Recent advances in the characterization of a Ps beam

Hyperf'me Interactions 73(1992)133-145 133

RECENT ADVANCES IN THE CHARACTERI ZATI ON OF A Ps BEAM

G. LARICCHIA, N. ZAFAR, M. CHARLTON and T.C. GRIFFITH Department of Physics and Astronomy, University College London, Gower Street, London WCIE 6BT, U.K.

Recent developments in the field of beams of positronium (Ps) atoms formed in charge-exchange reactions of slow positrons with gaseous targets are reported. The beam production efficiencies with respect to target species and density have been measured, together with a determination of the population of the quantum states of the atoms in the beam. Estimates of the total scattering cross section of Ps with He and Ar targets, at intermediate projectile velocities, have been obtained.

1. Introduction

Following on from the verification of the forward-peaked nature of the differential Ps formation cross section [1] and the development of a timed energy-tunable Ps beam [2], investigations have been carried out in order to characterize such a beam with respect to efficiency of production and projectile parameters of importance for the study of collision phenomena. In the context of the latter, the distribution of kinetic energies and states of different principal quantum numbers was investigated in a range corresponding to energies between 7-41 eV of Ps atoms formed from He and Ar targets.

The production technique exploits the natural collimation of Ps formed by the reaction

e + + A --~ Ps + A +,

where A is one of the atoms in a gaseous target intercepted by a variable-energy e* beam. The degree of collimation is determined by the behaviour of the relevant differential cross section with respect to the positron incident energy E+ and target atom, whilst the Ps kinetic energy Tps is given to a first approximation by

Tps = E+- I + B,

where ! is the first ionization potential of the target atom and B = 6.8/n z eV is the binding energy of a Ps atom in a state of principal quantum number n. It might be worthwhile to note that the Ps atom in the beam will be in a triplet state configuration (o-Ps), the singlet being virtually untransportable at velocities typical of atomic physics experiments. In addition to the energy spread of the incident e + beam and Ps formation in states of different n-values, contributions to the spread of Tps might

�9 J.C. Baltzer AG, Scientific Publishing Company

134 G. Laricchia et al., Characterization of a Ps beam

also arise from Ps formation events simultaneous to other inelastic processes, for example,

e + + A ~ Ps + (A+) *,

where (A+) * represents the residual ion in an excited state. It has been estimated [3] that this process occurs with a 5 - 1 0 % probability in the scattering of 11-20 eV e + from CO2.

Beams of Ps atoms produced by charge-exchange collisions of positrons with a gaseous target have been used to observe the specular reflection of Ps from a LiF crystal [4]. However, it is because of the potentially large spread of Ps velocities that recent experimental effort has focussed on the production of timed beams with the concomitant attraction that they provide superior signal/noise ratios much needed in studies with these exotic atoms.

In section 2, the main components of the experimental apparatus will be described with particular emphasis on the improvements over our previous arrangement [2]. The results will be presented and discussed in section 3 and future investigations with these beams will be delineated in section 4.

2. Experimental method

With reference to fig. 1, a timed positron beam is generated by detecting the secondary electrons liberated upon slow e + impact on the remoderator M2. The impact energy is - 4 0 0 eV and the remoderator consists of a set of four superimposed 90% transmission meshes of annealed W. The electrons are counted by a set of channel-electron-multiplier arrays and focussed onto these by a negatively biased potential (VT) applied to the central tube which transmits the incident positrons. The energy of the remoderated positrons is varied by the potential applied to M2 with respect to ground. A timing efficiency of 45% was thus achieved, with a remoderation efficiency of 15%. A magnetic field of 30 Gauss guided the positrons to a 20 mm long gas cell incorporating a cylindrical entrance aperture (7 mm in diameter and 11.8 mm long) and a conical exit aperture ( 7 -10 mm in diameter and 22 mm long), the latter minimizing the aperturing of the Ps beam flux whilst still decreasing the cell gas conductance. Good localization of the gas target is needed to reduce the time jitter on the Ps time-of-flight (TOF) to a second set of channel plates (CEMA2). The transmitted remoderated e + were prevented from reaching CEMA2 by a retarding aperture arrangement, whilst the transmitted primary e + and secondary electrons were repelled by suitably biased grids close to CEMA2.

Measurements of the duration of 10-250 ks were performed in vacuum and at gas pressures in the range 0 .07-1.60 Pa, incident e + energies of 16-52.5 eV and Ps flight lengths dps between 0.137-0.431 m. The vacuum runs were adopted as one of the methods to assess the background in the gas runs. Alternatively, this was determined as described in [5] or simply estimated from a flat portion of the gas

G. Laricchia et al., Characterization of a Ps beam 135

i

z

~ II I

~ o~x/ I I O ~ ~ < < # 1 I ~ _J L

c

<

o o ~ J

ta 0

, ~1.

i,#'i

t= 0

Ill

",=1

r

t L


spectra. All three methods yielded consistent results. The Ps energy can be deduced from its TOF spectra [2] and the yields of a particular Ps quantum state were determined by summing up the counts within :1:2 eV of the mean energy corresponding to the relevant formation threshold. The yields were normalized to the number of scattered e +, the solid angle subtended by the detector to the mid-point of the cell and, where possible, also corrected for in-flight-annihilation. The number of scattered e + was computed from known total scattering cross sections [6,7], having checked that the effective length of the cell-aperture arrangement, 44.3 + 1.3 mm for He and 43.8 5:1.9 mm for Ar, was not a function of gas pressure. In the study of Ps yields as a function of incident e § energy, the upper limits on the pressure range were chosen to be 0.53 Pa (4 #m Hg) for He and 0.13 Pa (1 / tm Hg) for Ar in order to minimize effects due to e + multiple scattering and Ps loss from collision with the target atoms. The pressure range was extended to 1.56 Pa (12 # m Hg) for both gases in the determination of the Ps production efficiency as a function of target pressure.

3. Results and discussion

An example of a Ps TOF spectrum and its conversion to a Ps energy distribution are shown in fig. 2(a) and (b), respectively. The signal displayed in the figure was obtained by subtracting from a run at 0.9 Pa (7 #m Hg) of He one taken under identical conditions in vacuum. The conversion to an energy distribution was achieved by summing up counts in steps of 1 eV Ps energy. The incident e + energy is 53 eV and the Ps flight distance is 0.431 m. The two peaks present in the distribution are located at approximately 35 eV and 30 eV, namely 18 and 23 eV below the e + incident energy. With a first ionization potential of 24.5 eV for the target gas, the 35 eV and 30 eV peaks appear to correspond to formation of Ps in the ground and first excited state, respectively. The experimental resolution, however, does not warrant the strict identification of the 30 eV peak with the n = 2 state and must thus be considered as comprising Ps atoms formed in an n > I state, although production of higher n-states are expected [8] to decrease progressively according to n -3.

That the peak at 35 eV corresponds to ground-state Ps was confirmed by an investigation of its intensity as a function of flight distance. The latter was varied between 0.148 m and 0.431 m. By assuming the differential cross section to be constant within the corresponding angular range 9.70-3.3 ~ the Ps counts per scattered e + per steradian I were plotted versus flight times tps according to

In I = In Io - to~/~,

where lo is the initial number of Ps formed in the ground state and "c its vacuum lifetime. The results obtained for "f by such a method at various impact energies on an Ar target at 0.53 Pa (4/.tm Hg) are shown in fig. 3, from which a mean lifetime of 152 + 16 ns was extracted. In the case of He, z" was deduced to be 128 :t: 28 ns.


xlO -4 cw..vr3 !2

e . . . . . . . i . . . . . . . . I . . . . . . . i L> f ' I i . . . . . . . . . i . . . . . . . . . i . . . . . . i ~ . . . . . . " . . . . . . . l . . . . . ~ . . . . . . . . "

i i iO, CL

t S,

4. 7, 4"

I~,

I i

~ "L++ + 1 l + I I ,+

- 1 + ~ I 4 + t + ~ I I i

xlo-4

!

-. 4- IM i

4

I

- ~ i . . . . . . . . ~-+ , . . . . . . . . . . . . . . . . . , . . . . . . . . . , * , , . . . . . . t . . . . . . . I . . . . . . . . . , . . . . . . . .

is ~b ds ~b "~'s 4b +~ sb ss

Fig. 2. (a) Ps time-of-flight spectrum and (b) its conversion to a Ps energy distribution. The target gas is He at 0.9 Pa and the incident e + energy is 53 eV.


Lifetime (ns) 500

450

400

350

300

250

200

150

100

50

0 20

I I I I I I

25 30 35 40 45 50

Positron energy (eV)

Fig. 3. Verification of a ground-state Ps component in the beam: �9 measured lifetime (see text); �9 .- expected lifetime.

Both values are in broad agreement with the expected vacuum lifetime of 142 ns for the 1 3S 1 state of Ps. A similar analysis for the other peak in fig. 2 was inconclusive, indicating the possible mixture of states with different n and l, the orbital momentum quantum number.

The variation of the measured yields of ground- and excited-state Ps with incident e + energy are shown in fig. 4, where they have been normalized to scattered e +, solid angle and, in the case of the ground-state component, in-flight-annihilation. Similar features are evident from both target gases, with the yield increasing by a factor of - 3 within approximately 10 -20 eV from threshold, after which the dependence on energy is very much reduced. It might be of interest to note that the highest values for the n = 1 component are approximately three times greater in He than Ar. Given that the Ps formation probability in the two targets is comparable in this energy range, this implies that the differential Ps formation in He is, in comparison to Ar, more peaked at small angles. At the lowest e + energy investigated, no significant quantities of excited Ps was detected from either gas. It should be stressed that the uncorrected data in the figure represent actual measured yields and as such neglects possible differences between CEMA2 detection efficiencies for e + and Ps in its various states. Neither does it allow for their possible dependence on panicle impact energy.

G. Laricchia et al., Characterization o f a Ps beam 139

e ~

r

t . < ~ -+- _._

I

q - " l

--~ §

I P f o O ~t~ ~ r

0

.=

0

h o

=, . - .

... ~o

v

il , d

~

e5

t3

I

Q

q-

+

§

f I I I

c5 c5

Q

§ r

~ ~

+ ~ v

II

.~.-.

2

140 G. Laricchia et al.. Characterization of a Ps beam

Ratio 1

0.8

0.6

0A

0.2

0 24 26

, l , t , i , , , , J i ,

28 30 32 34 36 38 40 42 44 46 48 50 52 54

Positron energy (eV)

Fig. 5. Rat ios o f n > lln = 1 Ps in the b e a m from: He (m) exp and ( - ) theory [8]; Ar (A) exp.

The ratios of the measured signal for excited-to-ground state Ps flux are presented in fig. 5, illustrating that, over the range investigated, the excited-state components represent 16-50% and 25-71% of the ground-state flux in He and Ar, respectively. Equivalently, it may be stated that the n > 1 components represent 14-33% and 20-42% of the total flux in He and Ar, respectively. Consistent calculations of the differential Ps formation cross section for different quantum states are not available for the targets and energy range investigated. The solid line in fig. 5 represents ratios, equivalent to the experimental ones, deduced from calculations of the total Ps formation cross sections for He in the ground-and first-excited states [9]. These have been corrected for the proportion of states annihilating in flight in the experiment. If not fortuitous, the reasonable agreement with experiment would imply that 7 -12% of the amount of Ps formed in the n - 1 state is formed in the n = 2 states and of these, up to 80% may be in the metastable 3St state (1100 ns lifetime) at Ps energies in the range 17.2-34.7 eV.

Although the data in fig. 4 suggest a higher degree of collimation of the Ps atoms formed in He, the magnitude of the total Ps formation cross section in Ar exceeds that for He at their maximum by nearly an order of magnitude. This fact is reflected in fig. 6, where the Ps counts per incident e § per unit solid angle are

G. Lar icchia et al., Character iza t ion o f a P s beam 141

O .

O~

d}

W 0

E .lo ,~_ >-

0

I I I I I I

v

I I ! I !

0 0 0 0 0

T-

0 ~D

0 tO

0

v

0 r

t " o

It} 0

0 ~ " t'Xl

0 v -

0 0

0 ~D

0 i t )

0

Q)

C o.

o.~

0 0 iX.

0 v -

0 0

:I:

ca

"d

v , v ~

~ E

-i-

c

E

- r


Ps beam production efficiency (x 10E-5) 10

9

8

7

6

5

4

3

2

1

0 0

.....---o Z J

J

z

I I I ~ I I I I I I I

1 2 3 4 5 6 7 8 9 10 11

pressure ~mHg)

• Measured yield 0 Expected yield

Fig. 7. Ps beam production efficiency with Ar gas pressure. The e + beam energy is 45 eV and the o-Ps flight distance 0.33 m.

12 13

presented for He and Ar, both at a pressure of 0.13 Pa; again, only the n = 1 yields have been corrected for in-flight-annihilation. These measurements show that at this pressure, over twice the n = 1 yields and 3 - 5 times the n > 1 yields are obtained from Ar in comparison to He.

Ignoring self-annihilation, the intensity of Ps atoms in a given state ll, s present in a beam produced by I0 positrons incident on a target of number density p at the center of a cell of effective length l is given by

lpJlo = {[1 - e x p ( - p l a t ) ] / ~ } f o'v~(0, #) dfl, (1) a'

where o't is the total e + scattering cross section and avs(O, #) is the differential Ps formation cross section integrated over the detector solid angle iT. The limit on the validity of the above expression, for increasing values of p, is set by the magnitude of the Ps scattering cross section. An example of the actual variation of ground-state Ps per positron of 45 eV incident energy with Ar gas pressure is shown in fig. 7. Here, it can be seen that the Ps production efficiency saturates at - 0 . 8 Pa (6 ]zrn Hg) and decreases after - 1.3 Pa (10 #m Hg). It might be of interest to note that the beam energy width did not deteriorate with increasing gas pressure. The solid line in the figure represents the yields expected by extrapolating the low pressure values using eq. (1). The latter will then be related to the measured intensity (Ivs)m by

(Ips)m = Ips exp(-PO'clps),


where tre is the Ps total scattering cross section and Ips is the effective cell length for Ps. The latter was estimated as the difference between 1 and the point along l where half of the total amount of Ps had been formed, the latter being a function of gas pressure. It was therefore necessary to apply corrections, amounting in total to -10%, to account for the increased Ps flight path at the highest pressures, affecting both the decayed fraction and the detector acceptance. In this manner, estimates of the total scattering cross section for ground-state Ps with He and Ar atoms were obtained and are presented in fig. 8. Here, o'c is found to vary between

10 Ps cross-section (tO ~mz)

r I I i I t

0 10 20 30 40 50 60

Positronium energy (eV)

Fig. 8. Energy dependence of the averaged values of the Ps (n = 1) total scattering cross sections measured in this experiment with He (11) and Ar (+) targets; ( - - ) He (theory).

70

(1.8 + 0.7 and 2.8 + 0.7) x 10 -2o m 2 in He, while increasing continuously from (4.5 :!: 0.8 to 7.6 + 0.8) x 10- 20 m 2 in Ar over a Ps incident energy range of 7 - 4 1 eV. The method was found to be unsuitable for the excited state components, probably due both to the mixture of states present and their expected larger scattering cross section. The latter would invalidate the pressure range used to determine Sa-,,trps(O, ~)dfL

The main processes expected to occur in the scattering of ground-state Ps, with energies comparable to those in this work, off other neutral atoms are indicated as follows:


elastic scattering

projectile quenching

projectile excitation

projectile ionization

target excitation

target ionization

Ps + A--> Ps + A

o-Ps + A ---> p-Ps + A

Ps + A---> Ps* + A

---> e+ + e - + A

Ps + A*

---~ ps + A +

Some guidance towards the relative importance of the above processes can be derived by available calculations. These are mainly confined to H and He and have recently been surveyed [10]. They indicate that the latter two reactions are comparatively improbable in H, whilst elastic scattering would be dominant even above the threshold for projectile excitation. Among the inelastic channels, Ps break-up is expected to be the most important at intermediate energies. For H, the conversion of o-Ps into p-Ps might be non-negligible even above - 10 eV above the threshold for inelastic processes. In the case of He, although calculations are even scarcer, quenching is expected to be much less likely since it would require an appreciable energy transfer. The solid line in fig. 8 presents the sum of theoretical estimates of the elastic [11] and inelastic [12] scattering cross sections which are found to agree with experiment only in order of magnitude. The form of the observed energy dependence of o'c for He and Ar would appear to suggest that elastic scattering is a more probable process in He than Ar.

4. Conclusions and future prospects

Recent progress in the development of beams of Ps atoms has been presented. Characterization of such beams has been accomplished in the Ps energy range 7 -41 eV with respect to production efficiencies from He and Ar targets and, to some extent, quantum states of the beam atoms. It has been found that the latter target is more efficient per unit target area density and that at the maximum 33% and 42% of the total beam flux contains excited Ps atoms in He and Ar, respectively. Comparison with theory would suggest that a large proportion of these are in the metastable 2S state.

The total scattering cross section of Ps with He and Ar was estimated to range from ( 4 . 5 - 7 . 6 ) x 10-2~ 2 in Ar for Ps energies of 17-41 eV and (1.8-2.8) x 10 -20 m 2 in He in the range of 7 - 3 5 eV.

Plans to perform direct Ps total scattering cross section measurements using a double cell arrangement [2, 13] are currently being implemented by the construction of a more intense e § beam [14]. In addition to the investigation of simple atomic targets amenable to theoretical calculations, we intend to study the interaction of Ps with targets which have exhibited anomalously large iZdt in e § lifetime studies [15].


Acknowledgements

This work was supported by the Science and Engineering Research Council under Grant No. GR/F/14550. G.L. and M.C. would like to thank the Royal Society.

References

[1] G. Laricchia, M. Charlton, S.A. Davies, C.D. Beling and T.C. Griffith, J. Phys. B20(1987)L99. [2] G. Larir162 S.A. Davies, M. Charlton and T.C. Griffith, J. Phys. E21(1988)886. [3] G. Larir162 M. Charlton and T.C. Griffith, J. Phys. B21(1988)L227. [4] M.H. Weber, S. Tang, S. Berko, B.L. Brown, K.F. Canter, K.G. Lynn, A.P. Mills, Jr., L.O. Roellig

and A.J. Viescas, Phys. Rev. Lett. 61(1988)2542. [5] P.G. Coleman, J. Phys. E21(1979)590. [6] T.C. Griffith, G.R. Heyland, K.S. Lines and T.R. Twomey, Appl. Phys. 19(1979)431. [7] W.E. Kauppila, T.S. Stein, J.H. Smart, M.S. Dababneh, Y.K. Ho, J.P. Downing and V. Pol, Phys.

Rev. A21(1981)725. [8] P. Mandal, S. Guha and N.C. Sil, Phys. Rev. A22(1980)2623. [9] P. Khan, P.S. Mazumdar and A.S. Ghosh, J. Phys. B17(1984)4785; Phys. Rev. A3(1985)1405. [10] M. Charlton and G. Laricchia, Comm. At. Mol. Phys. 26(1991)253. [11] G. Peach, in: Positron Scattering in Gases, ed. J.W. Humberston and M.C.R. McDowdl (Plenum,

New York) abs. [12] A.M. Ermolaev (1989), private communcation. [13] N. Zafar, G. Laricchia, M. Charlton and T.C. Griffith, in: Positron Annihilation, ed. L. Dorikens-

Vanpraet, M. Dorikens and D. Seger (World Scientific, Singapore, 1989), pp. 306 and 596. [14] N. Zafar, G. Laricchia, M. Charlton and T.C. Griffith, this issue. [15] M. Charlton, Rep. Progr. Phys. 48(1985)737.

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Recent advances in the characterization of a Ps beam