Schwartz, H. M.

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Note Concerning Cloud Chamber Experiments with Positrons

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Journal of the Arkansas Academy of ScienceVolume 4 Article 181951Note Concerning Cloud Chamber Experimentswith PositronsH. M. SchwartzUniversity of Arkansas, FayettevilleFollow this and additional works at: http://scholarworks.uark.edu/jaasPart of the Atomic, Molecular and Optical Physics CommonsThis article is available for use under the Creative Commons license: Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0). Users are able toread, download, copy, print, distribute, search, link to the full texts of these articles, or use them for any other lawful purpose, without asking priorpermission from the publisher or the author.This Article is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Journal of the Arkansas Academyof Science by an authorized editor of ScholarWorks@UARK. For more information, please contact scholar@uark.edu, ccmiddle@uark.edu.Recommended CitationSchwartz, H. M. (1951) "Note Concerning Cloud Chamber Experiments with Positrons," Journal of the Arkansas Academy of Science:Vol. 4 , Article 18.Available at: http://scholarworks.uark.edu/jaas/vol4/iss1/18105NOTE CONCERNING CLOUD CHAMBER EXPERIMENTSWITH POSITRONSH. M. SCHWARTZUniversity of Arkansas, Fayetteville, Arkansas*1. IntroductionHo Zah-Wei and W. Bothe' have called attention to the interest attachedto cloud chamber studies of energetic positron-electron collisions. This in-terest arises from the possibility of observing energy transfers in excess of50 per cent, a possibility which is of course nonexistent in the case of theinteraction of particles which are completely identical. The results obtainedby Ho Zah-Wei 2 seem to confirm in a general way the formula for positron andelectron elastic collision cross sections calculated by H. J. Bhabha 3,but in detail there appear deviations both for large and for small energytransfers, the former being especially noteworthy.It is intended to point out briefly here additional reasons for the de-sirability of obtaining reliable data on the hard collisions between positronsand electrons [§2] , some limitations of the present data of Ho Zah-Wei[§3], and some experimental possibilities for significant extension ofthese results [§4J . Preliminary measurements bearing partially on thepresent suggestions have been made with the Brookhaven National Labo-ratory high pressure cloud chamber 4, and a brief report of the results willbe given in the concluding section of this paper.2. Significance of Cloud Chamber Experiments on Scattering and Annihi-lation of Fast Positrons.Bhabha's derivation of the differential elastic scattering cross sectionsof electrons and positrons is based on Miller's quantum -relativistic theoryof the collision of two free electrons 8 and on the elementary phase ofDirac's "hole theory" of positrons 6. A reliable verification of Bhabha'sformula is of interest in connection with both of these theories.The most direct check on Miller's theory would naturally involve ex-perimentation on energetic electron electron collisions. It is somewhatsurprising that the only experiment of this nature so far performed datesback to 1932 7. Champion's results although of interest as providing general*Part of the work on which this note is based has been done at BrookhavenNational Laboratory under the auspices of the Atomic Energy Commission.•Fiat Report 1132, May 29, 1947.*ibidand C. R. 226 (1948) 10838 Proc. Roy. Soc. A 154 (1936) 195-206.4Hoke, O'Neill, and Shutt, October 1949, private communication."Ann. der Physik, 14 (1932) 531.6 A good discussion of this subject is to be found in Heitler's The QuantumTheory of Radiation, Chapter IV.7 F- C. Champion, The Scattering of Fast P-Particles by Electrons, Proc. Roy.Soc. A. 137 (1932) 688.105Journal of the Arkansas Academy of Science, Vol. 4 [1951], Art. 18Published by Arkansas Academy of Science, 1951106 ARKANSAS ACADEMY OF SCIENCEfirst-order agreement with theory, cannot, however, be used as conclusiveevidence in what concerns the large angle deflections, but itis the resultson these energetic deflections that would be crucial in a significant checkof Miller's method. Thus it appears quite evident when one examines theessential hypotheses of Bhabha's and Miller's formulations, that carefulmeasurements of the energetic collisions of positrons and electrons espe-cially for sufficiently fast positrons, would also be decidedly worth havingby way of confirmation of the relativistic two-body quantum treatment ofMiller. It would also appear that the cloud chamber would be the simplestinstrument to use for such an investigation, provided, of course, that thetechnique employed is adequate.As to Dirac's theory of positrons, at least in what concerns its first ap-proximation, it has been sufficiently successful in all the applications sofar made of it, that mistrust in the present case would not be indicated.Nevertheless, the particular application which Bhabha makes of Dirac'spositron theory, involving as it does an interesting employment of Pauli'sprinciple, would make a direct check of Bhabha's conclusions based onthese ideas, of independent interest.Of even more immediate interest in connection with Dirac's theory ofpositrons, is a good quantitative confirmation of the differential cross sec-tions for annihilation of positrons and electrons computed withits aid. Suchannihilation (as well as creation) enters also in Bhabha's treatment ofpositron electron scattering, but only in the virtual states. Real annihila-tion of positrons colliding with electrons is of course a very well estab-lished experimental fact, but quantitative experimental determinations ofthe energy dependent probabilities of its occurrences are very scarce. 8Quite recently there have been announced some interesting results dealingwith a delayed coincidence counter determination of annihilation probabil-ities for slowed down positrons. 9 Similar determinations for fast positronsdo not appear as feasible with simple counter techniques. Again it wouldappear that a suitable cloud chamber technique, such as the one suggestedin this note, for example, would provide the simplest attack on this problem.3. Discussion of Ho Zah-Wei's Results.Since the main object of this note is to point out ways of significantlyextending the present experimental results on positron-electron collisions,it will suffice here to call attention very briefly to a few obvious limitationswhich attach to the published data of Ho Zah-Wei and which it would be de-sirable to reduce in further experimentation of this type. The following arethe most apparent of these limitations:i)The average energy of the positrons involved in these data is not ashigh as would be required for a significant check of the M^ller-Bhabhaformula.'For theory and experiment see for instance Heitler, loc. cit., especially pp. 208-209 (in the second edition) for the existing experimental evidence.'James W. Shearer and Martin Deutsch, The Lifetime of Positrons in Matter,Phys. Rev. 76 (1949) 462 (a).106Journal of the Arkansas Academy of Science, Vol. 4 [1951], Art. 18http://scholarworks.uark.edu/jaas/vol4/iss1/18ii)The statistics are not sufficiently ample for the purpose of making thedesired deductions from the data.iii)The possible sources of error in the energy determinations do notappear to have been sufficiently accounted for, at least as far as canbe surmised from the actual published description of the experiments.Regarding point i) two observations need to be made. In the first place,since the radioactive sources used for the experiments in question wereMn" in one set and F18 in the other, the mean /3+ energies available wereof the order of only 0.2 to 0.3 Mev. at most. Indeed the highest estimatesof the maximum end points of the spectra of these two nuclides are 0.75Mev. and 0.95 Mev. (to 20%) respectively. 10 On the other hand, an examina-tion of Bhabha's theoretical results discloses that only at considerablyhigher energies and for large percentage energy transfers do the specificrelativistic and "exchange" terms in the formula in question begin to havea sensible effect upon the scattering cross sections."What has been said above applies also in part to the observation underii). The interesting information is to be gotten from the collisions withhigh percentage energy transfers and these, if Bhabha's formula is at allcorrect, are relatively few in number. It becomes, therefore, necessary ascan be seen by a simple calculation involving the probabilities and per-centages in question, to have available statistics at least by an order ofmagnitude more than the 323 meters of total usable length (reduced to normalconditions) that were obtained in the experiments under discussion. Thispoint is made quite clear in connection with the question of annihilationcross sections of positrons in flight. The three photographs of such annihi-lation found by Ho Zah-Wei are obviously not enough to serve as a reliablequantitative check on the theory of this process. But an increase by one ormore orders of magnitude of the total equivalent track length coupled withsome positron energy selection could be expected to provide evidence of atleast a preliminary nature on the quantitative validity of the differentialcross sections for the annihilation process.Little can be said in elaboration of remark iii),since the experiments inquestion have so far been written up in a rather sketchy manner. Neverthe-less, the absence of any mention of such considerations, for instance, asthe effect of multiple scattering on energy calculations using track curvaturein a magnetic field, in the papers under discussion, would lead one to thepresumption that such effects were perhaps neglected in the energy calcu-lations. That such effects are not at all negligible for the range of pres-sures and magnetic field strengths that were employed, is a rather wellestablished fact. An interesting paper to consult in this connection isBethe's "Multiple Scattering and the Mass of the Meson." 1210G. T. Seaborg and I. Perlman, Table of Isotopes, Rev. of Mod. Phys. 20(1948) 585."In connection with a critical analysis of questions related to these points, Iam indebted to Dr. S. Goudsmit of Brookhaven National Laboratory for enlighteningdiscussion.12 Phys. Rev. 70 (1946) 821.107107Journal of the Arkansas Academy of Science, Vol. 4 [1951], Art. 18Published by Arkansas Academy of Science, 1951108 ARKANSAS ACADEMY OF SCIENCE4. Some Suggestions for Obtaining Higher Positron Energies and IncreasedStatistics.There exist at present a number of possibilities for obtaining positronsources with mean energies near or in excess of 1 Mev. The source offastest positrons available at present would appear to be the pairs from theX-rays generated by the 100 Mev. betatron. A rough preliminary calculationof the positron intensity to be expected from such X-ray conversion, basedon an estimate of the X-ray spectral intensity distribution for the 100 Mev.betatron made by G. C. Baldwin and G. S. Klaiber 13 points to the feasibilityof such a source. However, from a practical point of view, it would behardly expected that one could count on the availability of the 100 Mev.betatron for the experiments under discussion when it is the only one nowin existence. The availability of a 20 Mev. betatron would of course be aneasier possibility. Unfortunately, the question of the adequacy for the ex-periment under discussion of the positron flux intensity obtainable in thisway becomes rather critically dependent upon the Xiayintensities that canbe produced with these instruments. One would require knowledge of thisintensity and perhaps also rather careful estimates regarding the variouscross sections and geometric factors which enter in a determination of thebeam intensity of the positrons which actually enter the cloud chamber.Another possibility for obtaining high energy positrons is provided bythe gammas from the Li7—H1 reaction dt the resonance energy of about]4 Mev. Positrons from the pairs created by such gammas have indeed beenused in scattering experiments. 14 But here again, the positron beam in-tensity that could be made available for the type of setup that is beingsuggested in this note, becomes a matter requiring closer scrutiny.What appears to be the simplest practicable procedure for obtaining asatisfactory source of energetic positrons is to make a proper choice ofradioactive substance. The requirements are obvious. This substanceshould be readily producible in a number of laboratories and in suitableform and activity, and its positive beta decay should have as large anenergy maximum as possible together with a proper half-life. An examin-ation of the Seaborg and Perlman Table of Isotopes 15 discloses that theradioactive arsenic isotope As" appears to come closest to satisfying theabove requirements. It can be made with cyclotron bombardment in a num-ber of practicable ways, its positive beta maximum lies at about 2.8 Mev,and itha s a quite convenient half-life of 26 hr.A means for obtaining adequate statistics is provided by the combinationof an arrangement for magnetically focusing a collimated beam of positronsthrough a thin window of the cloud chamber and into a large arc across thefull length of the chamber, with an anticoincidence setup which wouldpermit the photographing of an event only if it consists in either a largeangle scattering or in the annihilation of the positron in the chamber.13Phys. Rev. 71 (1947) 3.14Fowler and Oppenheimer, Scattering and Loss of Energy of Fast Electronsand Positrons inLead, Phys. Rev. 54 (1938) 320.I5Loc. cit.108Journal of the Arkansas Academy of Science, Vol. 4 [1951], Art. 18http://scholarworks.uark.edu/jaas/vol4/iss1/18The magnetic focusing arrangement can be designed for instance alongthe lines of H. R. Crane's setup in his electron scattering experiments atthe University of Michigan.16It would obviously be pointless to enter here into any specific sugges-tions regarding the choice of geometry, cloud chamber gas and pressure,magnetic field strengths, and anticoincidence scheme, that would be suit-able for the experiments under discussion, beyond the mere statement thatpreliminary calculations indicate that such a choice is indeed possible.It may perhaps also be helpful to call attention to the possible advantageof using in connection with the anticoincidence setup a triggering devicethat actuates not the chamber expansion, but the supply of light for thephotographing of the tracks, thus permitting steady operation of the cloudchamber. Although the author is under the impression that such a triggeringscheme may already have been utilized at the very beginning of cosmic raycounter work, its employment in connection with scattering experimentsseems to have been made only recently.' 7It hardly needs to be pointed out that the possibility of selecting positronenergy bands in the suggested setup would be an aid in the study of theenergy dependence of the cross sections under investigation. Moreover,since such energy dependence studies can only be of rather limited scope,owing to inherent cloud chamber limitations, it would not become necessaryto keep the width of these bands below comfortably practicable limits.5. Preliminary Results with the Brookhaven High Pressure Cloud Chamber.Owing to the availability at Brookhaven National Laboratory of the highpressure cloud chamber while filled with helium during part of the fall of1949, R. Hoke, G. O'Neill, and R. P. Shutt took some photographs of tracksobtained in the chamber upon the introduction of a minute trace of radio-active arsenic. The radioarsenic was introduced into the chamber in liquidsolution, this being the only means of getting readily into the interior ofsuch a type of cloud chamber. 18 Because it was not feasible to operatethis cloud chamber with a pressure below 70 atmospheres while at thesame time it was of course necessary to employ a low magnetic field (700gauss were actually used), it was expected that excessive track distortionby scattering in the gas would preclude the drawing of reliable quantitativeconclusions from the photographs, and therefore only a rather limited num-ber of these were taken.A set of these cloud chamber photographs were kindly sent by Dr. Shuttto the author for examination, and in spite of their limited scope, twoA valuable paper to consult in connection with this and related problems ofcloud chamber technique and analysis is "The Single Scattering of Electrons inGases," R. B. Randels, K.I.Chao, and H. R. Crane, Phys. Rev. 68 (1945) 64.17 The Scattering of Fast Beta-particles through Large Angles by Nitrogen Nuclei,F. C. Champion and R. R. Roy, Proc. Phys. Soc. 61 (1948) 532.I8Its construction is described in: A Hydrostatically Supported Cloud Chamberof New Design for Operation at High Pressures, T. H. Johnson, S. DeBenedetti,and R. P. Shutt, Rev. Sci. Inst. 14 (1943) 265.109109Journal of the Arkansas Academy of Science, Vol. 4 [1951], Art. 18Published by Arkansas Academy of Science, 1951¦110 ARKANSAS ACADEMY OF SCIENCEinteresting though qualitative observations could be deduced from roughmeasurements made on the clearly visible tracks.First, it was found that the photographs contained a considerable pro-portion of positron tracks corresponding to energies in excess of 1Mev.and well into the 2 Mev. region, thus definitely establishing the suitabilityof radioactive arsenic as a high energy positron source. Because of thelimitations to which many of the photographed tracks were subject 19,it wasnot possible to construct a significant energy distribution curve for thepositrons, but the following rough distribution found among 40 tracks ofpositrons having energy in excess of 0.75 Mev. may be of some interest:Energy interval (in Mev.) 0.75 - 1.25 1.25 - 1.75 1.75 -2.25Number of tracks 25 9 6The other observation concerns the proportion of collisions with energytransfers in excess of 50 per cent that could be observed in these photo-graphs. Although it was not possible, owing to the aforementioned limita-tions, to obtain a result of quantitative significance, it could neverthelessbe inferred upon careful examination of the data and of the relevant prob-abilities, that this proportion was definitely smaller than that to be expectedfrom a comparison with the results of Ho Zah-Wei, and more nearly of thesame order as predicted by Bhabha's theory. This tentative result indicatesat least the desirability of repeating Ho Zah-Wei's experiments with somesignificant extension of method.In. addition to the aforementioned scattering, contributing causes were alsothe originating of tracks at the bottom of the vertically placed chamber where thedissolved radioactive substance was to be found, and the strong curving actionof the magnetic field whose strength of 700 gauss chosen as a compromise for theminimizing of the gas scattering was still otherwise too high by about a factorof 2.110Journal of the Arkansas Academy of Science, Vol. 4 [1951], Art. 18http://scholarworks.uark.edu/jaas/vol4/iss1/18

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Note Concerning Cloud Chamber Experiments with Positrons

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