N2 as the production gas. The
results of this study are shown in Fig. 7. Although H2
remains the better converter at lower energies, N2
becomes more efficient as the Ps energy is increased.
3.3. Ps total cross-section
Fig. 8 shows a plot of the Ps–He total cross-section,
the simplest target to be addressed both experimentally
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Fig. 6. Positron annihilation rate, Zeff ; for (a) butane; (b)propane; and (c) ethane; as a function of positron energy
(Gilbert et al., 2002).
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–3126
and theoretically with Ps projectiles. Shown in the plot
are the direct beam data of Garner et al. (1996, 2000),
estimates for the momentum transfer cross-sections
(Coleman et al., 1994; Nagashima et al., 1998; Skalsey
et al., 1998) and theoretical determinations by Black-
wood et al. (1999), Biswas and Adhikari (1999), Sarkar
and Ghosh (1997) and Basu et al. (2001b). Below 10 eV,
apparent discrepancies are found, however, Blackwood
et al. (2002) have pointed out that the comparison of the
momentum transfer cross-sections with the total cross-
sections calculations is not appropriate since, even at
very low energies, the differential cross-section may be
not isotropic. This finding is in qualitative agreement
with the earlier results of Garner et al. (2000) who found
significant forward scattering effects.
3.4. Ps–He projectile ionization cross-section
Among the processes that can occur in Ps–He
collisions, projectile ionization of Ps is thought to
dominate the scattering process at intermediate energies
(Biswas and Adhikari, 1999; Blackwood et al., 1999) and
to play an important role in the slowing down of
positrons in dense media (Laricchia and Jacobsen,
1986). Recently, this process has been observed (Armi-
tage et al., 2002) and its cross-section has been
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Fig. 7. Variation of the Ps production efficiency, ePs versus target gas pressure and Ps energy for H2 and N2.
Incident Ps energy (eV)
0 10 20 30 40 50 60 70 80 90 100 110 120
Cro
ss-s
ecti
on
(x10
-20 m
2 )
0
2
4
6
8
10
12
14Garner et al 1996Garner et al 2000Nagashima et al 1998Skalsey et al 1998Coleman et al 1994Biswas & Adhikari 1998Blackwood et al 1999Basu et al 2001
Fig. 8. Experimental and theoretical results for Ps–He total cross-sections. Those of Coleman et al., Skalsey et al. and Nagashima et al.
are for the momentum transfer cross-section.
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–31 27
measured. The results are shown in Fig. 9. The
uncertainty (+8/�(20–30)%) is associated with
the determination of the detection efficiency for posi-
trons and Ps (Armitage et al., 2003). As can be seen from
the figure, the present Ps–He projectile ionization cross-
section measurements are in good agreement with the
coupled-state theory of Blackwood et al. (1999). How-
ever, as shown in Fig. 8, a significant discrepancy exists
with this theory in the case of the total cross-section.
Blackwood et al. underestimate the beam total cross-
section measurements (Garner et al., 2000) above 10 eV
by up to 30%, suggesting either an underestimate of the
elastic cross-section and/or of target inelastic effects.
Estimates of the cross-sections for He excitation and
ionization from Ps impact have been made by Black-
wood et al. (1999) within the first Born approximation
and found to be negligible at these energies. Recent work
on Ps–H, He scattering (Basu et al., 2001a, b; Blackwood
et al., 2002) indeed points to the importance of including
(virtual and real) target inelastic channels in Ps scattering
theory. Further studies into target inelastic effects would
now seem to be urgently needed in order to progress with
the understanding of the Ps–He collision system.
Although the predicted total cross-sections of Biswas
and Adhikari (1999) are in much better agreement with
the beam measurements, the projectile ionization cross-
section overestimates the measurements made in this
study by roughly a factor of two.
The Ps–He projectile ionization study was undertaken
using a time-of-flight detection system, enabling a
measure of the longitudinal energy distributions of
the residual positrons from Ps ionization, as shown in
Fig. 10. The data have been summed into 1 eV bins and
normalised to unity for shape comparison. A peak is
apparent just below half of the residual energy
(Er ¼ TPs26:8 eV), which is suggestive of electron-loss-to-the-continuum (Ludlow and Walters, 2001).
4. Summary and outlook
Concerning positron collisions, the e+–H problem
appears reasonably well understood but problems arise
already with He and, among the alkali atoms, with Na.
Recent studies of Ps formation from the inert atoms
display a degree of convergence, however, structure is
observed which is not fully understood. It might arise
from excited state Ps formation and direct measure-
ments of this process would be valuable. A simple
empirical scaling formula for ionization cross-sections
has been found, the physical basis of which is unclear.
Further investigations with different types of projectiles
and ionization processes might aid future developments.
Differential ionization measurements are powerful
probes of collision dynamics, hence the unexplained
energy shift observed in the energy spectrum of the
ejected electrons from H2 should be examined further.
Measurements of the energy dependence of the annihila-
tion cross-section from simple atoms are needed to
further our understanding of such a fundamental
physical process.
Regarding collisions with Ps projectiles, direct QT
measurements at low E are needed to guide theory on
the importance of virtual target inelastic collisions. The
angular and energy distributions need to be separated in
Ps fragmentation measurements. Theoretical and experi-
mental studies of target inelastic processes (with and
without Ps fragmentation) should begin.
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Energy (eV)
0 5 10 15 20 25 30 35 40
Ps P
roje
ctile
Ion
izat
ion
Cro
ss-S
ectio
n (1
0-20 m
2 )
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Fig. 9. Ps projectile ionization cross-sections: solid line—Blackwood et al. (1999); dashed curve—Biswas and Adhikari (1999);
Armitage et al. (2002a): squares—upper limit; full circles—lowest limit; triangles—average.
G. Laricchia et al. / Radiation Physics and Chemistry 68 (2003) 21–3128
Acknowledgements
The authors thank the European Union (EPIC), The
Royal Society (ESEP) and EPSRC (GR/S16041/01) for
supporting positron research at UCL. GL also wishes to
thank the conference organizers for their invitation and
kind hospitality.
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Energy (eV)
0 5 10 15 20 25 30 35 40
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
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.
Energy (eV)
Arb
. Uni
ts.
Energy (eV)
Arb
. Uni
ts.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 2 4 6 8 10 12 14
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 5 10 15 20
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Er/2
Er/2
E=25eV
E=13eV E=18eV
Er/2Er/2
E=33eV
Fig. 10. Residual positron longitudinal energy distributions. Ps energy shown at the top of each graph.
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