-
+ O2
(15) CH302 + NO CH30 +- NOz (16) CH30 NO or O2 CH,O IlNO or H02 (17) CH3
+
403
J. Phys. Chem. 1900, 84, 483-488
CH302
(6) J. M. Heuss and W. A. Glasson, fnviron. Sci. Techno/., 2, 1109 (1968); S.L. Kopczynski, R. L. Kuntz, and J. J. Bufalinl, ibid., 8, 648 (1975). (7) S.L. Kopczynski, Int. J . Air Water Pollut., 8, 107 (1964). (8) T. Katou and Y. Hanai, Bulletin of the Instfiute of Environmental Science and Technology (in Japanese), Vol. 2, Yokohama National University, 1976, p 1. (9) K. Nojima, K. Fukaya, S. Fukui, and S.Kanno, Chemosphere, 5, 247 (1974). (10) N. Washida, G. Inoue, H. Akimoto, and M. Okuda, Bull. Chem. SCC. Jpn., 51, 2215 (1978). (11) N. Washida, H. Akimoto, H. Takagi, and M. Okuda, Anal. Chen?., 51, 910 (1978). (12) M. Hoshlno, H. Akimoto, and M. Okuda, Bull. Chem. SOC.Jpn., 51, 718 (1978). (13) H. Aklmoto, M. Hoshino, G. Inoue, M. Okuda, and N. Washida, Bull. Chem. Soc. Jpn., 51, 2496 (1978). (14) P. S.Bailey, Chem. Rev., 58, 925 (1958); W. P. Keaveney, R. V. Rush, and J. J. Pappas, Ind. Eng. Chem., Prod. Res. Devel., 8, 89 (1969). (15) W. H. Chang, R. J. Nordstrom, J. G. Calvert, and J. H. Shaw, Envirtn. Sci. Technol., 10, 674 (1976); C. H. Wu, C. C. Wang, S.M. Japar, L. I.Davis, Jr., M. Hanabusa, D. Killinger, H. Niki, and 8. Weinstock, Int. J. Chem. Kinet., 8, 765 (1976); R. A. Cox and R. G. Derwent, J. Photochsm., 6, 23 (1976/77). (16) D. A. Hansen, R. Atkinson, and J. N. Pitts, Jr., J . Phys. Chem., 79, 1763 (1975). (17) R. Atkinson and J. N. Pitts, Jr., J. Phys. Chem., 78, 1780 (1974). (18) R. A. Perry, R. Atkinson, and J. N. Pitts, Jr., J . Phys. Chem., 111, 296 (1977). (19) E. Orovenstein, Jr., and A. J. Mosher, J. Am. Chem. Soc., 92, 3810 (1970). (20) K. R. Darnall, R. Atkinson, and J. N. Pitts, Jr., J . Phys. Chem., 113, 1943 (1979). (21) H. A. Wiebe, A. Villa, T. M. Hellman, and J. Heicklen, J. Am. Chem. SOC.,95, 7 (1973); W. A. Glasson, Environ. Sci. Technol., 9, 1048 (1975); P. M. Cox, R. G. Derwent, P. M. HoL, and J. A. Kerr, J. Chem. SOC.,faraday Trans. 1 , 72, 2044 (1976).
+
were done for m- and p-xylene. For the high-boiling point products, products were almost the same found in the case of o-xylene except for the difference in the isomers of the products. In the low-boiling point products, biacetyl could not be found and the amount of methylglyoxal was increased. In the case of m- and p-xylene, since biacetyl, which should be measured with both FID GC and GC/ PIMS, was absent, results for the high- and low-boiling point product measurements could not be combined.
References and Notes (1) W. A. Lonneiman, T. A. Bellar, and A. P. Altshuller, fnviron. Sci. Technol., 2, 1017 (1968); A. P. Altshuller, W. A. Lonneman, F. D. Sutterfield, and S. L. Kopczynski, ibid., 5, 1009 (1971); W. A. Lonneman, S.L. Kopczynski, P. E. Darley, and F. D. Sutterfiekl, ibM., 8, 229 (1974). (2) N. Ito, K. Nakano, S. Izumikawa, T. Hirono, MI. Funashima, K. Asakuno, H. Kobayashl, M. Hayafuku, H. Yokoto, and T. Ohdaira, “Fbsearch and Survey 01 Photochemical Smog in Tokyo”, 3rd report, The Tokyo Metropolitan Research Institute for Environmental Protection (in Japanese), 1974, p 307; T. Chikamoto and K. Sakoda, J. Jpn. Soc. Air Pollut. (in Japanese), 12, 389 (1977). (3) K. R. Darnall, A. C. Lloyd, A. M. Winer, and J. N. Pitts, Jr., Environ. Sci. Technol., 10, 692 (1976). (4) R. E. Huie and J. T. Herron, Prog. React. Kinet., 8, I (1975). (5) National Research Council, Committee on Medical and Biologic Effects of Environmental Pollutants, ”Ozone and Other Photochemical Oxidant!?.. Aerosol”, Washington D.C., National Academy of Sciences, 1977.
Positraniurn Formation and Quenching in Argon-Oxygen Mixtures’ Richard L. Klobuchar2 and Paul J. Karol* Department of Chemistry, Carnegie-Mellon fJniversity, Pittsburgh, Pennsylvania 152 13 (Received August 8, 1979; Revised Manuscript Received October 12, 1979) Publication costs assisted by the National Science Foundation
The cross section for the quenching of orthopositronium by molecular oxygen was determined to be (1.0 f 0.1) X cm2. Both lifetime measurements and the two-photon coincidence rate difference method were used. The latter technique also provided a measurement of the fraction of positrons which form positronium in argon-oxygen mixtures as a function of composition at a total pressure of 5.60 atm.
Introduction Two of the major directions in the field of positronium chemistry in the past several years have been the study of the formation (or inhibition of formation) of positronium and the quenching of orthopo~itronium.~The various experimental techniques measure the annihilation of positronium into two or three annihilation photons. Quenchiing of long-lived orthopositronium (0-Ps) may be conveniently grouped into three processes (conversion, pickoff, and chemical reaction) each possessing a characteristic reaction rate (K, A,, and Ach). The cross section (u) for each process may be obtained from the reaction rates with elementary relationships K =
A, = nu+
(1) (2)
Xc. = n u , h u
(3)
nuku
0022-3654/80/2084-0483$01 .OO/O
where Uk, up, and Uch are the effective cross sections for conversion, pickoff, and chemical reaction, respectively; n is the concentration of the species affecting the desired removal; u is the average velocity of thermalized positronium (v = 7.6 X lo6 cm s-l at 25 “C). The individual rate constants can be deduced from observed changes in twophoton or three-photon annihilation rates by application of appropriate annihilation relationships. Alternately, since the three processes “shorten” the lifetime of positronium, the rate constants may be deduced from changes in the logarithmic slope of decay curves obtained in lifetime measurements. Quantitatively, quenching cross sections for chemical reactions are typically on the order of cm2,while cross sections for conversion and pickoff in a number of gasses O2 are on the order of and cm2,re~pectively.~,~ and NO are examples of gases which quench via conversion and noble gases via pickoff mechanisms. Compounds 0 1980 American
Chemical Society
484
The Journal of Physical Chemistry, Val. 84, No. 5, 1980
which have been observed to quench via chemical interaction include the halogens and NO2 (N20,).5 The fraction of positrons which form positronium in a given medium is determined by microscopic “slowing down” properties of the medium and the availability of electrons. Ionization potentials and the accessibility of efficient channels for removal of excess kinetic energy are particularly important. The fractional change in the gross two-photon coincidence rate upon adding a quenching species to a pure background gas offers a convenient method by which enhanced quenching can be separated from enhanced formation of positronium. It has been employed for the first time in this work as a means for determining both the 0-Ps quenching cross section on oxygen and the variation of positronium formation probability with composition in argon-oxygen mixtures. In conjunction with other experimental methods, the gross two-photon method is a useful additional tool for elucidating complex positron and positronium interactions. The major disadvantage is that high pressures ( 5 atm) are required to stop a significant fraction of positrons in the gas. N
Klobuchar and Karol
SOURCE -DETECTOR GEOMETRY T W O - P H O T O N APPARATUS ,Lead
/ L e f t Detector
Lead
Cham bar
Ta - Backed
Right D e t e c t w
Source Region of High Detection E f f i c i e n c y
Figure 1. Two-photon collinear coincidence arrangement of detectors, sample chamber, and tantalum-backed positron source placed off-axis. ‘?Na SOURCE
rn POWER
Experimental Section The positron source, 22Na,was obtained from ICN Corp.6 in the form of carrier-free 22NaC1dissolved in 0.5 N HC1. The activity was diluted and individual sources were prepared by pipetting and slowly evaporating the liquid to dryness in a teflon beaker to drive off the HC1. Teflon was chosen because of the slight tendency of carrier-free radiosodium to exchange with the sodium atoms in glass. Since teflon is hydrophobic, the evaporating droplets of solution did not disperse as they would on glass. For lifetime studies, less than 10 pCi of 22Nawere deposited on a 0.25-mil mylar film (-0.9 mg cm-2) and evaporated to dryness. The activity was confined to a spot with a diameter less than 3 mm. The spot was “fixed” by spraying the mylar with a thin film of clear Krylon. The Krylon added less than 0.3 mg cm-’ to the total source thickness. The mylar film was then folded over and cemented to a stainless steel wire loop with Varian highvacuum epoxy cement and suspended in the experimental chamber. Sources prepared in this manner were estimated to have less than 6% self-absorption of 22Na positron^.^ For the two-photon coincidence rate studies, a different source configuration with a higher specific activity (approximately 40 pCi) was found to be satisfactory. As above, the activity was transferred by micropipet, but was “fixed” as a spot of less than a 3 mm diameter on a 6.1-mil tantalum (Ta) foil. Tantalum is virtually immune to chemical attack by common acids and bases at temperatures less than 150 “ C and possesses a large backscatter coefficient for 22Napositrons.8 This latter feature makes it feasible to position the source away from the region of high detection efficiency and to “beam” the positrons into that region thus minimizing undesirable source and wall effects. The chamber which contained the pressurized gas sample was a type 304 stainless steel cylinder with an outer diameter of 12.7 cm and a volume of 2 L. Auxilliary ports were employed for pressure measurements and gas manipulations. A Trerice 500X compound gaugeg was used for precise pressure determination from vacuum to 300 psi with an absolute accuracy of *1.5 psi and sensitivity of h0.5 psi for relative measurements. Other ports used were for high-pressure inlet and high-vacuum exhaust. The oxygen was commercial grade (Linde,lo 99.6%). Strongly interfering impurities such as NO2 (and N204)and the halogens were removed by passing the gas through a dry
\%
2r=276nsec
Figure 2. Two-photon coincidence counting electronics block diagram showing NaI detectors, photomuttipllers (Ph4T) and their bases (B) dynode (d) output to preamplifier (PA), amplifier (A) stabilizer (S),timing single-channel analyzer (TSCA), coincidence module (C), multichannel analyzer (MCA), and clock control (CTB).
ice/acetone cold trap. The experimental chamber was filled with oxygen to near atmospheric pressure. Argon was added through a dry icefacetone slurry until the total chamber pressure reached the operating level (75 psi). The oxygen concentration was varied by bleeding out a small quantity of mixture and repressurizing with argon. Preliminary experiments revealed that the results obtained with the bleeding technique were substantially the same as when the chamber was totally evacuated and repressurized for each measurement. To check if the slightly different stopping power of oxygen was adversely affecting the range distribution of positrons and ultimately the coincidence count rate, similar counting experiments were performed with neon-argon mixtures. No deviation in the count rate attributable to changes in the range distribution was ever observed. This seems plausible in consideration of the relatively flat pressure-count rate plateau evident in the argon measurements described below. The diluting gas would have to have a radically different stopping power to shift the plateau perceptibly. The two-photon coincidence apparatus and lifetime spectrometer system were standard arrangements. Figure 1 shows the two-photon coincidence geometry of the tantalum-backed 2*Na positron source, the two collinear NaI(T1) detectors, the lead shielding, and the sample chamber. The positron source was positioned away from the detector-detector axis to minimize detection of source events. Lead shielding was also arranged to limit direct detection of source annihilations and 1275-keV y rays.
The Journal of Physical Chemistry, Vol, 84, No.
Positroniuim Formation and Quenching in Ar-0,
SOURCE
5, 1980 485
-
DETECTOR GEOMETRY LIFETIME SPECTROMETER /Lead
Chamber
I I'
F Stop D e l e c l o r S t a r t Detector
,
61n
I
Flgure 4. Geometric arrangement of lifetime system.
TABLE I : Summary of Oxygen Quenching Cross Sections ( U k ) " I b 10-1g U k , cm2 -3.4 -0.87
Flgure 3. Positron lifetime spectrometer electronics block diagram showing detector anode output (a) to constant fraction timing discriminators (4,63). Other components as in Figure 2.
Figure 2 is a block diagram of the coincidence counting electronics employed in this investigation. Gain changes manifested as shifts in the y-ray energy spectrum were eliminated by analog gain stabilization. The stability of the entire two-photon coincidence system was periodically checked and long- and short-term stability limit13 were established. For relative experiments which were performed over an interval of less than 24 h, counting data could be obtained (provided sufficient statistics had been accumulated) with instrumental contribution of less than 0.2% to the total uncertainty. Over a period of 10 days, the worst drift ever observed was less than 0.9%. For the cross section experiments, count rate stabilikg of the apparatus was accurate to 0.25% over an interval of 3 days. This latter value also includes errors in repetitive loading of the chamber with the required amount, of oxygen and pressurizing it with argon and is considered t o be more typical of the data precision obtained in this work. Experiments were performed which verified that changes in the coincidence rate are due to the introduced impurity and not due to potential errors in filling the chamber at fixed geometry to an established working pressi.ue. These experiments employed pure argon as a pressurizing gas, in which the two-photon counting rate was found to be constant to within 1%over the interval 60-90 psi, with the apparent center of the plateau a t 75 psi. Ovorall, the two-photon coincidence apparatus which was designed, constructed, and characterized for these investigations proved to be adequate and stable in all respects. The lifetime spectrometer was assembled as a fast-slow coincidence system with a resolution of 4.4ns (see Figure 3). This was sufficient for determination of the long-lived 0-Ps lifetimeti. The lifetime spectrometer detector arrangement is shown in Figure 4.
Results a n d Discussion The quenching of positronium by oxygen-argon mixtures has been previously studiedl, most recently by Mokrushin and Goldanskiill a t 30-1120 atm. Quenching cross sections in the past have been measured for pure gases by three-photon counting, annihilation singles counting, two-photon coincidence counting, electric and magnetic field studies, delayed coincidence techniques, and positron lifetime spectra. The merits and pitfalls of each technique have been thoroughly discussed in ref 12. It is
method
delayed coincidences two-photon coincidence and annihilation spectrum -1.1 annihilation spectrum 1.1i 0.1 lifetime spectrum >2.9 lifetime -1.0 electric field 3.2 i 0.6 narrow component in angular correlation 2.3 lifetime spectrum 1.2 * 0 . l c lifetime spectrum 1.0 i 0.1 lifetime spectrum and two-photon coincidence difference method
ref
14 15
16 17 18 19 11 5 20 this work
Velocity of thermalized positronium u = 7 . 6 X l o 6 cm Intrinsic decay constant of 0-Ps: h t = 7.05 X 10" Annihilation on 0, in pores of silica gel with diarnes-l. ter > l o 0 A . a
s-l.
sufficient to note that quenching cross sections derived from the logarithmic slope of the long-lived component in lifetime spectra are the least ambiguous and most easily obtained. Nevertheless, various authors have employed all of the listed techniques with varying degrees of success over the past 25 years. The cross sections for positronium quenching by oxygen are summarized in Table I. In all cases, the average velocity of thermalized positronium has been normalized to 7.6 X lo6 cm s-l and the intrinsic decay constant13 for orthopositronium has been set to 7.05 X lo6 s-l. Inspection of the tabulated results prior to this work reveals that the quenching of positronium by oxygen can be explained by a cross section on the order of 1 to 3 X cm2. The reason for this apparent imprecision is unknown. However, the role of strongly quenching impurities cannot be ruled out due to inadequate experimental descriptions for most of the published results. In this work two methods, lifetime measurements and the fractional change in the two-photon coincidence rate upon the introduction of oxygen aliquots, were used to study quenching by oxygen and just the latter method was used to study the change in the probability of positronium formation as a function of argon-oxygen composition. For a precise determination of positronium formation by the two-photon difference mode it is insufficient to know that the cross section ranges from 1 X 10-19-3 X cm2, For that reason, several lifetime spectra were recorded with the lifetime spectrometer. Spectra were recorded for pure argon and for argon containing varying quantities of oxygen. All decay curve data were fit by a nonlinear least-squares fitting routine21 to determine logarithmic slopes. The decay constants obtained from the logarithmic slope of the decay curves actually represent a sum of various quenching processes: from conversion on the pararnagnetic oxygen, from pickoff of the background argon gas (eq 1and 2), and from the intrinsic decay
The Journal of Physical Chemistry, Vol. 84, No. 5, 1980
486
Klobuchar and Karol
TABLE 11: Summary of Argon Quenching Rates (A,') 106hp0, SK' atm-'
method
ref
0.253 i 0.005 0.249 i 0.036 0 . 2 5 1 i. 0.05 0.236 i 0.016 0.24 i 0.02 0.255 f 0.015 0.25 i 0.011 0.276 i 0.003
annihilation spectrum lifetime lifetime lifetime lifetime lifetime lifetime lifetime
16 22
I
I
I
17 23 24 25 26 27
TABLE 111: Summary of Measurements of the Probability of Positronium Formation in Argon probability
method
* 0.03
three-photon with magnetic field relative rates of two- and threephoton counting in conjuction with magnetic and electric fields 0.36 i 0.06 singles annihilation spectrum with magnetic and electric fields -0.30 angular correlation with magnetic fields lifetime spectra in huge chamber 0.37 i 0.03 to minimize wall effects 0.352 i 0.035 two-photon counting 0.31 -0.33
ref 28 29
30, 3 1
32 33 34
constant of orthopositronium, A., To calculate the probability of two-photon annihilation prior to the introduction of quenching species, one must know the quenching rate (or cross section) of the background gas. Fortunately, argon has been thoroughly studied and the results of numerous workers agree quite well. The decay constants for argon are typically expressed as quenching rates per unit pressure (atm) or per unit density (amagats) rather than as a cross section. Since the quenching rates are strictly density dependent, one must calculate the density from nonideal gas relationships. In this work, the pressure was sufficiently low so that the density in amagats equaled the pressure in atmospheres to within 1%. Consequently, all quenching rates are expressed in the more familiar pressure units. A summary of the published rates in pure argon is given in Table 11. The average value yields a quenching rate of A,O = (0.25 f 0.01) X lo6 s-l atm-l corresponding to a pickoff cross section of 1.3 X cm2. For the purpose of this investigation, the quenching rate has already been determined sufficiently well that a redetermination was deemed unnecessary. The total quenching rate, A, was calculated from A, = pA,O
I 6
+ n02ukv= A, + n02uku
When corrected for the contribution due to pickoff quenching by argon the results of this work for the 0-Ps quenching cross section on O2 is (1.0 f 0.1) x lo-'' cm2. Our result may be compared to the results presented by Celitans, Tao, and Green17who processed lifetime spectra for six decades of O2 relative pressure. The comparison is shown in Figure 5 for total pressures of 17 and 12.5 atm. The curves predicted by using the results of the current determination describe the experimental data at both high and low oxygen pressures remarkably well. It should be pointed out that the two calculated curves are absolute and are not normalized to the data. The probability of positronium formation in argon has been studied by several workers and a summary of their results is presented in Table 111. A persistent problem with many of the earlier investigations of positronium formation probabilities has been the high level of strongly quenching impurities, such as oxygen, which not only affect
1
I
10.~
I
I
to-,
'01
Relative 0, Pressure
Figure 5. Dependence of 0-PS quenching rate A, on relative oxygen pressure in argon at total pressures of 12.5 and 17 atm. Data points taken from Celitans, Tao, and Green (ref 17). Solid curve calculated from results of this work.
the probabilities of two- and three-photon annihilation but also the probability of positronium formation. Another, less serious problem with the early determinations of the probability of positronium formation was that pickoff by the background gas was largely ignored. Therefore, the value of the probability of positronium formation used in this investigation is the weighted average of only the two most recent determinations, those of Falk and Jones33(P = 0.37 f 0.03) and Leung and PauP4 (P = 0.352 f 0.035), which combine to give a formation probability of 0.362 f 0.023. Significantly, Leung and Paul employed two-photon counting with source-to-detector distance of 2.1 m and a well-shielded positron source to limit detection of both wall and source events. Spurious effects due to the detection of 1275-keV quanta were also minimized. To measure the probability of positronium formation, Falk and Jones employed the lifetime method in a 35.6-cm diameter spherical chamber. In such a large chamber, the fraction of positrons reaching the walls was negligible, and the fraction of positrons annihilating in the source was estimated to be 0.02. Consequently, Falk and Jones could measure the probability of positronium formation from the relative intensities of the various components of a lifetime spectrum. Using their result of P = 0.37 f 0.03, Falk and Jones also determined that 69 f 7% of all positronium is formed in the ortho state, in agreement with the statistical estimate of 75%. Positronium formation in gas mixtures has not been as thoroughly studied as the corresponding quenching phenomena. Heinberg and Page32investigated the angular correlation of annihilation quanta for 02-Ar mixtures in the presence of applied magnetic fields. Their results were interpreted by Obenshain and Page35in 1961 to be consistent with a probability of formation of about 0.5 in pure oxygen. Celitans, Tao, and Green17measured the probability of positronium formation in oxygen from the intensity of the long-lived component in a lifetime spectrum and arrived a t a value of 0.40 f 0.04. More recently, Mokrushin and Goldanskiill have measured angular correlation curves in a series of 02-Ar mixtures and derived a semiempirical relationship for the probability of posi-
The Journal of Physical Chemistry, Vol. 84, No. 5, 1980 487
Positronium Formation and Quenching in Ar-0,
troniuml formation to simulate their results. In pure argon, Mokrushin and Goldanskii have set the probability of positronium formation equal to 0.30. In pure oxygen, the corresponding formation probability is 0.45. For mixtures with Os partial pressures greater than about 1 % their results indicate that the probability of positronium formation is virtually the same as in pure oxygen. An unfortunate aspect of their theoretical interpretation is that the value for the probability of formation in the pure argon was based on earlier, less reliable results (cf. Table 111). In addition the oxygen quenching cross section Mokrushin and Golldanskii used was too high in Comparison with most other results including the Goldanskii et ale9investigation in 1975 and also this investigation (Table I). The limiting probability (pure 0,)of postronium formation in oxygenargon mixtures used in this investigation was 0.45 to facilitate comparison with the Mokrushin and Goldanskii experiment by using our two-photon coincidence change technique. It can be shown36that the fractional change in the observed two-photon coincidence rate (AA2,/A2?) upon the introduction of a quenching impurity may be calculated as A(PW2,) - AI’ (4) AA2,lAzyO = G - P(l- W2;) where I* is thle initial probability of positronium formation, W2,0is the initial fraction of positronium annihilating via two y rays, A(PWz,) is the change from PWZ,O to PW2, upon introduction of a quencher, and AP is similarly defined. lNzyis irelated ta the quenching rates associated with the various quenching mechanisms. A p p r ~ x i m a t e l y ~ ~
0 46 *.---
_---------
-
,‘ /’
,‘
0 40
0 38 I’
(5) where At is the intrinsic 0-Ps decay rate, and the total 0-Ps quenching rate A, is given, in general, by A, = K + A, + Ach (6)
G is an effective chamber constant and is given by
G = -l + c 1-R
(7)
where
in which f is the fraction of positrons which stop in the gas in a region where the detectors are sensitive, f’is similarly defined for positrons stopped in the walls and in the source, E is the efficiency for detecting two-photon events in the gas, E , is the efficiency for detecting wall and source events, 4@+) is the flux of positrons, and B is the background. R is t;he ratio of three-gamma efficiency (e3?) to the two-gamma efficiency (E) for the geometry shown in Figure 1: The results of the two-photon coincident rate measurements in argon-oxygen mixtures are shown in Figure 6. As can be seen, the fractional change in the coincidence rate at high oxygen concentrations is about 15%. At intermediate oxygen concentrations, the fractional change shows aL relatively flat, region which falls off gradually but with increasing uncertainty at the lowest oxygen concentrations. The dashed line in Figure 6 marked P = 0.45 corresponds to the fitted fractional change in rate calcu-
---- Mokrushin 8 G o l d a n s k i i This Work
488
The Journal of Physical Chemistry, Vol. 84, No. 5, 1980 I
201
lot P 5
10 9 90-
I
I
I
€ f
76-
3-
I
I
on cross-section data now known to be erroneous. The explicit variation of P in Ar-02 mixtures should serve as a useful and simple test for detailed models on positron and positronium interactions with molecules in the gas phase.
Acknowledgment. The support of the National Science Foundation is gratefully appreciated.
54-
References a n d Notes
L
m
a
I
Klobuchar and Karol
P z=1 5i . 05 a0t m ~ 02/Ar Celltans and Green d a t a -Calculated
( t h i s work)
Research supported in part by National Science Foundation Grant GP38390. Center for Naval Analyses, Arlington, VA 22209. Recent reviews of positronium chemistry include: V. I.Goldanskii and V. G. Firsov, Annu. Rev. Phys. Chem., 22, 170 (1971); H. J. Ache, Angsw. Chem., Int. Edit. fngl., 11, 179 (1972); J. A. Merrigan, J. H. Green, and S.Tao, “Physlcal Methods of Chemlstry”, Vol. I11 D,501, A. Weissberger and B.Rosstter, Ed., Wiley, New York, 1972, p 501; V. I. Gddanskil, Acc. Chem. Res., 10, 153 (1977); A&. Chem. Ser., No. 175 (1979). S.J. Tao, Appl. Phys., 3, l(1974). S. Y. Chuang and S. J. Tao, Phys. Rev. A , 9, 989 (1974). ICN Corp., Isotope and Nuclear Division, 26201 Miles Road, Cleveland, OH 44128. R. L. Klobuchar and P. J. Karol, Nucl. Instrum. Methods, 152, 447 (1978). I.K. MacKenzie, C. W. Shuke, T. Jackman, and J. L. Campbell, Phys. Rev. A , 4, 135 (1973). H. 0. Trerice Co., 12950 W. Eight Mile Rd., Detroit, MI 48237. Union Carbide Corp., Linde Division, National Specialty Gas Office, 51 Cragwood Rd., South Plainfield, NJ 07080. A. D. Mokrushin and V. I. Gobnskii, Sov. Php. JETP, 28,314 (1968). V. I.Goldanskii, At. Energy Rev., 8(l), 1 (1968). T. C. Grifftth, G. R. Heyland, K. S.Lines, and T. R. Twomey, J. Phys. B , 11, L743 (1978); D. W. Gidley, A. Rich, P. W. Zitzewitz, and D. A. L. Paul, Phys. Rev. Lett., 40, 737 (1978). M. Deutsch, Prog. Nucl. Phys., 3, 131 (1953). E. P. Dulk, Ph. D. Thesis, Massachusetts Institute of Technology, 1956, in J. H. Gteen, ”Postron Annihllation”, A. T. Stewart and L. 0 Roellig, Ed., Academic Press, New York, 1967, p 98. F. F. Heymann, P. E. Osmon, J. J. Veit, and W. F. Williams, Proc. Phys. Soc., 78, 1038 (1961). C. J. Celitans, S.J. Tao, and J. H. Green, Proc. Phys. SOC.,83, 833 (1984). P. E. Osmon, Phys. Rev., 140, A8 (1965). L. A. Page in J. H. Green, see ref 14. V. I.Goldanskii, A. D. Mokrushin, A. 0. Tatur, and V. P. Shantarovich, Appl. Phys., 5, 379 (1975). R. L. Klobuchar, Ph.D. Thesis, 1976 (available as 76-19329 from Universlty Microfilms, Ann Arbor, MI 48106.) B.G. Duff and F. F. Heymann, Proc. R. Soc. London, Ser. A , 270, 517 (1962). R. H. Beers and V. S.Hughes, Bull. Am. Phys. Soc., 13, 633 (1968). P. H. R. Orth and G. Jones, Phys. Rev., 183, 7 (1969). S.J. Tao, Phys. Rev. A , 1, 1257 (1970). P. G. Coleman and T. C. Griffith, J . Phys. 6,6, 2155 (1973). P. G. Coleman, T. C. Griffih, G. R. Heyland, and T. L. Kileen, J. Phys. B , 8, 1734 (1975). T. A. Pond, Phys. Rev., 85, 489 (1952), cited in V. I.Goldanskli, see ref 12. E. P. Dulit, B. Gittelman, and M. Deutsch, Bull. Am. Phys. Soc., 1, 69 (1956). S.Marder, V. W. Hughes, S.C. Wu, and W. Bennett, Phys. Rev., 103, 1258 (1956). V. W. Hughes, S.Marder, and C. S.Wu, Phys. Rev., 98, 1840 (1955). M. Heinberg and L. A. Page, Phys. Rev., 107, 1589 (1957). W. R. Faik and G. Jones, Can. J . Phys., 42, 1751 (1964). C. Y. Leung and D. A. L. Paul in “Positron Annlhilation”, see ref 14. F. E. Obsenshain and L. A. Page, Phys. Rev., 125, 573 (1962). P. J. Karol and R. L. Klobuchar, Nucl. Instrum. Methods, 151, 149 (1978). The exact expression for Wpy is given by
[ 1114X:
+ 4456KXt + 4448(hq - K)X, + 15.957K(Xq -- K )
3.989(Xq - K)2]/[4456X:
+ 4458KXt + 4460(X, - K)Xt -I16K(Xq - K ) + 4(Xq - K)2]
and is the form used in all calculatlons. A. Ore, Univ. Bergen, Arbok, Naturvifensk. Rekke, No. 9 (1949). K. F. Canter, P. G. Coleman, T. C. Griffith, and G. R. Heyland, Appl. Phys., 3, 249 (1974). D. M. Spektor and D. A. L. Paul, Can. J. Phys., 53, 13 (1975); Appl. Phys., 5, 383 (1975). P. G. Coleman and J. D. McNutt, Phys. Rev. Lett., 42, 1130 (1979). J. D. McNutt, S. C. Sharma, M. H. Franklin, and M. A. Woodall, 11, Phys. Rev. A , 20, 357 (1979). C. J. Celitans and J. G. Green, Proc. Phys. Soc., 83, 823 (1964).
