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 electron (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 emphasized 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). The earliest experimental information on Ps scattering was extracted from measurements of its lifetime in a host gas (e.g. [2]). In high density/low temperature gases, Ps was found to annihilate from a region of lower-than-average density (i.e. a ‘‘bubble’’) due to exchange repulsion with the gas *

Corresponding author. Tel.: +44-207-679-3470; fax: +44207-679-2564. E-mail address: [email protected] (G. Laricchia).

electrons. From the depth of the potential ascribed to the ‘‘bubble’’, zero-energy elastic-scattering cross-sections, rel ð0Þ, 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-resolved Doppler broadening (TR-DB) (e.g. [6]) of the annihilation radiation. These methodologies restrict measurements to low energies. More controlled investigations have been enabled by the production of Ps beams (e.g. [7,8]). The efficiency for the production of collimated Ps, a quantity related to the differential Ps formation cross-section (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 the light mass of Ps, recoil should be significant in its scattering from atomic and molecular targets, as is

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2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.03.032

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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 developments.

ployed, CEMA1 is removed from the beamline and the full intensity eþ beam used. In both cases, the detector signals are recorded using two multichannel scalars and the coincidences using a multichannel analyser.

2. Experimental arrangement

EPs ¼ Eþ
I þ 6:8 eV=n2 ;

Fig. 1 shows a schematic diagram of the Ps beamline at UCL. A radioisotope of sodium (22 Na) provides the source of bþ particles, which are moderated by a solid argon film [20] and accelerated to the required beam energy. The slow eþ are then guided by a magnetic field produced by 11 Helmholtz coils. A Wien filter is used to separate the slow eþ beam from the flux of fast particles 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 investigation 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 gamma-ray detector (NaI or CsI) in coincidence with CEMA2 [9,14]. When this latter system is em-

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. Measurements 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 defined as the number of Ps atoms produced per incident eþ per steradian in accordance with

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

NPs D; XNþ

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, molecular hydrogen to be the best converter at low energies [9] whilst N2 is better above 90 eV and useable up to 250 eV [10]. Recently, investigations

NaI-Photomultiplier

Axial Magnetic Field

Incident 22

Na

Wien Filter Na

ð1Þ

Retarding Gas In Arrangement

CEMA2 Gas In

Primary Positrons

Primary Positrons

o-Ps

RGS Moderator Production Cell

Scattering Cell

Fig. 1. Schematic diagram of the Ps beam at UCL [9–14].

Retarding Arrangement

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G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 0.6 0.5

Ps Production Efficiency (Ps e+ -1 sr -1 )

0.35

0.6

E Ps=30eV

E Ps=41.5eV

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

E Ps=65eV

0.30 0.25 0.20 0.15

0.0

0.10 0.05

0.0 0

2

4

6

8

10

12 14 16

18

0.00 0

2

4

6

8

10

12

14

16

0.08

0.12

E Ps=120eV

E Ps=90eV

0.10

0

2

4

6

8

10

12

14 16 18

0.010

E Ps=250eV

0.008

0.06

0.006

0.08

0.004

0.04

0.06

0.002 0.04 0.000

0.02 0.02

-0.002

0.00

0.00 0

2

4

6

8

10

12

14

Gas Pressure (µmHg)

16

-0.004

0

2

4

6

8

10

12

14

Gas Pressure (µmHg)

16

0

5

10

15

20

25

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].

have been extended to Xe [11] following an analysis 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

0.002

counts per sec per e

+

0.003

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 drPs ðn ¼ 1Þ=dX [24] (possibly due to its large static interaction or to the non-zero angular momentum of 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 drPs ðn > 1Þ=dX and/or higher rT for excited states.

0.001

4. Differential Ps formation cross-sections 0.000

(n=1)

The Ps beam production efficiency [9] can be expressed as

-0.001 10

20

30

40

50

Ps Energy (eV)

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].

(

1 ePs / f1
expð
qlþ rTþ Þg rTþ  expð
qlPs rTPs Þ;

Z 0

h0

) drPs sin hdh dX ð3Þ

120

EPs=50eV

100

80

80 60

+-1

-1

63

100

EPs=30eV

(10 Ps e sr )

60

-3

Ps atoms per incident positron per steradian

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

40 40 20

20

0

0 0

2

4

6

8

10

12

14

16

18

20

0

2

Gas Pressure (µmHg)

4

6

8

10

12

14

16

18

Gas Pressure (µmHg)

+ Ps Ps per positron per steradian per µmHg * (ε /ε )

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].

0.5

He

0.4

0.6

0.3

Ar

0.4

0.2 0.2 0.1 0.0

0.0 0.8

H2, N2

0.6

Xe

0.6 0.4

0.4

0.2

0.2

0.0

0.0 0

20

40

60

80

100

120

Ps Energy (eV)

140

0

20

40

60

80

100

120

140

Ps Energy (eV)

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].

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 through a 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

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35

Xe 50

-20

2

Cross Section (10 m )

30

N2

25

40 20

30 15

20

10

10

5 0

0 0

50

100

150

200

250

Energy (eV)

300

0

10

20

30

40

50

60

Energy (eV)

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 for the 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 crosssection measurements performed with the Ps beam [9,12,14] are compared in Fig. 7 with recent calculations 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
 kT I0 rT ¼ ln ; ð4Þ pL I where I0 ðIÞ is the net incident (transmitted) flux, k is 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 low energies, there is a considerable discrepancy between the two rm values [6,45]. In the case of Ar, the results of coupledpseudostate (no exchange) approach of McAlinden 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 at an 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, Blackwood 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 considerable forward-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 coupling calculation [37] reduces this discrepancy. At low energies, significant disagreement remains among theories and among experiments, although a degree of convergence is beginning to emerge. It

G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 30

20

H2 2

Total-Cross-Section (10

-20

Ar

m)

14

-20

25

16 2

m)

18

Total-Cross-Section (10

65

12 10 8 6 4

20

15

10

5

2

0

0 0

10

20

30

40

50

60

70

80

90

100

110

0

120

10

20

30

40

50

60

70

80

90

100

110

120

Ps Energy (eV)

Ps Energy (eV) 14

He

Total-cross-section (10

-20

2

m)

12

10

8

6

4

2

0 0

10

20

30

40

50

60

70

80

90

100

110

120

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 triangle) 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]; (longdashed line) Biswas and Adhikari [35]; (short-dashed line) Basu et al. [37]; (dash-dot line) Sarker et al. [36]; (dotted line) McAlinden 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 the measured total cross-section, ðrT Þm , increased for decreasing detection solid angle due to forward scattering according to

 ðrT Þm ¼ rT


 dr DX; dX

ð5Þ

where rT is the ‘true’ total cross-section, hdr=dXi is 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

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

7. Integrated cross-section for Ps fragmentation The absolute cross-section for the fragmentation of Ps in collision with He, rf , has been determined by detecting the remnant positrons [19] and is given by
Ps  Nþ e rf ðEÞ ¼ rT ðEÞSG þ ; ð6Þ ðNPs Þscatt e where Nþ is the number of residual eþ ; ðNPs Þscatt is the number of scattered Ps atoms, rT ðEÞ 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 efficiencies 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 determinations shown in the figure arise from the systematic uncertainty in the determination of the positron- and Ps-detection efficiencies [29]. It can

fragmentation cross-section (10-20 m2)

4.0 3.5 3.0 2.5

be noted that the theoretical determination of Biswas and Adhikari [35] overestimates the measurements by approximately a factor of two. A good 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 residual positrons Since the fragmentation study has been undertaken 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% of the residual energy (Er ¼ EPs
6:8 eV) becomes increasingly apparent in the spectra with increasing 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 fragmentation are confined by the axial magnetic field, the energy 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 classical-trajectory-Monte Carlo simulation [50]. Here an asymmetry has been found between the energy spreads for the two residual particles. This prediction awaits experimental investigation.

2.0 1.5

9. Outlook

1.0 0.5 0.0 0

5

10

15

20

25

30

35

40

Ps incident energy (eV)

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].

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 efficiency for 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

G. Laricchia et al. / Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 60–68 1.4

1.4

E=13eV

1.2

Arb. Units.

Arb. Units.

0.8 0.6

0.8 0.6

0.4

0.4

0.2

0.2

0.0 2

4

Er /2

1.0

Er/2

0

E=18eV

1.2

1.0

6

8

10

12

0.0

14

0

5

Energy (eV)

10

15

20

Energy (eV)

1.4

1.4

E=25eV 1.2

1.2

1.0

1.0

Arb. Units.

Arb. Units.

67

0.8 0.6 0.4

Er/2

E=33eV

0.8 0.6 0.4

0.2

Er/2

0.2

0.0

0.0 0

5

10

15

20

Energy (eV)

25

0

5

10

15

20

25

30

Energy (eV)

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 Research Council is gratefully acknowledged for supporting this work under grant no. GR/S16041/ 01 and for providing D.E. Leslie with a studentship.

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