Experimental Aspects of Positron and Positronium Physics

ADVANCES IN ATOMlC AND MOLECULAR PHYSICS. VOL 22

EXPERIMENTAL ASPECTS OF POSITRON AND POSITRONIUM PHYSICS T. C. GRIFFITH Department of Physics and Astronomy University College London London WClE 6BT, England

I. Introduction Positron physics has, during the past few years, experienced a period of rapid expansion resulting from the application of positron beams of well-defined energies to an increasing range of experiments. The development of positron beam technology has been crucially dependent upon the discovery and design of efficient moderators to produce the low-energy (about 1 eV) positrons. The re-emission of a substantial number of such positrons on thermalizingfast positrons in certain materials was first reported by Groce et al. ( 1968)and this was followed by the discovery by Canter et al. ( 1972)and Coleman et al. (1973) that MgO powder could be employed to provide positron beams of such intensities that accurate cross-section measurements were possible. Further major improvements in the yield of low-energy positrons came from the use of heat-treated tungsten moderators by Dale et al. (1 980) and then by the use of clean single crystal metal targets, such as Cu(III), under ultra-high-vacuum conditions as reported by Mills (1980). There are currently at least two laboratories where intense beams of nearly monoenergetic positrons are being generated either from strong radioactive positron emitters produced in situ near a nuclear reactor or from an electron linear accelerator via the bremsstrahlung process. It is intended that these beams should have intensitiesof up to 1O8 or 1O9 positrons per second with a narrow energy spread and capable of being focussed and collimated into a narrow pencil suitable for the performance of precise experiments. There is little doubt that the motivation for the development of these beams had stemmed, initially, from the challenge of performing atomic physics cross-section measurements with positrons of a quality that would compare with those already in existence for electrons. Today, however, their 37 Copyright 0 1986 by Academic Rws,Inc. All rights of reproduction in any form -4.

38

T. C.Grijith

use has been extended to embrace several other fields of research such as: measurements of low-energy positron diffraction, LEPD (Canter, 1982, 1984); a study, using positron beams in combination with 2 y-annihilation angular correlation apparatus, of the momentum density of electrons in surfaces and of defects in material samples as a function of spatial position (Lynn and Frieze, 1984; Lynn et al., 1985; Howell et al., 1985); the use of polarized positron beams for studies of surface magnetism and of optically active molecules (Rich, 1980, 1985);a detailed study of positronium formation in very clean surfaces and of positronium spectroscopy and fundamental experiments testing certain aspects of quantum electrodynamics (Berko and Pendleton, 1980; Gidley, 1980; Gidley and Coleman, 1984). The content of this article is mainly concerned with recent investigations of and results on the interactions of positrons with gaseous atoms and molecules. Experimental determinations of total cross sections for the scattering of positrons ofenergiesin the range 1 - 1000eV in different gases have played a dominant role for several years, but the emphasis has recently shifted to the measurement of partial cross sections for the various inelastic channels in positron interactions. Among these channels positronium formation is a unique capture channel which has no analog in electron scatteringand is, for this reason, particularly important. Positronium itself can now be produced in abundance and the stage is already poised for qualitative studies of positronium scattering in gases. The impact of the availabilityof intense positron beams on atomic physics experimentsas well as on other groups of experiments is only just beginning. It is now, for example, possible to think in terms of planning accurate measurements of positron differential scattering cross sections for some of the inelastic channels; positron scattering by atomic hydrogen as well as other similar experiments have already reached an advanced stage of planning. Alongside the above, perhaps rather dramatic developments, the older technique of studying positron lifetime spectra is, in a modified form, continuing to produce significant results. As a measure of its importance, and of the varied insight gained by studying the annihilation of positrons in gases at various pressures and temperature and under the influence of electric fields, a substantial discussion of the recent results obtained by this method will be included. Several reviews have been written on the topics covered by the present article; most of the relevant background to its content has been reviewed by Griffith and Heyland ( 1978), Griffith ( 1979), Rich (1980), Stein and Kauppila (1982),Heyland ef al. (1982),and Charlton (1985a).Progress in the field has, however, been so rapid that there is, one hopes, little overlap with earlier works.

POSITRON AND POSITRONIUM PHYSICS

39

11. Annihilation Spectra for Positrons in Gases A. LIFETIME PARAMETERS

In contrast to the modem investigations using positron beams, the basic principles behind the methods of measuring lifetime spectra for positrons in gases have remained unaltered for more than 30 years. The electronic equipment employed for the present work has, however, become so sophisticated that data can be accumulated at a rate which is a few orders of magnitude faster and, with the aid of elaborate computer programs, can be subjected to much more precise analysis than was possible I5 years ago. The cross sections for annihilation are only comparableto those for atomic interactionsat very low velocities and it has to be emphasized that lifetime spectra, therefore, provide information at positron energies which are, as yet, not attainable with positron beams. This information is usually displayed in the form ofa number of parameterswhich describeboth the free positron annihilation rates and the annihilation ofthe positronium, Ps, formed during the positron slowing-down process in the gases under study. In terms, respectively, of the gas density p, of the classical radius of the electron r,, of c, the velocity of light, and n, the number density of the gas in the immediate vicinity of the positron (with u p = nricn), the five main parameters can be defined by where Ifand 1,are the density-dependent equilibrium decay constants for thermalized free positrons and for orthopositronium, 0-Ps, respectively, and ,,Ip is the vacuum decay rate of orthopositronium. The theoretical value of ,,Ip = 7.039 0.006 ps-l predicted by Caswell and Lepage (1 979) is close to the various measured values quoted by Gidley and Coleman ( 1984). 2, is the effective number of atomic or molecular electrons available to the positron for annihilation at agiven gas density and temperature,while z,,is the effective number of electrons available in similar circumstances for annihilation of the positron in the 0-Ps. The bars over these quantities signify that they represent the weighted mean for annihilation over the thermalized positron or positronium energy distribution. Another important lifetime parameter is the positronium formation fraction F, which is defined as the ratio of the total number of positronium events (ortho plus para) to the total number of gas events in a given lifetime spectrum. Positronium is formed by positrons with incident energy E,,, greater than the Ps formation threshold energy Eh. In the inert gases positrons surviving with energy below Eh can only lose energy by elastic collisions; the energy loss then occurs at such a slow rate that the positrons

+

40

T. C.Griflth

frequently annihilate before thermalization, thus giving rise to the characteristic shoulders observed in the spectra of these gases. In the molecular gases,with the exception of nitrogen, the thermalizationtime is so short that shoulders are not observed. Being dependent on the combined effect of elastic scattering and annihilation as a function of velocity, structural details of the shoulders for the inert gases are obviously critically dependent on the momentum transfer and annihilation cross sections.Ps atoms can be formed at positron energies of several hundred electron volts, but those with energy greater than 6.8 eV are believed to be rapidly dissociated in subsequent atomic or molecular collisions in the gas. A large contribution to F is, therefore, expected to be from Ps formed at energies in the range Em < E,, < E,, known as the Ore gap, with E, defined as the first excitation energy. As discussed by Schrader and Svetic (1982), there will be some contribution to Ffrom Ps formed in the range E, < E,, < Ei, where Eiis the ionization energy. Jacobsen et al. (1982) have argued that there is also a contribution to Ps formation in dense gases from spurs formed near the end of the positron trajectory and there is now strong experimental evidencethat the simple Ore model for Ps formation has only a limited range of validity. In most gases the measured values of F are found to be density dependent and this is a feature that cannot be explained by the Ore model because its predictions rely solely on threshold energies and cross-section values. It is of interest to note that important advances have lately occurred through the application of dc electric fields across the annihilation volume. Under these conditions the lifetime parameters are modified and the information contained in the data is analogousto that in the work performed with electron swarms. Methods have now been developed for the determination of drift velocities and, as reported by Davies et al. (1985) and by Charlton (1985b),the preliminary results, discussedin Section II,E, are very encouraging. All the above parametershave been carefully discussedby Heyland et al. (1982) and Charlton (1985a) and these articles review most of the experimental background to the determination and analysis of lifetime spectra and contain a comprehensive survey of the significance of the vast amount of data accumulated for all the inert gases for a wide range of molecular gases and for various mixtures of gases.

B. RESULTS FOR THE INERT GASES Several factors of interest have been revealed by a study of the shouldersin the inert gases and of the parameters Z,and F. It was shown by Campeanu and Humberston ( 1977)and by Humberston and Campeanu (1980) that an investigation of the shape and width of the shoulder in the spectrum for

41

POSITRON AND POSITRONIUM PHYSICS

helium together with the measurement of pe5provide a sensitive and independent test of the accuracy of the wave functions used for the evaluation of the total cross sections for e+-He scattering using the Kohn variational principle. The agreement between theory and experiment is very good. Similar investigations, with varying degree of success, have been carried out for the other inert gases. Campeanu ( 1981, 1982) has performed calculations relating to the shoulders in Ne, Ar, Kr, and Xe, while McEachran er af. (1978, 1979, 1980),using the polarized orbital method, have evaluated for the same gases. In Table I a summary of these results for is given, together with the measured values and estimated maximum and minimum values of F as predicted by the Ore model. The results for pure Kr and Xe gases at low densities are particularly important because of the small values of Fobserved in these gases. Another feature ofinterest for both these gases is illustrated for the case ofXe in Fig. 1, where there is definite evidence for the existence of two fast components close to r = 0 in the annihilation spectrum. The fast components have been linked to the observed dearth of 0-Ps in these gases. The rapid rise in the values of the total crosssection, a, for Kr and Xe at the Ps threshold together with the direct measurement of the Ps formation cross section, a,, for these gases presented in Section II1,C show that, under single collision conditions, 0-Ps is in fact copiously formed. The addition of small amounts of Kr and Xe to He as a base gas as reported by Charlton et af.(1979)also confirms that a, for these gases, as determined in a lifetime experiment, is large. It has been suggested by Griffith er af.(1982)and Wright et al. (1985)that

z,

TABLE I

EXPERIMENTAL AND THEORETICAL VALUESOF Gas ~

Zca(expt)

Zcr(theor)

Fmin F,,

3.85d 7.0f0.3e 27.6d 57.6f2.9e 2 1 7 f 11'

0.14 0.09 0.17 0.20 0.26

zcr

AND

Fa

F(expt)

~

He Ne Ar Kr Xe

3.94 f0.02b 5.99f0.08* 27b 65.7f0.3C 320fgc

0.28 0.32 0.43 0.49 0.56

0.23b 0.26b 0.33b O.llc 0.03'

a At room temperature for the inert gases (Fmin and F- are Ore model lower and upper limits). Griffith and Heyland (1978). Wright et of. (1985). Grover et al. ( 1 980); based on work of Mchchran ef al. (1977, 1979). 9 Schrader and Svetic (1982), based on work of Mchchran et af. (1978, 1980).

ze5

T. C.Grifith

42

. .

I.

Xenon

.

lNFR SHOULDER

I 150

10’

.

I

Channel Number

200

0-Ps

I I 80

I

I

I

1..

300

520

7LO

960

,

Channel Number

FIG.1. Lifetime spectrum for annihilation of positrons in Xe at 9.64 amagat and 297 K. Details of the “fast” (FF)and “less fast” (SF) components are shown in the inset.

POSITRON AND POSITRONIUM PHYSICS

43

both the small values of F and the existence of fast components in the annihilation spectra of pure Kr and Xe can be explained by postulating that the 0-Ps atoms, moderating in the gas, pass through at least two energy regions where resonant states of the form Kr-Ps and Xe-Ps are formed. These states are short lived and, if the cross sections for these processes are large, then two fast components would be detected in the spectra. These conjecturesare given further support by the observation that the addition of small amounts of He (or Ne) to either Kr or Xe as a base gas lead to an increase in the value of F. This is precisely what would be expected if the slowing-down process for 0-Ps is enhanced by the light He or Ne atoms in such a way that it makes fewer collisions in the energy regions where the resonant states are formed. For Kr-He mixtures the value of F increases from 0.1 1 at zero concentration of He to 0.39 at a He concentration Of 5090. The latter value of F lies within the limits of the Ore model. The addition of molecular gases, such as H2, D,, and N,, give similar results but are effective at much lower concentrations. In all cases the addition of the contaminant gases leads to a rapid decrease in the intensity of the fast components and to a drastic reduction in their lifetimes. In pure Kr the values of the decay constants for the fast components are 5 1.2 k 2.2 and 177 f 9 p s - l amagats-I and the corresponding values in pure Xe are 91.6 f 2.6 and 396 -t 11 ps-' amagats-I.

c. ANNIHILATIONFROM CLUSTERS In their study ofthe values of Fdand Ifasa function ofdensity for pure Xe and for mixtures of Xe with the molecular gases H,, D,, and N,, Wright et al. (1985) have proposed that positrons in Xe are annihilating after selftrapping in clusters of gas molecules in the gas at room temperature. This observation confirms that the phenomenon of clustering is now reasonably well understood both experimentally and theoretically.Cluster formation in different gases at various temperatures and densities has been investigated in several laboratories. It was first reported for helium at low temperature by Roellig and Kelly ( 1965)and later by Hautojarvi et al. ( 1977).The phenomenon has also been studied in detail for N, by Rytsola et al. ( 1984), and some of their observations are reproduced in Fig. 2. The clustering effect has been treated theoretically for the inert gases He, Ne, and Ar by Manninen and Hautojarvi (1978) using a density-functional formalism in which the static properties of the cluster were calculated with the aid of an assumed (simple) positron -atom potential in order to evaluate If and FeBat each density and temperature. Rytsola et al. (1984) have interpreted their results for N, in a similar fashion using a Van der Waals

I

I

i 120 K

0

50

100 Density (Amagotl

150

FIG. 2. Annihilation rates illustrating the effect of positrons trapped in clusters of gas molecules. The top diagrams are the results for “He(right)and ’He (left) observed by Hautojarvi et al. (1 977). The lower diagram is for nitrogen, as observed by Rytsola et al. (1984). Numbers on the graphs are temperature in degrees K.

45

POSITRON AND POSITRONIUM PHYSICS

equation of state and an optical pseudopotential for the positron - molecule interaction. In a full description of the N, data the zero-point energy of the positron on localization had to be evaluated and an allowance for the correThe sponding velocity incorporated in the final calculation of Ifand effect of clustering manifests itself as an increase of the measured values of 1, above that expected for a linear extrapolation from low densities. The divergence becomes prominent at certain densities for temperatures T 5 2T,, where T, is the critical temperature of the gas. As illustrated in Fig. 2, the rise for He is almost a step function but in N2the divergence is more gradual. A general review of theoretical aspects of the clustering phenomenon has been given by Iabukov and Khrapak (1982). In Xe the critical temperature is 289.9 K, so that clustering might be expected at room temperature. It was therefore rather surprising to find that instead of diverging upwards from the linear extrapolation from low density the values of Ifin pure Xe diverged in the opposite direction. It was argued that the observed discrepancy between the measured and calculated values of 2,given in Table I could be explained if in pure Xe at room temperature the positrons are not fully thermalized and that the full effects of clustering would also be masked if this was the case. The addition of small amounts of a molecular gas to pure Xe should ensure full thermalization of the positrons should then be close to the true values and the observed values of Ifand for thermalized positronsin pure Xe. Typical results for a mixture formed by the addition of 8.4% H2 to Xe at various densities at T = 297 K are shown in Fig. 3. The values of Af are now consistentlyhigher than those expected for a linear extrapolation from low densities and are, therefore, exhibiting a behavior that would be expected for pgitrons annihilating after self-trapping in clusters in the gas. The values of 2,rise sharply from the value at low density and are everywhere higher than for pure Xe. Other examples of the characteristicrise of 2,have been reported for different gases by Canter and Roellig (1975) for Ar, McNutt et al. (1975) for CH,, Wright et al. (1983) for C02,Heyland et al. ( 1985)for CO, and SF,, as well as for N, by Rytsola et al. (1984), and in each case the effect has been attributed to cluster formation.

zd.

z,

D. SPURMODEL FOR POSITRONIUM FORMATION It has already been demonstrated that a study ofthe positronium fractions F i n Kr an Xe has led to unexpected results. The proposed explanation of these observations implies a strong interaction between the 0-Ps and Kr and Xe atoms, but there is hardly any other experimental or theoretical information on the elastic or inelastic interactions of Ps atoms. As discussed by Schrader and Svetic (1982), it is observed that, as a function of gas density,

T. C. Grijith

46

1 4

I.;

lb) 0 0

0

0

350

ZCff

300

2 50

200

140 Density of Xe (amagats)

FIG.3. Values of (a) Ifand (b) Z,,in Xe as a function of de_nsityat297 K: (0)pure Xe; (0) Xe after the addition of 8.4%of H,; (0)theoretical value of Z,, (see Table I).

the values of F are only constant as required by the Ore model for He, Ne, and Ar; pronounced density dependence is observed for most other gases, In the molecular gases there are factors other than the Ps formation cross sections, ops,and Ps interactions which influence both the magnitude and density dependence of F. One such factor which has assumed increasing importance of late is the formation of Ps in spurs. In this model, proposed for the liquid phase by Mogensen ( 1974)and extended to dense molecular gases by Jacobsen (1982) and Mogensen (1982),the spur, formed by a positron as it loses energy and approaches the end of its range in any medium, consistsof a localized concentration of positive ions, electrons, excited molecules, etc., as well as the positron itself. If the e+- e- separation is small enough for there to be significant Coulomb attraction between them, the pair can unite to form Ps. The process is described by the reaction [e+ e-] + [PSI in contrast to the Ore model reaction e+ M + M + Ps. Spur reactions are expected to occur when the free electrons and the positron become thermalized in a medium of permittivity E , at temperature T, and their separation is of the same order of magnitude as the Onsanger distance r,, which is given by

+

r,

= e2/4mkT

+

+

(2)

47

POSITRON A N D POSITRONIUM PHYSICS

This is the separation for which the Coulomb potential energy between the (e+,e-) pair is equal to the thermal energy and Ps formation may occur if the spur radius R is also of the same order of magnitude as r,. Other processes such as e--ion recombination, negative ion formation, etc., may occur and both the positron and electrons may diffuse out of the spur. An expression for F which incorporatesboth the Ore and spur models has been written in the following form by Jacobsen ( 1 984):

- F,) exp(-&)[

F = Fo 4- (1

1 - exp(- r,-/R)]

(3) where Fo is the Ore model contribution and zh is the Ps formation time in the spur which is defined in terms of p, the sum of the electron and positron mobilities, by the expression

zR = 4eR3/3e/

(4)

Equation (3) takes account of both the density and temperature dependence of F and, as shown in Fig. 4, has been applied reasonably successfully by Jacobsen (1 985) to describe the data of Heyland et al. (1 985) for C 0 2 .As

07

06

F

05

O L

I 0

5

1

10

I 15

1

M

~~

-

1 25

I

5

I-

10

-1

15

. I 20

p Lamagalsi

FIG.4. Density dependence of the positronium fractions F in CO, at different temperatures. (a) ExpeFimental results of Heyland et a/. (1984): (-0-) 273 K, (--V--) 297 K ( ...A ...) 314 K, (-V-) 350 K, (-0-) 423 K. (b) Correspondingvalues calculated by 273 K, (---) 297 K, (---) 350 K (lower curve). Jacobsen (1985) using Q. (3): (-)

T. C.Gr.@th

48

expected, Fis dominated at low densitiesby Fo,the Ore model contribution. In most gases F increases with density up to a certain point and then decreases. Qualitatively, this can be explained by the argument that the spur contribution increases with gas density because more Ps is formed for the smaller R expected at high densities; at a certain density, however, the positronsin the spur may have a higher probability for free annihilation than for forming Ps so that F tends to decrease beyond this point. Further evidence in support of the spur model has recently been reported by Curry and Charlton (1985) from an investigation of the effect of adding small concentrations of electron-scavenging molecules CC1, and CC12F2to C02.As illustrated in Fig. 5 , the values of Fwere observed to decrease as the concentration of CCl, and CC12F2was increased. The results are interpreted as being due to the inhibition of Ps formation in the spur by the presence of the alien molecules. On repeating these experiments with Ar instead of C02, the values of Fwere, however, observed to increase with concentration. This behavior conforms to the view that Ps in Ar is formed according to the Ore model, i.e., F = F,, and that the increase in Fisdue to the contribution to Ps formation from the alien molecules.

X

X

0

c

POSITRON AND POSITRONIUM PHYSICS

49

E. POSITRON MOBILITIES IN GASES Many lifetime experiments have been performed with a uniform e.xtric field applied over the annihilation volume. Most of the measurements, such as those of Lee and Jones ( 1 974), were taken before the present-day techniques of analysis had been developed and are, therefore, of limited usefulness. The calculationsof Campeanu and Humberston (1977) include some predictions of the variation of Z,with electric field in the case of He and measurements currently underway at University College London should soon close this gap between theory and experiment. Measurements of this nature in different gases should, indirectly, provide information on the momentum transfer cross sections below 1 eV. Another important advance in this direction has been fostered by Charlton ( 1985b),who has developed a method of measuring the drift velocity, w, of positrons in low-density ( < 1 amagat) gases under the influence of a uniform electric field. The positron mobility, p+, determined in such an experiment, provides information on a , the momentum transfer cross sections. Other methods that have been used for similar measurements were discussed by Davies et al. (1985). Mills and Pfeiffer (1976, 1977)have used a Doppler shift method for positrons annihilating in condensed media, while in low-density gases Paul and Tsai ( 1979), Bose et al. (198 I), and Paul and Bose (1982) have taken some measurements by monitoring the fraction of positrons reaching a target, after drifting in an electric field, using the known annihilation rate as a clock. The success of the method used by Charlton ( 1985b)and by Charlton and Laricchia (1985) is largely due to the refined techniques of analysis that can these days extract relevant information from very weak signals. As illustrated in Fig. 6, the simple vessel used for this work consists of two brass electrodes with a potential difference Vbetween them, which also constitute the walls of the chamber containinggas at subatmosphericpressures. With the use ofthe technique developed by Coleman et al. (1972), positrons from a 10 pCi 22Nasource were detected as they traversed a thin plastic scintillator of thickness 0.25 mm before entering the volume between the electrodes through a thin Melinex window. The annihilation y rays were detected in the 125 X 100 mm plastic scintillator on the other side. The timing system successfully identifies the 0.1% of the positrons that annihilate in the gas from the 99.9% that annihilate in the vessel walls to appear as a massive prompt peak. The gas signal correspondsto the annihilation of free positrons that have been thermalized in the gas and also the annihilation of Ps atoms formed in the cell. Application of the electric field means that some of the

50

T. C,Grifith

FIG.6. Schematicdiagramofthe apparatus used by Charlton(1985b)to measure positron drift velocities.

thermalized free positrons will annihilate prematurely following field-induced drift to the electrode. This happens if the maximum drift time r,d is and the typical lifetime spectrum,illustrated in Fig, 7, comparable with (If)-' is characterized by an abrupt terminus at rmd, which is preceded by the 0-Ps and free positron decay components. z,d is observed to be dependent on 4, the applied potential. Assuming that the thermalized free positrons are uniformly distributed between the electrodes, then z,d is specified by those positrons which have drifted the entire drift length, d, between the electrodes. The drift speed is then o = d/rmdand the positron mobility is In the approximation that, in the low-energy region, the positron momentum transfer collision rate averaged over the positron energy distribution is independent of the velocity u (viz., a , a l/u), it follows that where n,u+ is the density-normalized mobility.

105

%

..)r

-

*

0-Ps + free1 Y

95

Y Y

Y

I

t

YI

d .

C

s

$

85

free only

-1 I I I

-

1

Y

I I

75

65

FIG.7. Typical lifetime spectrum for SF, gas at 98 torr and 827 V cm-' taken by Charlton and Laricchia (1985). Maximum drift time is T , ~ . The prompt peak lies at channel 155 ( I channel = I .97 ns). x 106

a

b

!

10

5

6

7

8

06

10

15

E I P ( Vcm-' tor,.')

FIG.8. Positron drift velocitiesas a function of ( E / p )for (a)SF, ( 100torr, 297 K)and (b) N, (400 torr, 297 K), as measured by Charlton and Laricchia (1985).

T. C. GriJith

52

TABLE I1 VALUESOF p+n, p-n,"

AND a, FOR VARIOUSMOLECULAR GASESAT T = 297 Kb

H2

D2

0,

N,

CO

C02

CH,

SF,

1940 1200 29

2200 1080 26

1440 4460

1560 930 36

1430 1800 40

480 660 119

370

300

154

190

~~

p+n p-n.

a,(A) a

40

-

-

In units of cmz V-* s-l amagat.

* Average errors in p+n are typically 10- 1 5%. Examples illustrating the dependence of the measured values of the drift velocities on E/p, where E is in V cm-' and p is the gas pressure in torr, is given for SF, and N, in Fig. 8. Preliminary values of the positron mobilities and of a , calculated using Eqs. ( 5 ) and (6) are given in Table 11. Some of the electron mobilities reported by Peisert and Sauli ( 1984) and by Crompton and Elford (1973) are also tabulated.

111. Cross-Section Measurements with Positron Beams A. TOTALCROSS SECTIONS Only a brief account of some of the more recent results of total cross-section measurements for positrons and electrons at various energies in different gases need to be discussed in this article because a number of comprehensive review articles have already been written on the subject. Gnffith and Heyland (1978), Kauppila and Stein (1982), Raith (1983), and Charlton ( 1985a) have all described the different experimental techniques, and their limitations, used for these investigations. They have also summarizedall the main results that were available up to the end of 1984. As a general observation it is fair to comment that, considering the diversity of experimental methods that have been used, the agreement between measurements from different laboratories is exceedingly good. All the measurements are based on an observation of the transmission or attenuation of an incident positron (or electron)beam of energy Eand intensity Z,(E) in a gas column oflength 1, at temperature T and pressure p , to its transmitted intensity Z(E).The total

53

POSITRON AND POSITRONIUM PHYSICS

cross section (TT(E)at the given energy is then written as

%w)= l n [ ~ o ( ~ ) / W ) I / n ~

(7) lo2’

where the number of target molecules per unit volume, n = 9.67 < (PIT), with p in pm Hg and Tin degrees kelvin. One area of continuing interest is that at intermediate energies- from roughly 20 eV upwards-where it is likely that, as the various theoretical approachesbecome stabilized,there will be a need for more precise measurements of U, and more detailed comparison of positron and electron data taken under the same experimentalconditions as has been done by Hoffman et af. (1982), Dababneh et al. (1982), and Kwan et af. (1983). Another important measurement would be that of e+- atomic hydrogen scattering, which is of considerable theoretical interest and also of interest for the interpretation of certain astrophysical observations (Drachman, 1982; Leventhal, 1985)-at present it still remains as a challenge to the experimentalists. Some recently published measurements of the e+-He total cross sections at energies between 0.6 and 22 eV by Mizogawa et al. (1985) are illustrated in Fig. 9a. As shown in Fig. 9b, these results, after applying corrections for forward scattering, are very close to the theoretical values of Campeanu and Humberston (1 977).

1

I

I

1

I

0 .15

I

(a)

0 .10

0.15 I

N

-

05 - 00.15

NO

E

0

b ’

0.10

b ’

0.10

O.OE

1

2

3

L

Positron Energy lev)

5

6

0.05

0

1

2

3

L

5

6

Positron Energy (eV)

FIG.9. Total cross sections for positrons in He. (a) The results of Mizogawa et al. (1985) with axial magnetic field values of 8 gauss (W) and 13 gauss (O),respectively,compared with the data of Stein et al. (1978) (A); Sinapius ef al. (1980) (V); and Canter ef al. (1973) (0).The theoretical curve (solid line) has been deduced from the work of Campeanu and Humberston (1977), Humberston and Campeanu (1980), and OMalley ef al. (1962). (b) Corrections for forwardscatteringappliedtothedataofMizogawaef al.( 1985). Solidlinesarethesameasin(a).

T. C.Grifith

54

Other recent work of interest has been the measurement by Floeder et al. (1985) of oT for the scattering of both electrons and positrons by a large family of hydrocarbon gases. CH,, C?H,, CzH4,C&, C,H, (propene and cyclopropane), C,H (n-butane and isobutane), and C,H, have been studied, and at positron (and electron) energies between 100 and 400 eV all the cross sections conform to an empirical fit represented by

o$(E)= uN,E-I/~[1 f b exp(- cE)]

(8)

where a, 6, and c are constants and N, the number of electrons in the molecule. The proportionality between o$ and N, at 100 and 200 eV is demonstrated in Fig. 10. These authors have also noted that for a given molecule a;(,!?) is always less than a&!?) and that both cross sections increase with the size of the molecule. They also note that atoms with the same number m of carbon atoms have cross sections of very similar magnitude and that these values were well spaced from those for the molecules with m 1 carbon atoms. The measurements of o, for alkali metal vapors by Stein et al. (1985) are an important technological achievement. Apart from atomic hydrogen the alkali metal atoms are the most important “single-electron’’ atoms to be studied. They also have the additional feature that their ionization potential lies below 6.8 eV so that they have no Ps formation threshold. Technically this experiment has almost the same degree of difficulty as that envisaged for atomic hydrogen experiments. The problem of confining the vapors to the

+

0

10

20

Ne

30

10

20

30

Ne

FIG.10. Total cross-sectionsfor (a) 100-and (b)200-eV positrons(+) and electrons (0)as a function of the number of electrons in the hydrocarbon target gas molecules, as measured by Floeder et al. (1984). The straight lines have been fitted using Eq. (8).

POSITRON A N D POSITRONIUM PHYSICS

55

interaction region has been solved using the high-temperatureoven or target illustrated in Fig. 1 1. Two-channel electron multipliers, out of direct line of the hot oven apertures and protected behind the cold end caps, are used to measure the incident and transmitted positron beam intensities after deflection of the beams in the repeller cages on either side of the oven. Results for 0;and a , determined for potassium with this apparatus are given in Fig. 12, and the notable feature of these results, not seen for any other target atoms, is the close similarity between the values of the cross sections for electrons and positrons. It is suggested that this is due to the fact that the high polarizability of the K atoms essentially swamps the static part of the interaction at these energies so that little difference between of and a, should be expected. Some new results by Kwan et al. (1985)for the scattering of electrons and positrons of energies in the range 1 to 500 eV in 0, and similar data by Kauppila et al. (1985a) for N,O, CH,, and SF, are very interesting because they show structural variations in the values of oTwhich are in remarkably close agreement with similar measurements reported by Charlton et al. ( 1980a) and Charlton et al. ( 1983a) for positrons in H,, N,, O,, CO,, and CH,. A series of measurementsfor electrons ofenergiesup to 50 eV taken in the same gases under the same conditions as for positrons was reported by Griffith et al. (1 982). Magnetic Reld Coils,

Input Aperture Plate,

output CEM

Piotes

Removable Cylinder’ (wlth Heater)

-

0

I

2 3 4

5cm

Cold Cap with Aperture

0

Thermocouple

FIG.1 1. Schematic diagram of the apparatus used by Stein et al. (1985) for measurements of alkali metal scattering cross sections.

T. C. Grifith

56 n

0

0

P

P

P 0

0

P

Energy (ev)

FIG. 12. Total cross sections for (0)positrons and (0) electrons scattered by potassium atoms as measured by Stein er al. (1985). Theoretical estimates for the elastic cross sections QB (--,Guha and Mandal, 1980;-,Bordonaro et al., 1976)andpositronium formation cross sections QPs(Guha and Mandal, 1980) obtained usingthe distorted wave approximation (---) and the first Born approximation (V) are shown.

Sueoka and Mori ( 1984) have also reported measurements of gT for positrons in N2, CO, and CO, . The abrupt rise in 0, at the threshold for the formation of excited-statepositronium, Ps*, in C02noted by Charlton et al. ( 1983a)and by Kwan et al. ( 1984) is quite noticeable in Fig. 13 and will be discussed again in Section II1,D. It is of interest to note that the same feature is also present for the N20 data of Kwan et al. (1984). B. DIFFERENTIAL ELASTIC SCATTERING CROSS SECTIONS

Differential cross sections for the elastic scattering of positrons were first reported by Coleman and McNutt (1979) for positrons in argon. They made

POSITRON AND POSITRONIUM PHYSICS

51

16

15

f

14

13

I

T

12 a,

I

1’

inad)

10 9

8

I 6

5 L

0

I

I

I

I

I

4

8

12

16

20

I 24

I

1

28

32

Energy lev)

FIG. 13. Total cross sections for positrons scattered in CO,: (B)Hoffman ef al. (1982); (0) Charlton ef al. (1 980a); (0)Charlton er al. ( 1 982a). The theoreticalcurves are by Horbatschand Darewych (1983). Curve (---) uses a fixed cutoff, and curve (-) an energy-dependent cutoff parameter in the polarization potential.

use of the fact that in the time-of-flight method discussed in Sections III,E and III,F the time-of-flight spectrum of the scattered positrons in the inert gases is solely dependent on the angular distribution for the scattering provided the incident positron energies are less than ER (in which case there is no inelastic scattering).As the angle of scatteringincreases so does the time of flight of the scattered positron and the time-of-flight spectrum can be partitioned according to the scattering angles. The spectra for positrons of energies between 2.2 and 8.7 eV scattered in argon were analyzed to yield the values of a(@, the differential scattering

T. C.Griflth

58

cross sections, in the range 20" < 8 < 60".They were found to be in reasonable agreement with the theoretical calculations of McEachran et af. ( 1979) and Schrader (1979). Coleman et al. (1980) have given a detailed analysis of the limitations of their method. Ideally, measurements of this nature would be better performed with narrow positron beams of well-defined energies in a crossed-beam arrangement. Such an experiment, for 100-eV positrons in Ar, has recently been reported by Kauppila et af. (1985b). Their system is illustrated in Fig. 14, where a low-energy positron beam (-2 X lo4 e+ s-l) is generated from a 50-mCi 22Nasource with an electrostatic beam transport system and an atom -beam source consisting of a multichannel capillary array in a differentially pumped scattering chamber. The incident positron beam is deflected on emerging from the chamber by the repeller into a channeltron detector placed off the direct line of fast positrons from the source. The scattered beam is detected at various angles by another channeltron detector whose entrance window is defined by a set of collimators viewing the scattering region. Retarding potential elements are used to reject inelastically scattered positrons. The system can be used with either positrons or electrons. The preliminary results for a range of angles between 30" and 120" are shown in Fig. 15, where the experimental data have been normalized at 45" to the theoretical curve computed by A. D. Stauffer and R. P. McEachran (private communication) using the polarized orbital approximation.

\*Y

Chonneltron Detector rY2 ,-Collimators

Lens Elements

U

L G o s Beom

[ e* Differential

Scattering Setup

FIG. 14. Apparatus used by Kauppila et al. (1985) for positron and electron differential elastic scattering cross-sectionmeasurements.

POSITRON AND POSITRONIUM PHYSICS 4

59

i

FIG. 15. Comparison of the differential elastic scattering cross sections for positrons (O), measured by Kauppila ef al. (1985), with the theory (-) of Stauffer and McEachran (private communication).

C. TOTALCROSSSECTIONS FOR THE FORMATION OF POSITRONIUM Experimental determinations of o , the positronium formation cross sections, have been discussed at length in recent review articles by Griffith ( I 984), Coleman ( 1 985a,b),and Charlton (1 985a). Positronium formation is undoubtedly the most interesting of the inelastic channels for positron atom/molecule interactions and its study continues to present surprising o were first obtained from the plots of and unexpected results. Estimates of , the total cross sections 0, for the inert gases as a function of positron energy. A linear extrapolation of the elastic cross sections gel,from below the Ps formation threshold Epsup to Eex,the first electronic excitation energy, gave a value of , o at Eexusing the simple difference expression, , o = 0, - o,,. It was also possible, on adopting a number of plausible assumptions,to deduce a value for both oh and the excitation cross section oa, at the ionization threshold Eifor all the inert gases by using the values of the Ps fractions F determined in the lifetime experiments reported by Coleman et al. ( 1 975) and from the gas mixture results given by Charlton et al. (1 979). All the above work is now superseded by three differentand independent

60

T. C,Grifith

methods that have been used for a direct determinationof a, as a function of positron energy using positron beams. In the first of these methods the University College London (UCL) group (Charlton et al., 1980b, 1983b; Griffith, 1984) have measured the 37 coincidence rate for 0-Ps formed in a differentially pumped gas cell through which the variable-energy positron beam was steered in the same manner as for the total cross-section measurements. Fornari et al. ( 1983)at the University ofTexas at Arlington (UTA),in a sharply contrasting method, have observed the transmission of positrons in a strong axial magnetic field through an extended gas cell; the number of positrons “lost” during transmission through the gas was attributed to the formation of either paraps or 0-Ps. The third measurement, also distinctly different, has been that by Fromme et al. (1985), where a, in helium was deduced by distinguishing between the ions formed by impact ionization and those due to formation of para-Ps and 0-Ps (see Section 111,E).All three measurementsshow a rapid rise in a, from the threshold E, for all the gases investigated,and they also indicate that a substantialamount of Ps is formed at positron energies above 100 eV. There has, however been a serious disagreement between the values for , a measured by the first two groups, with UTA reporting cross sections of magnitude about three times greater than the UCL results at some energies. The preliminary results for helium by Fromme et al. (1985) appear to favor the UTA data. The magnitude of the values of , o are large, but recent calculations for He by Khan and Ghosh (1983) give values which are only slightly lower than the UTA results. The results for He and H2 are reproduced in Figs. 16a and 16b, respectively. The UCL results cover a range of energies from 5 to 150 eV in all the inert gases and the molecular gases H,, N, ,0, ,C02,and CH, .The earlier UTA measurements were restricted to He, Ar, and H and for these gases there is good agreement with the UCL data at energies up to about 2 eV above the E, thresholds and then the measured values diverge sharply as the energy increases. The UTA workers have recently extended their Ar data to 441.3 eV (Diana et al., 1985a) and have also reported some preliminary results for Kr and Xe at energies up to 350 eV. Both experiments may be subject to systematic errors, but, as discussed by Charlton (1985a),the UCL data were subjected to various tests to check the effect of premature quenching of the 0-Ps on the cell walls and also to investigate the escape of fast positronium through the exit aperture. The UCL data were normalized using the values of , a obtained from a, on the assumption that the elastic cross sections could be extrapolatedlinearly from below E,. Recent calculations by Brown and Humberston (1985)for atomic hydrogen indicatethat a, is in fact decreasingat energiesgreaterthan &and that the normalization procedure used by the UCL group might involve an underestimate of the cross sections by as much as 30%. Brown and Humberston (1985) have also

61

POSITRON AND POSITRONIUM PHYSICS

o'67 !N I

I

2

01

I

hsitron Energy (eV)

0

10

20

30

40

50

60

70

80

Positron Energy (eVI

FIG. 16. Positronium formation cross sections as a function of energy. (a) Helium: (H) Charlton et al. (1983); (V)Fornari et al. (1983); (A) Diana ef al. (1985); (0)Fromme et al. (1985); (-*-) theoretical curve by Khan and Ghosh (1983). (b) Molecular hydrogen: (0) Fornarief al.(1983);(0)Charltonetal.(1983);(-X-)LifetimedataofCharltonetal.( 1979); ()curve for u,, = (ar- ue,);(- .. -)theoretical curve by Bussard et al. (1979) for chargeexchange cross sections.

noted that, for atomic hydrogen, the emission of positronium formed in the collisions becomes increasingly confined to the forward direction as the positron energy increases. If this is true then the tests that were performed to check for the escape of fast Ps were possibly limited to aperturesthat were too large to observe significant variations. These two factors alone should bring the measurements closer together, but there are plans at UCL for remeasur, a ing . It is of interest to re-emphasize that the UCL method is based on direct observation of 0-Ps, while the other methods observe both 0-Ps and para-Ps without distinguishing between them. It has been suggested that (e+,e-) correlations (see Section II1,F) might account for some of the difference between the measurements at the lower energies but, as noted by Coleman (1 985b),the difference increases with energy and is much too large to be due to correlation effects. Coleman (1985a)has suggested that the discrepancy is due to 0-Ps quenching on the walls of the gas cell. It is observed that curves diverge sharply at roughly 2 eV above the positronium thresholds and, if this effect is due to wall quenching, it might be of some significancefor the study of Ps- surface interactions. There are good reasons for investigating the source of the discrepancy and the ultimate check will be that, at any energy, the sum of the elastic, impact ionization, Ps formation, and excitation cross sections, all measured independently, should add up to the measured value of a,.

T. C. Grijith

62

The possibility that the Ps formed in e+-atom collisions is peaked in the forward direction, as noted by Brown and Humberston (1985), has important consequences for the production of Ps beams and hence for studying Ps scattering and Ps- surface interactions. It is a way of producing Ps beams of well-defined energy. The alternative proposal for such beams, suggested by Mills ( 198l), would involve a much more complicated system; his method is based on the production of a beam of Ps negative ions, Ps-, by passing positrons through a thin carbon foil and then photoionizing the Ps-to get the 0-Ps beam. Mills and Crane (1985) have, however, recently reported that energetic 0-Ps is also produced by positrons traversing thin carbon foils. Preliminary measurements on the angular dependence of Ps emission in e+-argon collisions have been reported by Laricchia et al. (1985a) and look very promising. The positron beam was passed axially through an 8-mm input aperture into a gas cell of length 20 mm. The 0-Ps formed in the gas emerged through the upper half of an 8-mm-wide slot in the output plane to be detected, 120 mm downstream from the center of the gas cell, in a channel electron multiplier (CEM) positioned initially on the axis of the positron beam. Suitably biased grids in front of the CEM excluded any background due to electrons and slow positrons so that only the 0-Ps atoms impinging on the CEM were counted. The measurements displayed in Fig. 17 show the CEM counting rates, obtained from alternate gas and vacuum runs, as a

8r---------,

0

’

”

”

5

”

10 Positron Energy

(eV)

”

”

’

7

XlO’

l5

FIG. 17. Channeltron detector counts due to DPS formed in e+-Ar collisions with the detector placed (0)on the beam axis; (A) 1 cm off the axis; and ( x ) 2 cm off the axis. Measurements by Laricchia et d.(1985a).

POSITRON AND POSITRONIUM PHYSICS

63

function of positron energy. The counts are seen to increase as expected at the positronium formation threshold for argon. On displacing the CEM off-axis through transverse distances of 10 and 20 mm, respectively, the counting rates at the same positron beam energy fell rapidly, and it is concluded that 40% of the 0-Ps formed in argon by positrons of energy greater than 20 eV are confined within a forward cone of angle less than 5 '. There are grounds, therefore, for reasonable optimism that substantial beams of positronium of well-defined energies, given by E+, = E,, - E,, will soon be available for experiments.

D. THEFORMATION OF EXCITED-STATE POSITRONIUM IN GASES Conclusive demonstration that positronium in its first excited state, Ps*, could be detected was given by Canter et al. ( 1975). This was accomplished by detecting the uv radiation of energy 5.1 eV from the 2P- IS transition of Ps* using a photon counter and an NaI(T1) scintillator, which detected one of the annihilation y rays from the decay of the ground state Ps, in delayed coincidence. The reaction involving the Ps* transition is as follows Ps;-2+

.1

3.2 ns

hv

+

Ps

-37

3.

142 ns

Ps* does not survive to be detected in lifetime experiments,but in positron beam experiments, using gas at low density, the chance ofa Ps* collision with a gas atom/molecule is so small that it has a high probability of experiencing a 2P- 1Stransition to its ground state. Laricchia et al. (1985b) have shown that it is possible to detect Ps* under these conditions and have investigated its production yield as a function of positron energy in a number of gases. The binding energy of the first excited state is only 1.7 eV, so that the formation threshold is very close to the ionization threshold and the results Ar, and Ne show the characteristic rise from the Ps* given in Fig. 18 for H2, threshold that was familiar for the work on ground-state Ps discussed in Section III,C. The scattering chamber used by Laricchia et al. (1985b) is illustrated schematically in Fig. 19. A positron beam of variable energy traverses the differentially pumped gas cell placed between the Ps Lyman-a counter and the NaI(T1) counter which detects the annihilation y ray. The photon counter was a water-cooled EM1 9829A photomultiplier with a sensitivity range for photons of energy between 2.1 and 6.2 eV and a dark count of about 50 s-*. The walls of the chamber were lined with glass which was

T. C. Grifith

64

70

12

14

16

18

20

22

24

26

28

30

32

34

36

Positron Energy 1 eV)

FIG.18. Measured yield of Ps*as a function of positron energy for (0)HZ; (0)Ar; and (A) Ne, as measured by Laricchia el al. (1985b).

coated with A1 and M C 2 to enhance the uv reflectivity. Provisions were made for the insertion, when required, of a 3-mm-thick borosilicate glass shutter between the gas cell and the photon counter in order to stop photons of energy 24.3 eV from reaching the counter. The time resolution of the system was 8 ns FWHM and a typical spectrum for argon gas, taken without the glass shutter, is shown in Fig. 20; it shows the long-livedcomponent with a decay rate of 7 - 10 pus-' to the left of the prompt peak at t > 0 and also a significant signal to the right at t < 0. Insertion of the borosilicate shutter usually removed the long-lived component, thereby confirming that this signal was due to the photons of energy 2 4.3 eV attributed to the Ps* transitions. The signal at t < 0 was always unaffected by the shutter and has been attributed to reactions of the type e+ A + e+ A**, where the prompt annihilation of the positron into 27, on striking an aperture in the scattering cell, givesthe start pulse and a stop pulse results from a delayed photon due to the highly excited (n 3 3) atomic (or molecular) state, A**. Laricchia et al. (1985b) have estimated the maximum yield of Ps* in most Ps* per incident e+, and it is noted that this yield gases to be around 5 X is a factor of 14greater than that quoted by Schoepf et al. (1 982) for positrons incident upon a cleaned polycrystalline tungsten surface in high vacuum. It was mentioned in Section II1,A that the results of both Hoffman et al. (1982) and Charlton et al. (1983a) show a sharp rise in the values of oT for CO, at the formation threshold for Ps*. CO, was, therefore, an obvious

-

+

+

POSITRON AND POSITRONIUM PHYSICS

65

uv reflecting surface of glass tubing with Al + Mg F, overcoats

/cornposed

1

Nal ( T I 1 counter

FIG. 19. Schematic illustration of the scattering cell used for the Ps* measurements by Laricchia ef al. (1985b).

candidate for investigation to see whether a large amount of Ps* was indeed formed in this gas. The spectrum given in Fig. 2 1 shows a large signal both at t > 0 and t < 0. Insertion of the borosilicate shutter, however, only removed a small amount ofthe (supposedly)Ps* signal at 1 > 0. It has to be concluded, therefore, that the sharp rise in 0, and the large signal observed in this experiment is due to some process that may involve ground-state Ps but not the formation of Ps*.

'1

T. C.Grijlith

66

-*

30

25

In

;20

a

u z c

0

z

10 35 10

5

.*

0

0

5

10

15

20

25

Channel

30

35

40

45

50

Number

55

I

XlOl

60

FIG.20. Photon-annihilation p r a y spectra (4.0 ns per channel) obtained for 17-eV positrons in Ar gas: (0)glass shutter retracted (run time = 53 000 s); (*) glass shutter inserted.

E. POSITRON IMPACTIONIZATION CROSSSECTIONS The first attempt to unravel the inelastic processes for positron-atom/ molecule collisions was reported by Griffith et al. (1979), where incident positrons of well-defined energy were used in a time-of-flight method and the energy distribution ofthose positrons inelastically scattered by helium atoms was recorded and analyzed. It was concluded that, at incident positron energies between 100 and 500 eV, impact ionization appeared to be the dominant process and, assuming known values for the excitation cross sections 0, for electrons and the positron elastic cross sections,they were able to estimate some values for aznat these energies. Using a similar time-of-flight technique Coleman and Hutton ( 1980)and Coleman et al. ( 1982) have investigated and obtained values for the excitation (over a limited range of energies) and for the sum of excitation plus ionization cross sections at positron energies up to 50 eV in He, Ne, and Ar. A similar method, modified in such a way (see Section II1,F) that excitation and ionizing collisions can be separately assessed, has been used by Sueoka ( 1982)to extend the measurements in He up to 120 eV. At energies 22 30 eV the values reported for ofnare close to those observed for electrons and this observation may, cautiously, be interpreted as implying that the exchange contribution in electron-atom scattering is not very large at the higher energies.

POSITRON AND POSITRONIUM PHYSICS

67

lo3 0

8

... . 0 .

6

.. .. *.

L

.' .

*.

*.

v)

U 0

c

2

al u

0

...

0..

0.

.-0

U

x

?!

' lo2 F

-. .*

.*

... ... .

... .

.*

1.8

r >

-$

.. ..*

6

.. .. .*

L

*.

.

2

10'

. .....

I

I

I

-160

-a0

o

I

I

ao

I

I

,

160

l

2co

1

1

320

1

1

1

LOO

Time in ns re!ative to t = 0

FIG.2 1. Photon-annihilation pray spectrum for 14-eV positrons in CO, gas, as measured by Lancchia e? al. ( I985b). The run time was 64 000 s ( 1 channel = 4.0 ns).

More recent investigationsof positron ionizing collisionshave used different methods from those discussed above. Diana et al. (1985b)have investigated positron impact ionization of helium atoms at energies up to 200 eV by detecting the ejected electrons using a retarding field analyzer. Their results are included among others in Fig. 22b. Another novel method of measuring both impact ionization and Ps formation (see Section III,C) has

T. C.Grifith

68

I Positron Energy (eV)

Positron Energy (eV)

FIG.22. (a) Sum of impact ionization and positronium formation cross sections for psitrons in He as a function ofenergy:(0)Fromme ef al. (1985);(-X-) theoretical calculations by Willis and McDowell (1982); (-) qo, for , electrons by Montague et al. (1984). (b) Positron impact ionization as a hnction of energy: (0)Fromme ef al. (1985); (*) Sueoka (1982); (A) Diana ef al. (1985); (- * -) theoretical curve by Basu et al. (1985); (-) electron results of Montague ef al. ( I 984).

recently been developed at Bielefeld, and results from this work have been reported by Fromme et al. (1985). In their method the ions produced by positron collisions with gas atoms in a long thin tube are extracted by being accelerated down the tube in a weak electrostatic field. As shown in Fig. 23, beam transport is accomplished using a longitudinal magnetic guiding field and electrostatic lenses (the ions are also confined by the magnetic field). An E X B field analyzer at the exit of the scattering chamber is used to separate the ions and the positrons. The positrons are only slightly affected by the analyzer so that they continue on their path to the microchannel plate detector at the end of the system. The ions are, however, deflected sideways through 90" and accelerated up to 4 kV and into another microchannelplate (MCP) detector at the side. Delayed coincidences between the two detectorsare recorded, and a peak in the time distribution corresponds to detection of the positron and ion involved in the impact ionization represented by He e+ ---* He+ ee+. When Ps is formed according to the reaction He e+ 4He+ Ps only the ions alone are recorded. A count of all the ions on one hand and of those ions in coincidence with the positron on the other gives the ratio of

+

+ +

+ +

69

POSITRON AND POSITRONIUM PHYSICS

Stainless steel tube Glass tube Tunpsten spiral

Detector 2

Coils

Positron source

Moderator

n l I To pump

lions]

ector 1 ’ (positrons)

Scattering tube

I

0

PUMP

E Y 6 mass spectrometer

FIG.23. Apparatus used by Fromme ef al. (1985) to measure ionization cross sections for positron- He collisions.

total ionization (Ps plus impact) to impact ionization. The authors report that fewer than 10%of the expected number of ions were detected, probably because the axial magnetic field was not large enough. This factor, together with the uncertainty about the efficiency of the MCP for ion detection, meant that some normalization procedure had to be adopted to evaluate cross sections. This was accomplished by repeating their observations with electrons instead of positrons and matching the relative values of a , obtained with electrons to the electron data of Montague et al. (1984). At energies above 200 eV the convergence of the values of a;f and:a reported by Kauppila et al. ( 1981) was used for the normalization of (a, of) to a ; , assuming that ,a + 0 at these energies. The normalized results for (oh a;,) as a function of energy are compared with the theoretical estimates of Willis and McDowell(l982) in Fig. 22a. In Fig. 22b the normalized values of a&, obtained from the delayed coincidence counts are shown to be in good agreement with the theoretical values of Basu et al. (1985). They are, however, significantly larger than the correspondingvalues measured by Sueoka (1982) and also the values of a ; , for electrons measured by Montague et al. ( 1984). It is difficult to avoid the conclusion that there may be a systematicerror in one of the measurements. The values of a, obtained from the difference between (a, of) and a ; , (coincidence) are given in Fig. 16b and were discussed in Section II1,C.

+

+

+

70

T. C.Grijith F. CROSS SECTIONS FOR ATOMICEXCITATION IN POSITRON COLLISIONS

In their estimates ofa, for the inert gases from lifetime spectra (seeSection III,C), Coleman et al. (1975) were also able to extract approximate values of the excitation cross sections a& for these gases at the ionization energy Ei. Direct measurements of at; were later performed by Coleman and Hutton ( 1980) using the time-of-flight technique mentioned in Section III,E. These authors analyzed the energy distribution of positrons with incident energies E,+ of 5 30 eV scattered by He atoms and concluded that at energies up to 10 eV above the first excitation threshold E,, the secondary peak in the spectrum of the scattered positrons was due to positrons that were exclusively associated with atomic excitation. At higher energies it was not possible to distinguish between positrons that were involved in excitation from those associated with ionizing collisions; only the sum (ot; a;,,) could, therefore, be deduced at the higher energies. Coleman et al. (1982) have used the same apparatus to extend these measurements to incident positron energies of 50 eV in He, Ne, and Ar. It was concluded that at positron energies up to 30 eV in helium the dominant channel appears to be that due to 1'S-2'S excitation. Careful examination of the secondary peaks at low energy have also led to the conclusion that, after the collisions, the positrons involved with atomic excitations in He were confined to angles 5 50" of the forward direction and to smaller angles in Ne and Ar. These observations are in agreement with the recent calculations for He by Purcell et af. (1983). The recent work by Sueoka (1 982), mentioned in Section III,E, was performed using a similar time-of-flighttechnique, and values of af at energies up to 120 eV have been determined. This was achieved by using a retarding field on a grid in front of the CEM detector at the end of the flight path to exclude positrons involved in ionizing collisions, viz., scattered positrons experiencing an energy loss ?(lie+- Ei).The results for G;,, discussed in Section III,E were obtained by subtracting the spectra obtained at a given positron energy with the retarding field applied from those with the retarding field switched off. The author reports that no ionizing collisions were detected in He at incident positron energies less than 30 eV. This is the energy region where the (e+,e-)correlations (see Section II1,C) might be expected to be strong and where the positron may either form positronium or some other complex which results in its annihilation. Klar (1981), Temkin (1982), and Geltman ( 1983)have all estimated the values of a;,, and ,a at energies near the threshold Ei, but their predictions are not in good agreement with one another. It might not, therefore, be unreasonable to expect that the measured values of o;,, for electrons are larger than those for positrons in the energy

+

POSITRON AND POSITRONIUM PHYSICS

71

0.1-

0.08

-

-

0.06 -

NO

n ti

1's - 2's

6 0.01-

-

b

0.020.0-

I

A I

A I

I

-

I

range Ei < E,, 5 30 eV. This appears to be the case for the values of &c determined by Sueoka (1982)but, as seen in Fig. 22b, the results of Fromme et a/. (1985) for positrons, discussed in Section III,E, lie above the corresponding electron values at all energies. The excitation cross sections for He are given in Fig. 24, where it is seen that for positrons of energy greater than 30 eV the values are appreciably greater than those for (,a l1S-2IS) alone for electrons. This observation implies that the contribution from higher excited states is appreciable in positron collisions at the energies under consideration. Most of the crosssection measurements discussed in this section and in Section III,E may be subject to systematic errors which have not yet been thoroughly assessed. Much further work is required before arriving at any firm conclusions regarding the true magnitude of the various cross sections that have been measured.

ACKNOWLEDGMENTS The author is much indebted to Dr. Michael Charlton for many valuable comments and discussion. Thanks are also due to the other members of the positron physics group at University College, namely Dr. G. R. Heyland, Dr. C. J. Beling, Dr. P. J. Curry, Dr. F. M. Jacobsen, Mrs. G. Laricchia Drinkwater, and Miss S. A. Davies. Much of the University College work

72

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discussed in this article has evolved from the inspired encouragement given by the late Sir Harrie Massey and as a tribute to his memory it is immensely pleasurable to acknowledge our gratitude to him. Grateful acknowledgement is given to Miss Una Campbell for preparing many of the diagrams and to the Photographic Unit for their invaluable assistance with the prints. Most of the University College work discussed in this article has been funded by the Science and Engineering Research Council, to whom we are duly grateful.

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