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A cloud chamber study of pair production Wolfe, Harry Bernard 1951

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A CLOUD CHAMBER STUDY OF PAIR PRODUCTION by HARRY BERNARD WOLFE A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of PHYSICS We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF ARTS. Members of the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA April, 1951 A CLOUD CHAMBER STUDY OF PAIR PRODUCTION ABSTRACT The present status of the Bethe-Heitler theory of pair production is analysed, and results are given which can be compared with experiment* The main points of interest in the pair formation process are the cross-section, energy and angular distribution of the electrons, the momentum imparted to the nucleus, and the manner in which these factors vary with photon energy and atomic number. Although the assumptions involved, such as the Born Approximation, appear to be justified, a review of the literature shows that ex-perimental results have not always been in entire agreement with theory. For instance, the experimental distribution of E^ -E.. follows neither the Bethe-Heitler nor the Jaeger-Hulme theory. The proposed experiment i s to be carried out with a cloud clamber using Xenon as the gas, and ThC" as the "tf-ray source. The errors involved in the method are discussed. To minimize scattering error a new method of analysis of cloud chamber tracks i s suggested, in which the angle between successive equidistant chords is measured. The nine inch chamber is of the rubber diaphragm type. The operation of the chamber and camera has been made entirely automatic. The magnetic field is obtained by a pair of Helmholz coils. Two General Electric F.T. 126 flash lamps provide sufficient light for photography. Stereoscopic pictures are obtained by the double mirror method. A great number of difficulties had to be overcome, especially in the functioning of the expansion valves, in order to get good electron tracks and consistent operation. It has been found that i t i s very important to use correct procedure in f i l l i n g the chamber and "cleaning" i t out for the production of tracks. Very nice electron tracks have been obtained with a ThC" source and Argon in the chamber. Preliminary observations indicate that the source may need to be shuttered, and that the chamber will need a thin window. ACKNOWLEDGEMENTS The author wishes to express his appreciation to Dr. J. B. Warren for suggesting the topic and for his continued interest in the work. Special thanks are also due to Mr. K. L. Erdman, for his assistance in the design and construction of some of the auxiliary apparatus. Part of the work was done vhile the author was a holder of a National Research Council Bursary (1949-50), TABLE OF CONTENTS Page ACKNOWLEDGEMENTS Front ABSTRACT Front I THEORY,OF PAIR PRODUCTION 1. Dijjrac's "Hole" Theory 1 2. Cross-section. 1 3. Angular Distribution 3 4* Nuclear Recoil 4 5. Corrections a* Born Approximation 5 b. Screening 6 c. Interaction 7 6. Other Types of Pair Production 7 II COMPARISON OF THEORY AND EXPERIMENT 1. Experimental Method. . 6* 2. Energy Distribution 9 3. Cross-section 10 4. Angular Distribution 11 5. Nuclear Recoil _ _ 1 2 6. Difference of Energy E+-E_ 13 7. Summary 14 III PROPOSED EXPERIMENT 1. Aim of Experiment 15 2. Discussion of Errors a. Scattering 17 b. Projection of the Track 20 c« Energy Loss 21 d. Turbulence 21 3« Method of Analysis 22 IV APPARATUS AND EXPERIMENTAL WORK 1. Cloud Chamber . . . . 24 2. Valves 26 3. Control Circuit 27 4. Lights 28 5. Camera 30 6. Collimator 31 7. Reprojection 32 V RESULTS 1. Operation of the Chamber a. Filling the Chamber 34 b # Clearing Process 35 c. Expansion Cycle 3 7 d. Photography 3 8 2 . Observations with a "2T-source a. Experimental Arrangement 3 9 b. Pictures 1+0 APPENDIX ~ Continuously Sensitive Cloud Chamber 43 BIBLIOGRAPHY 46 LIST OF REFERENCES 47 LIST OF FIGURES Page 1. Energy Distribution of Pairs Following 2 2. Cross-section for Pair Production Following 2 3. Distribution of Recoil Nucleus 4 4. Energy Distribution of Positrons 4 5. Angular Distribution of Positrons 12 6. Distribution of ^ r 1 _ Following 13 7. Error from Projection of Cloud Chamber Track 21 8. Geometrical Analysis of Cloud Chamber Track 22 9. Circuit Diagram of Step-Switch Following 27 10. Plan View of Camera Following 30 11. Cireuit for Automatic Camera Operation Following 31 TABLES 1. Pair Cross-Section per Atom of Pb. 6 2. Distribution of Nuclear Recoil 13 3. Expected Number of Tracks in Xenon 16 LIST OF PLATES Following Page 1. Filling Tube 25 2. Minor Expansion Valve 25 3. Main Expansion Valve 26 4. Control Circuit 27 5. wiring Diagram for Lamps 28 6. Diagram of Chamber, Coils, and Mirror Stand 30 7. Source Collimator 31 8. Picture of Collimator Beam 31 9. Tilting Table for Reprojection 32 10, Schematic Diagram of Experimental Arrangement 38 11, Cloud Chamber Apparatus 39 12-15.Electron Tracks 40 16, Electron Tracks 42 17. Diffusion Cloud Chamber 43 I — T H E O R Y O F P A I R P R O D U C T I O N D i r a c ' a H o l e T h e o r y D i r a c ' s r e l a t i v i s t i c w a v e e q u a t i o n f o r a f r e e e l e c t r o n g i v e s r i s e t o s o l u t i o n s f o r w h i c h t h e e n e r g y i s n e g a t i v e . T h i s i s b e -c a u s e t h e e n e r g y f o r a f r e e p a r t i c l e c a n b e w r i t t e n , E ^ J p + m ^ c 4 -These s t a t e s o f nega t i ve energy at f i r s t gave r i s e t o se r ious d i f f i c u l t i e s i n i n t e r p r e t a t i o n . D i r a c ' s " h o l e " T h e o r y g a v e t h e c o n n e c t i o n b e t w e e n t h e s e s t a t e s a n d t h e o b s e r v e d p o s i t r o n s — e l e c t r o n s w i t h a p o s i t i v e c h a r g e . A c c o r d i n g t o t h i s t h e o r y a n e x t e r n a l f i e l d a c t i n g o n t h e e l e c t r o n s i n t h e n e g a t i v e e n e r g y s t a t e s w i t h e n e r g y E= - | E ( a n d m o m e n t u m p* c a n c a u s e a t r a n s i t i o n t o a s t a t e w i t h p o s i t i v e e n e r g y E ' a n d m o m e n t u m p ^ . T h u s w e o b t a i n a p o s i t i v e a n d n e g a t i v e e l e c t r o n p a i r w i t h p N - p * E + = - E = l E l p t - p * E _ = E ' T h a t i s , t h e " h o l e " ( p o s i t r o n ) i n t h e n e g a t i v e e n e r g y d i s t r i b u t i o n h a s a p o s i t i v e c h a r g e a n d p o s i t i v e e n e r g y a n d a m o m e n t u m o p p o s i t e t o t h a t o f t h e n e g a t i v e e n e r g y s t a t e . T h e e n e r g y r e q u i r e d f o r t h i s t r a n s i t i o n i s E ' - E = E^t E J ?-2W-=1 1 > 022 M e v . T h i s e n e r g y c a n b e s u p p l i e d t h r o u g h t h e a b s o r p t i o n o f a i f - r a y o r b y i m p a c t w i t h a n e n e r g e t i c p a r t i c l e . A n o t h e r p a r t i c l e , a n u c l e u s f o r e x a m p l e , m u s t b e p r e s e n t t o c o n s e r v e e n e r g y a n d m o m e n t u m . C r o s s - S e c t i o n T h e p o s s i b i l i t y o f p a i r p r o d u c t i o n b y a X - r a y i n t h e f i e l d o f a nucleus was first pointed out by F. Perrin. The equations describing the behaviour of an electron interacting with a radiation field are far too complicated to be solved exactly. In all applica-tion of the theory, the interaction energy is considered as small and approximate solutions are obtained which are correct only to the first order in this energy. In 1933 Plesset and Oppenheimer2 gave a provisional order of magnitude for the cross-section of pair production as p - ~ L7^C^/ " £'7 " F O *?' <V"-where Z is the charge on the nucleus. The first comprehensive , treatment of pair production was provided by Bethe and Heitler^. In this treatment, the perturbation H' causing the transition consists of two parts: (1) H, the interaction of the light quantum k with the electron, and (2) V, the interaction of the electron with the nucleus. The process is considered as the reverse of Bremsstrahlung, except that the energy in the final state is negative. The result for the cross-section for creation of a positive electron with energy E + and a negative one with energy E_ is > w i I ' rr\C FIGURE I DISTRIBUTION OF POSITRON ENERGY f^-2.*rx FIGURE II > I \ \ \ \ \ \ \/ \ V X' ff /t) ZO ?o l«° 2°o Sim iota CROSS-SECTION FOR PAIR PRODUCTION The energy distribution i s plotted in figure 1. The cross-section i s given for the creation of a positive electron with kinetic 2-energy E + -mc , The numbers affixed to the curves refer to the are valid for any element; the curves for the higher energies, for which screening i s effective are calculated for P.b. For fev low quantum energy the distribution has a broad maximum where both electrons receive the same amount of energy. For very high energies the distribution has two maxima where one of the electons has a very small and the other one a very large energy. Finally, the distribution tends to an asymptote curve ( o£> ). By integrating equation (l) over a l l possible E, one obtains the t o t a l cross-section for pair production. The result i s plotted r a r 0 i n figure 2 with the cross-section i n units <f = -j^y The dotted curves show the cross-section for Compton scattering as comparison. We see from the graph that the behaviour for Compton scattering:: i s entirely different to that for pair production. For small energies the probability of pair formation i s generally much-smaller than that for the Compton effect, while at high energies the pair formation i s much more frequent than the scattering. Angular Distribution The number of electrons or positrons emitted at an angle © to the ~% -ray i s approximately proportional to T -ray energy i n units of mc2. The curves for k -6 and 10 mc2 Thus the average angle i s of order 0^ 0 Bethe^ obtained this expression by suitably integrating Equation ( l ) , under the assumption that the potential due to the atomic nucleus f e l l away exponentially as the distance from the nucleus. Nuclear Recoil A certain momentum q > w i l l always be transferred to the nucleus, where • q=k - p +- pt -(2) The nuclear impulse w i l l have i t s smallest value when a l l the momenta are' pa r a l l e l ; i n this case 9^^= £"= k-p +- p_ . Bethe^ has shown that most of the pair creations involve a momentum transfer between S" and mc to the nucleus, and that the probability $ (q) i s propor-tional to q in this region. Recent calculations by Jost et alia-' employing Feynman's methods have given results whose general be-haviour do not differ appreciably from those of Bethe. Figure 3 shows the typical momentum and ang_lar distribution of the r e c o i l nucleus for a if-ray energy of 4.08 Mev. FIGURE 3 M i N / 1 am 36° DISTRIBUTION OF RECOIL NUCLEUS Corrections (a) Born Approximation We note that equation (1) and the curves i n figure 1 are symmetric i n the energy distribution between the positive and negative electrons. This i s a result of using the Born approxima-tion, where V occurs squared and the sign of the charge disappears. The limit of v a l i d i t y for this approximation i s li r —e*"/tw <<. \ f where v i s the velocity of either electron. If this i s not satisfied then the exact wave functions must be used. In the exact calculation the positive electron e + would have more energy than the negative electron e. , because of repulsion of the e + and attraction of the e_ by the nucleus. Bethe and Heitler^ estimated the average difference i n energy to be -rv.c*"—/ '^ 7 Jaeger and Hulme^1 have treated the problem rigourously, using spherical wave functions and only numerical approximations. The results of their calculations for lead are shown in Figure 4 and Table 1, where Bethe and Heitler's results are given for comparison. The experimental points of Alichanow, Alichanian and Kosodaew''' for Th C" tf-rays (5.2mc^) are included i n the graph. The electrons w i l l of course, have the same distribution with the kinetic energy scale replaced by (1600 Kev - positron energy). Jaeger and Hulme's method gives somewhat higher values than those of Bethe and Heitler, but i t shows that the Born approximation should be good at high energies for even heavy elements. -6-Table 1 Pair Cross-section per atom of Pb o W Y B-H-) E V - E . _ (B.I4-) 3 0*67 0.34 0.33 Mev 0.6 Mev 5.2 3.1 2.5 0.55 0.6 Figure 4 / / / / / / 1 1 - 1 I 0 f°«>o liToo ( « v ENERGY DISTRIBUTION OF POSITRONS (b) Screening For equation (1) to be valid, the energies of both electrons must not be so large that the Coulomb screening by the orbital electrons becomes effective, i . e . 2E + E_ /h V <^ <137Z mc^. Thus screening becomes effective only at energies large compared with mc2. This i s because the pair creation can take place at a greater distance from the nucleus, and thus the effective nuclear Coulomb f i e l d i s lessened by the outer electrons. Wheeler and Lamb** have pointed out however, that i n the latter case energetic quanta w i l l produce pairs at a greater rate because of the additional possibility of collisions i n which the atom i s excited. (c) Electron Interaction In the present theory there i s no satisfactory way to include the interaction between the positive and negative electron, Heitler^ states that V+_ is probably the matrix element of a Coulomb interaction belonging to a transition from a positive energy state p*_ to a state with negative energy and momentum -p^ , and will vanish when momentum is conserved. Thus V+_ can be neglected in the approximation. Other Types of Pair Production Besides production by a photon in the field of a nucleus, pairs can also be created i f a heavy particle with kinetic energy greater than 2mc2 collides with another heavy particle^. Other possibil-ities of theoretical interest only are the production of pairs in vacuum by two quanta of combined energy greater than 2Mc , or by fast electrons passing through the field of a nucleus''"0. Of greater experimental importance is "triplet" production - the formation of a pair by a photon in the field of an electron. This has received considerable interest"'""'* ^  in the literature lately, but will not be discussed in detail here since the cross-section is small except at high energies. It has been shovm that the threshold energy for this process is 4 mc2 -2 ,04 Mev, The cross-section should be proportional to Z, there being Z electrons about a nucleus of charge Z, In contrast to pair production in the field of a nucleus, the recoil electron may receive considerable energy. In a cloud chamber we will therefore see a "triplet" — one positive and two negative electrons s t a r t i n g at a common apex. I I — COMPARISON OF THEORY AND EXPERIMENT Experimental Methods We have seen that the main points of interest i n pai r produc-t i o n by a photon are the cross-section, the energy and angular d i s t r i b u t i o n of the electrons, the impulse communicated to the nucleus, and the manner i n which these factors vary with the incident photon energy and the atomic number of the int e r a c t i o n nucleus. Accurate experiments on the phenomenon cannot be carried out with plates or f o i l s , since the electrons are strongly scattered and absorbed. To avoid multiple scattering, the f o i l must be 15 . thinner than the thickness given by Wentzel's c r i t e r i o n : X< , where p i s the e f f e c t i v e radius of the atom and n i s the number of atoms per c.c. Thinner f o i l s of course, mean fewer events. Consequently, accurate results of energy d i s t r i b u t i o n might be obtained, but not of angular d i s t r i b u t i o n . I t seems that the most r e l i a b l e method of investigation so far i s i n the gas of a Wilson cloud chamber, but, under such conditions, s t a t i s t i c s are very poor because of the small cross-section. Moreover, the work i s very tedious and the measurements d i f f i c u l t . Energy measurements are somewhat dubious i n t h i s case because of multiple scattering i n the gas d i s t o r t i n g the curvature (but not as badly as with f o i l s ) . Angular measurements are probably correct as we can see the effect of large deviations and small angle - 9 -scattering i s not very serious. Thus, early investigations^""^ of pair production by cloud chambers are unreliable chiefly because of insufficient s t a t i s t i c s . For instance, Simons and Zuber^ obtained a total ofa only forty-four pairs i n Argon and Methyl Iodide. Their results were therefore subject to a great deal of s t a t i s t i c a l error, especially i n the angular and energy distribution measurements. Pair spectrometer experiments would probably be good to deter-mine the dependence of cross-section on Z and quantum energy (except perhaps at low energies). Energy and angular distributions could not be obtained by this method, however. Statistics would probably be considerably improved i f one could devise a counter which would distinguish between positrons and electrons. This might be done by employing a s c i n t i l l a t i o n counter to detect the annihilation positron radiation from a ^- counter. One could thus get the angular distribution from coincidence experiments. It might also be possible to put the electron counter i n a confined magnetic f i e l d to make i t propor-tional, and thus obtain the energy distribution in addition. 2. Energy Distribution The f i r s t investigation involving sufficient statistics was 20 carried out by Groshev , who obtained 435 pairs i n nitrogen, krypton,xenon,using the 2.62 Mev tf-rays from ThC". His results were only qualitatively i n agreement with the theoretical calcu-lations of Jaeger and Hulme^, showing a slight asymmetry towasds the positrons i n the energy distribution. A later investigation by -10- 1 21 Roy with the tf-ipays of Ra (2.2 Mev) also showed only qualitative agreement. However, this latter experiment was carried out with f o i l s of various metals, introducing the errors mentioned above. •an A very recent experiment-^ by Powell, Hartsough, and H i l l on.the bremsstrahlung of 322 Mev electrons (1060 pairs), gives agreement with the theoretical curves, showing two maxima as predicted. Cross-section The Wilson Cloud Chamber permits a direct determination of cross-section. One counts N^, the number of pairs, and N£, the number of Compton r e c o i l electrons. Thus we get a ratio of the cross-sections <\>j KK 4>c , the cross section for the Compton effect, i s well known from the Klein-Nishina formula, and thus the cross-section for pair production <£j>can be calculated. Although this determination i s simple i n principle, i n practice i t i s very d i f f i c u l t to obtain the exact number of Compton and pair tracks originating i n the same volume of the chamber. For a i f -ray energy of 5*2 mc2 and Z= 82 (Pb), pp the theoretical ratio i s 0.20. An early experimental value*"6, of 0.22 i s shown i n Figure 2. Benedetti^ verified the proportionality of cross-section on Z 2, employing counter techniques. Groshev2^ also checked the dependence on Z 2 using the above method, but theoretical values were twice as great as the experimental values obtained. Most experiments on cross-section for pair production have been indirect. By measuring the total absorption coefficient of -11--rays, that i s the sum of the Compton, photoelectric, and pair processes, one obtains an indirect value of the pair cross-section from a knowledge of the other two cross-sections. Davisson and Evans 2^ found very good agreement with theory for Y-rays from .8 to 2.8 Mev, using various metals. A good summary of the work to date i s given in their report. A magnetic pair spectrometer experiment by Walker2^ employing 17.6 Mev tf-rays also gives good agreement with the Bethe and Heitler values corrected for screening, except at high Z (Pb). Lawson2^ and Adams^l also found the absorp-tion coefficient for Pb to be about 10$ too low at 88 and 19 Mev respectively. 4. Angular Distribution to yr According,,the Bethe and Heitler theory the average angles 6+ and 6- of the positron and electron with the incident photon, should both be of order mc2. This i s about 11° for 2.62 Mev. Groshev 2 0 found however, that the average angle was much larger than this (about 25°), and also that 8L was larger than 0+. The experimental curve of Roy2-'- follows the general shape of the theoretical distribution, but the maximum i s shifted towards larger values. (See Figure 5). Roy found an average angle of 30° between electron and positron, and a 3° difference i n 61-6+ . A recent experiment by Koch and Carter (thirteen hundred pairs) with betatron white radiation also found © (max) for both positrons and electrons for various energies a l l higher than corresponding theoretical values, el was larger than £> except i n the lowest energy range. 0 id 10 3o 4o St, to 7« to B^fde^he^i) ANGULAR DISTRIBUTION OF POSITRONS Nuclear Recoil Tbe iroclear momentum q has been calculated for 76 pairs i n N and 29 pairs i n Kr by Groshev and Frank (See reference 20). This i s done by measuring the experimental momentum of the pair (the vector sum of positron and electron momenta) and solving for q i n equation (2). Thus the r e l i a b i l i t y i s dependent on the accuracy with which one can measure both positron and electron energies K. 27 and the angle between them. Modesitt and Koch have also investi-gated recently the nuclear r e c o i l of the pairs from the betatron white radiation . No other experimental work on nuclear impulse during pair formation has been reported i n the literature. The results of Modesitt and Koch agree i n every f i e l d of comparison with the work of Groshev and Frank, for comparable energy ranges (2.62 Mev). Their results are compared i n Table 2. -13-Table 2 Distribution of Nuclear Recoil Groshev and Frank Modesitt and Koch Gas Kr Air 2h% 1.5 mc 49° 10% 1 .7 mc 20% 1 .6 mc 48° The experimental results indicate a most probable value of momentum transfer near mc and a rapid decrease in probability i n both directions away from mc. If we compare their values with those i n Figure 3, the experimental curves are found to be too low for smaller angles and too high for high momentum transfers, the disagreement for the momentum distribution being particularly sharp. They did not find a decrease of average momentum with increasing 28 quantum energy as predicted by theory . The average momentum q = l .6 mc for the experimental range 8-11 Mev i s i n disagreement 28 with the value 1 .0 mc calculated by Rosenbaum for a quantum energy of 10.2 Mev. Difference of energy E»- E-In Figure 6 I have plotted the theoretical curves of Bethe and Heitler-^ and of Jaeger and Hulme^ for E"+-IL against Z. The points found by various experimenters are also plotted. As we see there does certainly appear to be a dependence on Z. The "exact" curve of Jaeger and Hulme also appears to a better approximation than that of Bethe and Heitler, but this i s by no means conclusive. -14-Summary Figure 6 seems to exemplify the present state of affairs i n the description of the pair creation process. We have seen that there i s only qualitative agreement between theory and experiment i n a l l phases of pair production. Moreover, the experimental results of various authors are not too consistent within themselves for many aspects. There appears to be a great need for further work to be done i n checking and extending these results. 29 Lawson"-7 has discussed the limitations of the Bethe and Heitler t-.o theory, and believes that this theory i s not suitable for precise omparison with experimental results. For tf-rays of less than 3 Mev Lawson states that Jaeger and Hulme's calculation gives a correction of opposite sign to that required. The dis-agreement between theory and experiment arises since the Born approximation may not be applicable for heavy elements, while for light elements the Fermi-Thomas s t a t i s t i c a l gas model of the atom i s not trusted. -15-III PROPOSED EXPERIMENT 1. Aim of Experiment Previous investigations have suffered chiefly from insuf-ficent statistics. In the present cloud chamber experiment, i t i s hoped to increase the number of events, by using a stronger source of gamma radiation than available to earlier workers, and a high Z gas. It would be of great interest to use a gaseous lead compound, but there are none with sufficient vapour pressure. The most suitable gas appears to be Xenon (Z = 54)* Xenon has the additional advantage of being monatomic, so that a low expansion ratio can be used to attain sufficient supersaturation for the formation of tracks. The experiment 32 i s fi r s t t© be carried out with the 2,615 Mev tf-rays"^ from a 30 millicurie source ©f ThC", Later i t i s hoped t© extend the work in conjunction with the U,B,C, Van de Graaff generator, employing the 6,1 Mev V-radiation from F (p, ) and the 17.6 Mev Tf»s from Li (p, #)» As we have seen in Section II, the experimental measure-ments of interest are the number of pairs and Compton electrons originating in the same part of the chamber (through which the collimated tf-ray beam passes), the angles which the pair members make with the /-ray, and the energies of the positive and negative electron. The energies are obtained by measuring the radius of curvature 9 ©f the electron, in a known magnetic -16-field H. The energy can then be read off directly from suit-33 able graphs , where the kinetic energy ©f the electron i s plotted against Hp • Besides these measurements, we expect to have sufficient total track length to examine the pictures for single scattering, and annihilation of positrons in motion, as has been described by Ho Zah-Wei^ "*. Some incidental information should also be obtained on the relatively new field of investigation of "triplet" production. Table 3 Expected Number of Tracks in Xenon Source of radiation ThC" F(p, V ) Li (p, ) Energy of quanta 2.62 Mev 6.1 Mev 17.6 Mev Total number of quanta /sec. IG 9 3 107 106 </> /c c for pairs (sq.cm.) 2.86 10-5 10.8 10~5 22 10-5 1/6.5 1 4 Number of pairs per picture 1 0.15 0.01 Number of Comptons per picture 7 0.15 In Table 3 I have calculated the approximate number of pairs and Compton electrons per picture, that we should expect with the various sources. These figures have been obtained assuming experimental conditions of 50 cm. pressure of Xenon in the chamber, a •working volume of 2 0 ' c c , and a sensitive time of 0.025 seconds. The callimator subtends 0.001 steradians -17-at the source« (See Section IV)• The results of the table should be interpreted only as relative orders of magnitude, because of the many assumptions involved. The figures for the (p,2f) radiation hafre been calculated assuming a 10 microampere beam of protons in the Van de Graaff generator, with a bombarding energy of 1 Mev. The yield measurements (disintegration per proton) are those of Fowler 35 and Lauritsen for thick targets. If we assume that 75% of the pairs formed in the chamber w i l l be suitably oriented for photo-graphy and measurement, we can see from Table 3 that i t wi l l probably require about 4000 pictures to get approximately 1000 good measurable pairs for the ThC" source. About 25,000 pictures wil l be required to achieve the same statistics with the F (p, 1 ) radiation, with -the same solid angle of .001 steradians subtended at the source. 2. Discussion of Errors (a) Scattering Bethe^ has pointed out that because of scattering, the evaluation of the curvature of a charged particle i s significant only i f the velocity v/ i s greater than a certain critical value. To reduce multiple scattering, a gas of low atomic number should be used, and high magnetic fields are also desiroable. This i s because the mean angle of deflection due to multiple -IB-scattering in a given thickness of material, is inversely 3 7 proportional to the kinetic energy of the particle . The deflection due to a magnetic field i s only inversely propor-tional to the momentum. Therefore, at sufficiently low velocities, the scattering effect will be greater than the curvature in the magnetic field. This i s especially true for a gas of high atomic number (argon). In our experiment then, the member of the pairs with the greater kinetic energy, will have the lesser scattering error associated with i t . 3 7 Bethe derives an expression for the apparent radius of curvature due to scattering as where E i s the kinetic energy in Mev, X i s the distance through which the electron passes, B i s a correction factor close to unity, and there are LP nuclei per c c , where L is Loschamidt's number (L= 2 . 7 1 0 ), and P i s the number of atoms per molecule. The radius of curvature in a magnetic field.is Comparing the two radii, Below the "critical velocity ^ , the major contribution to the curvature arises from scattering, and curvature measure-•la-ments are useless. For Xenon at 50 cm. pressure, x = 10 cm., H=600 gauss, this c r i t i c a l energy i s about 4 kev, and i s thus not too significant i n our experiment. If we assume a verified multiple scattering law, Simons and Zuber^ have pointed out, that fluctuations of curvature as well as mean curvature can be u t i l i z e d for energy (and mass) measurements. This can be done by dividing a strongly curved track into a number of sections, say of 1-cm. length, whose curvatures are measured separately. This procedure is specially adapted for tracks with sharp bends due to single scattering, since large differences can be eliminated. Multiple scattering theories have been developed by Bothe^ , Williams- 7 7, Moliere , and Snyder and Scott . These 43 have been summarized by Groetzinger et a l i a and compared with the scattering of 132 beta-particles. The angular deflection <f> of the tangent due to multiple scattering, as projected on a plane of incidence, i s approximately normally distributed: where the correction factor for plural and single scatter-ing i s important for large angles only. The variance, or mean square deflection 6^ , can be expressed as a product of two factors Q and G, where Q depends on the interaction between the particle and the nuclei of the scattering atoms, while G -20 takes into account the structure of these atoms (screening, etc.), as well as statistical considerations. A l l the various theories give Q as: Q = 4 TTN x e 4 Z 2 / p V , where N i s the number of nuelei per c c , x the thickness of the scattering substance, and p and v are the momentum and velocity of the particle. The theories differ in their ex-pressions for G, as well as for Bothe^^ effectively replaces G, which i s approximately independent of mass and energy of the scattered particle, by the numerical value G = 4.125 (b) Projection of the track In analysing the curvature of the tracks, i t is actually not too necessary to project on the plane of incidence of the track. Figure 7 gives the percentage error in the projected angle, i f we project on a plane perpendicular to the direction of the magnetic f i e l d , °<, and <*£re respectively the angles between the directions of the track at the begin-ning and end of the section, and the plane of projection. Under our experimental conditions this error i s probably at most 0.5$. For large angles, one can .of course project onto the plane of incidence. Figure 7 Error from Projection of Cloud Chamber Track (c) Energy Loss Moliere^" has shown that the effect of energy loss due to collision i s negligible. For instance, for electrons with a final energy of 50 kev and a path length of 14 cm. in one atmosphere of argon, the difference i s less than 1%, (d) Turbulence The error due to turbulence in the chamber i s probably very small, since a low expansion ration (1.1) is used with monatomic gases, such as argon and xenon. A few high energy cosmic ray tracks (probably protons) which OGCUT incidents^ in our pictures, are only slightly curved, indicating l i t t l e i f any turbulence. -22-Figure 8 Geometrical Analysis of Cloud Chamber Track 3. Method of Analysis Rather than measure the angles <j>L between the tangents to the projected track at certain division points, I propose instead to measure the angles oc between successive chords* (See Figure 8 where the curvature i s exaggerated). This can be done by projecting the image of the track on a sheet of drawing paper giving the original size of the track, and then laying off, say 1 cm. sections by dividers. The sheet can be mounted on a drafting table, the points connected by straight lines, and the angles between successive chords measured by means of drafting machine. Let the mean of the angles be o , Then i f the section length is x, i£ follows from Figure 8: - -K1 +• J>^ - 2 -X.J=> ^ /z. -23-i f the angles involved are not too large ( <15°). This method of analysis has the above mentioned advantage of minimizing scattering error, and thereby minimizes the standard deviation of Z3. It should be of interest to calculate the experimental standard deviation of the ^o* , and compare i t with that of the various theories. Using the above method of analysis, I should estimate the random experimental error due to optics, photography, and personal error in measurement, to be less than 1°. -24-IV — APPARATUS AND EXPERIMENTAL WORK Cloud Chamber The cloud chamber used for this project i s based on drawings obtained from the Chalk River Laboratories of the National Research Council (refer Chalk River Report P. D. 204 by E. Almqvist), and has been previously described by 44 K. Parry. The whole cloud chamber unit has been assembled on a movable table for future use with the Van de Graaff generator of this department. The chamber i s the rubber diaphragm type, the expan-sion being effected by suddenly opening the back of the dia-phragm to a very low pressure. It i s ordinarily operated with the chamber gas at about two-thirds atmospheric pressure. The chamber i t s e l f consists of a plexiglass cylinder with demensions 23 cm. inside diameter and 5 cm height. Two black aquadag rings are painted aroung the cylinder leaving a two cm. d e a r space i n the middle to assist i n col11mating the l i g h t s . The background i s formed by black velvet stretched over a round ring whieh makes a snug f i t with the cylinder. The velvet makes a f a i r background for photography and helps eliminate turbulence set up i n the chamber by the expansion. The plate glass roof has an aquadag ring painted around the outside, for the clearing f i e l d ($00 v o l t s ) . A rubber tube, through which cold water continuously circulates, •25' i s wound around the base. This is necessary to keep vapour from condensing on the glass roof, and also to keep the chamber temperature constant. When the project was taken over, nice alpha tracks from Polonium and Radium sources were obtained and photo-graphed. Electron tracks, having a much lower specific ionization, are more difficult to photograph and could not be obtained at this point. It was thought this was due to several causes: the chamber was not absolutely leak-tight, the rubber diaphragm seemed to be too slitggish in response, and the vacuum volume was too small for quick expansions. In order to get the chamber leak-tight, a more uniform plexiglass cylinder was obtained and installed. Several types of rubber gaskets were tried, and very thin (1/32") neoprene gaskets lightly coated with Silicone Dow-Corning grease were found to be the best. The grease softens the rubber and a better seal i s obtained. A new f i l l i n g tube with a single outlet was installed. The base of the tube i s soldered directly to the base plate of the chamber, since i t was found after trying other methods that this was the only way to get that joint vacuum tight. A new cut-off valve of the bellows type was originally used. Although this system was very useful for operation, i t proved eventually to be unsatisfactory — one could not be sure that P L A T E I •GLASS & d fo fir rvr-i FILLING TUBE FOR CHAMBER -+4-_i_L PLATE 2 y6p\PfLt Plait. r -M-a-MINOR EXPANSION VALVE -26-the delicate bellows valve was always tight. Consequently, a glass stop-cock was attached to the f i l l i n g tube, using a modified Wilson seal. This has proved t© be very satisfactory and i s absolutely vacuum tight. The f i l l i n g tube and stop-cock are shown in Plate 1, To obtain faster adiabatic expansions, a new diaphragm of first 1/8" natural rubber and later 1/16", was tried. The latter has proved satisfactory for our purposes. The expansion valume of three litres was increased to nine li t r e s , by connecting three old mercury bottles in parallel. The system i s mounted on a permanent frame underneath the chamber, A Welch vacuum pump with an operating capacity of ICO litres per minute continuously evacuates the bottles. The above adjustments considerably improved the speed of expansion. Valves A great deal of time has been spent on trying to stabilize the two valves which control the expansion of the cloud chamber. In my opinion they have not proved to be too satisfactory. The main expansion valve i s the most important working mechanism on the chamber: i t opens the back of the diaphragm to the vacuum, and closes off the vacuum tank for the compression (see plate 3), This ?alve has had to be refitted several times, and several solenoid pins tried. The original brass pin has been replaced by a steel pin 3/16" MAIN EXPANSION VALVE -27-in diameter,; throughout its length, to avoid breaking by the sudden expansions and compressions. The valve relies on a grease seal to keep air from entering the expansion valume. This proved to be an unreliable vacuum seal. Any leaks will tend to Blow down the expansions, and poor tracks will result. During the compression, the bellows must rest squarely on the rubber gasket to close off the vacuum. Adjustment of this can be made by rotating the solenoid pin at the bottom. The secondary valve controls the slow expansions, which remove the old drops formed during the main expansion. The original butterfly-type valve was refitted several times, but the slow expansions were s t i l l unsatisfactory. A new "overhead" type valve was designed and built (Plate 2.). It was necessary to suspend a baffle plate above the valve, to prevent the rush of air forcing i t shut. A spring was attached to the cannon solenoid pin, to prevent the lever from striking the valve too hard. The slow expansions are now quite satisfactory. Control Circuit The control circuit is essentially the same as that developed at Chalk River by the N.R.C. It consists of a series of timing circuits, using thyratrons and a grid con-denser type of control. The condenser is charged up through Figure 9 CIRCUIT DIAGRAM OF STEP SWITCH -28-a variable resistance, and the thyratron "fires' 1 when the condenser voltage reaches the cathode potential of 2 0 0 volts. A pair of thjrratrons, working as a long period multivibrator, actuates a 2 5 positron, 6 bank telephone-type selector switch. This switch controls the whole automatic operation of the chamber. (See Figure 9 ) . The circuit was constructed at a time when good compo-nents were unavailable. Consequently, the electronics con-tinually broke down after a few hours of operation. Many parts of the circuit have had to be rewired in order to obtain stable operation. In addition, several modifications have had to be introduced. The selector switch has been rewired to actuate the minor expansion valve and the camera mechanism. To aid in the removal of old drops and ions, the clearing field voltage i s on during the minor expansions as well, instead of only previous to the major expansion. The control circuit wiring diagram, including modifications, i s shown in Plate 4. 4. Lights The light sources are two argon-filled General Electric F. T. 1 2 6 repeat flash lamps, each with a peak output of twelve million lumens for an input of seventy-two joules per flash. In order to improve the characteristics of the light flash, a three millihenry inductance was added to the conven-pilot light 71 PLATE 5 1 11 variac 2.5v C 1 o o ° 2X2 feoOOv \\0\ 60c CIRCUTT FOR FLASH LAMPS -29-tional circuit. This allowed the lamps to dissipate 35$ more energy, since i t is the dissipation rate which sets the upper limit. The effect of the choke, as observed by a photocell connected to an oscilloscope, was to lengthen the light pulse from 350 microseconds to 1100 microseconds and to halve i t s height. This makes a better light pulse for photographic purposes, because the film reacts better to the slower pulse. The lights are discharged from a 96 microfarad condenser bank at 2000 volts. Since the lamps are 5i" long, they dissipate 17 joules / inch / flash. Although the lamps are run over their recommended rating, no apparent i l l effects have been observed. The triggering voltage from the Ford coil (10,000 volts) had to be carefully insulated from both chassis and lamp case. The wiring diagram for the lights is shown in Plate 5» For protection, the 2000 volt line and return i s kept floating above ground by a 100K resistor, and in addition the condenser bank i s discharged through a diode when the set Is switched off. It i s very important to have as l i t t l e light as possible reflected off the velvet and the top glass plate with a chamber as small as ours, this is difficult to achieve. In order to line the lamps up, a 5000 volt transformer fed off a variac i s used to obtain a feeble light from the lamps, since the actual light flash i s much too short to be easily regis-tered on the eye. -30-Camera The camera used in the investigation i s a Kine-Exacta using 35 num. perforated film. It i s equipped with a Zeiss-Tessar 3«5 lens, focal length 5 cm. Unfortunately, this focal length i s not too suitable for taking stereoscopic pictures, since the camera must be mounted rather far from the chamber (28") with a consequent loss of light intensity. For instance, with a lens of focal length 4 cm., the camera could be mounted 22^" from the chamber, to achieve the same magnification, but the gain in light intensity would be over 50%. Another disadvantage is that only thirty-six pictures can be taken at one loading of the earner. For these reasons, i t may be advisable in the future to obtain a different lens, and construct a camera especially designed for the purpose, and capable of taking, say a hundred feet of film at one loading. The operation of the camera has been made entirely automatic and i s controlled by the major control circuit. A solenoid, composed of 1500 turns of #28 copper wire wound on a brass form, develops enough force through a lever system to trip the shutter. This solenoid i s designed to use 110 volts A. C, and holds the shutter open for approximately one-fifth second. The exposure time i s therefore effectively the whole light pulse from the flash lamps. A small fractional Figure 10 Exacta Camera Shutter Solenoid PLAN VIM OF CAMERA 1 PLATE 6 DIAGRAM OF CHAMBER, COILS, AND MIRROR STAND -31 —horsepower motor winds the film and cocks the shutter through a system of gears. The motor trips a reversal switch to rewind i t s e l f . The 12 volts D.C, required for i t s opera-tion i s provided by a pair of storage batteries. The camera, solenoid, motor and reversing switch are mounted on a brass plate (Figure 10), This brass plate is fastened onto a reinforced stand which is rigidly attached to the Helmholz coils. The circuit for the automatic camera operation i s shown in Figure 11, Stereoscopic pictures are obtained by the double mirror method. Front-surfaced aluminum mirrors (14" x 62") were made in the nuclear physics laboratory, according to the 45 procedure described by Strong , Aluminum f o i l was vapourized on tungsten filaments in a large evacuated vacuum bottle, which was large enough to contain the clean plate glass. The aluminum adhered to the glass, making a good reflecting mirror surface. These mirrors are attached to the camera stand, just above the chamber top. The camera i s mounted 28" from the chamber. The distances are such that a double stereoscopic view of the centre portion of the chamber (through which the gamma ray beam passes) i s obtained. The camera, stand, mirrors, and Helmholz coils are shown schematically in Plate 6. 6. Collimator The collimator (Plate 7) for the source i s designed Figure 11 Shutter Solenoid Mechanical Counter Rewind Motor . Reversing Switch Pe H 5T fe| I / V v Relay C i x V D C - I ' h -p. a-Ps - 0 4 P 7 (KO A-C-) 110 A C . CIRCUIT FOR AUTOMATIC CAMERA OPERATION PLATE 7 SOURCE COLLIMATOR Plate 3 Oollimated Seam -32-to cut down scattered electrons and gamma rays. The seven sections required were cast from lead in brass forms. The ends of the sections were then machined, and the sections inserted into a snug-fitting brass cylinder. The total length of the collimator i s 12", and there i s 1" clearance between the end and the chamber wall. By removing the front section, brass or lead plugs can be inserted into the collimator to f i l t e r the beam. A picture of the beam from the ThC" source as i t enters the chamber i s shown in Plate 8. This was obtained by prolonged exposure of a photographic plate wrapped in black paper. The impression on the plate indicates that the beam is well col 3 imated, and i s 1.1 cm. wide as i t enters the chamber. A plate similarly exposed at the other end of the chamber indicates the beam i s 2 cm. wide where i t leaves the chamber. This corresponds to a solid angle sub-tended at the source of .001 steradians, and checks with the angle expected from the dimensions of the collimator. Reprojection In order to carry out measurements on the cloud chamber tracks, i t i s necessary to reproject them to their original size and position. To do this, the stand with the camera and mirrors attached i s removed from the Helmholz coils and placed on the reprojection table. The film i s them replaced PLATE 9 TILTING TABLE FOR REPROJECTION -33-in the camera in the original position, the shutter i s kept open and a strong light beam i s aimed onto the film from above. The direct and stereoscopic images of the track are focussed onto the ti l t i n g table. The tilting table i s then adjusted so that the images come together. The analysis of the tracks can then be carried out. (Sec. I l l - 3). The til t i n g table was designed for speed and ease of adjustment. A cross-section view i s shown in Plate 9. Rather than employ the usual slower hemispherical steel ball and magnetic clamping method, a brass ball and socket is used which can be rotated in any direction up to 30°. The ball i s automatically held securely in any position by a spring. The tightness of the spring can be adjusted by a knurled knob. The screen consists of a 11" square aluminum plate, finished in white enamel so the image can be easily observed. This plate i s fastened to a short rod which passes through the ball and socket. The assembly is mounted on a vertical shaft provided with a 2" drive, in order that i t can be quickly adjusted to the correct height by rotating a knob. This shaft is held fast by tightening a set screw. The stable tripod base of the t able i s brought into correct horizontal alignment by a positioning screw. The vertical coordinate and the angle of dip that the table makes with the horizontal can be read directly from a steel rule and a compass. -34-V — RESULTS Operation of the Chamber a. Filling the Chamber The following procedure has been developed for the f i l l i n g of the chamber. The chamber i s fi r s t put together, with the top glass plate as clean as possible. The vacuum pump i s then attached to the f i l l i n g tube through a T-joint. The chamber i s pumped out for some time, say over-night, in order to remove a l l gases and condensed vapours. The f i l l i n g tube stop-cock i s then sealed off and the vacuum conditions are checked for a day or so, by means of a mercury manometer attached to the T-joint. The chamber must be absolutely leak-tight for proper operation, since leaks or eddies will distort the tracks or even prevent their formation. The gas (air, argon, xenon, etc.) is then admitted to bring the pressure up to the desired value, read on the mano-meter. This i s usually about 5 0 - 6 0 cm. of mercury. The chamber i s then sealed off by the stop-cock. The required liquid (about 5 c c ) , usually an alcohol-water mixture, i s then admitted into the top of the f i l l i n g tube. The liquid i s allowed to pass slowly through the stop-cock. Some of the mixture should be kept in the upper tube, to prevent air entering the chamber. The volume admitted should be just in •35-excess of the amount necessary to saturate the gas in the chamber, since too much liquid will render the velvet a poor background for photography. The liquid remains suspended in the lower tube, and i s allowed to evaporate and saturate the gas. The liquid must be renewed in the same manner, generally after ten days of operation, because the alcohol vapour diffuses through the rubber diaphragm. This latter effect is quite noticeable, since the odour of alcohol i s very evident when the pump i s fi r s t switched on, after the chamber has been idle for some time, b. Cleaning Process After the gas and vapour are introduced, no expansions are made until the movable plate controlling the expansion ratio i s screwed up as far as possible, giving a very low expansion ratio. The chamber i s then set in operation and expansions are made until any cloud formed shows signs of clearing up. This usually takes several hours, since the vapour must reach equilibrium and the dirt nuclei must be re-moved. The actual time required depends on the purity of the gas used. Tank "gas i s generally much cleaner than air, and can be cleared out sooner. The expanded time i s set at about 30 seconds during this period, so that cloud drops formed on dust particles will have time to settle before the chamber i s recompressed. The chamber expansions are observed by two -36-projection lamps aimed perpendicularly to the axis of vision, since the flash tubes give a far too brilliant and sudden illumination for easy visual observation. As soon as the chamber is fairly clear, the expansion screw i s rotated about 1/8 turn, and the process i s repeated. As the correct expansion ratio i s approached, tracks will appear fuzzy and diffuse at fir s t , and the final good expan-sion ratio (for electron tracks) will be just below the cloud-formation limit. It has been found that this procedure cannot be hurried, since otherwise an over-expansion can occur and the chamber will be f i l l e d with a fog of tiny droplets. Several hundred small expansions may be necessary to remove this fog, even after only one over-expansion. Also, droplets condensing on the chamber roof may form a film on i t . During the above cleaning process, the external room temperature (about 21°C) i s kept constant by a mercury thermostat which controls several strip heaters. In addition, cold water is circulated through the coils and the pipe surrounding the base, at a l l times. Once the chamber has been "cleaned" out, pictures can be taken continuously. One may have to adjust the expansion ratio slightly before commencing a set of pictures, to correct for any small changes in temperature. The above procedure must be repeated however, whenever additional liquid i s -37-admitted to replace the vapour whieh has diffused through the rubber. c. Expansion Cycle The following cycle has been found suitable for rapid picture-taking, after the chamber has been cleared out. (i) 0.0. sec. The chamber is compressed, ready for a main expansion, when the green light on the control panel goes on. The current through the Helmholz coils i s adjusted manually to the correct value by the rheostat, and the lights in the room are put out. The solenoid for the overhead valve should be actuated during this compression. ( i i ) 3.5 sec. The expansion takes place and the clearing field voltage i s removed at the same time. The camera shutter i s tripped by its solenoid. ( i i i ) 3.65 sec. The lights flash. It is important to adjust the light delay so that the drops have time to grow to f u l l sizej just before they start to f a l l . (Position 20 on the switch). Otherwise the tracks are very thin and photography i s extremely difficult. (iv) 28 sec. The chamber resets itself (compression). The clearing field goes back oni. The camera motor winds the film and cocks the camera shutter for another picture. Three clearing, or "minor" expansions follow, which remove the old drops. The compressed and expanded times are -33-the same for these as for the major expansion — that i s , each expansion takes 28 seconds. The complete cycle requires 112 seconds. It i s a very interesting fact that the correct expan-sion ratio i s a function of the compressed time. This effect i s not too clearly understood, but i t probably has to do with the attainment of both temperature and vapour equilibrium in the chamber. In any case, there i s no point in having a longer expansion cycle with a small chamber, i f the chamber i s cleaned out and i s functioning properly. d. Photography Kodak Ortho-Linagraph 35 num. film (clear base) has been found to be best for taking electron pictures. This i s a fast orthochromatic film with a relative speed of 500 in the blue. It is therefore several times as fast as Super XX and i s especially suitable for the light produced by the flash lamps. It i s also a convenient film to work with, since a Wratten series 2 safety light can be used in the dark room with i t , The clear base makes i t very suitable for repro-jection purposes. The film i s less expensive i f obtained in 100 foot reels. Strips of suitable length, say for thirty or thirty-five pictures, are cut off, trimmed, and wound in ordinary 35 num. cassetes. (See the Exacta Guided) This operation takes perhaps a minute in the darkroom. After PLATE 10 LEAD SHIELDING / C0LUMAT0R CHAMBER SCHEMATIC DIAGRAM OF EXPERIMENTAL ARRANGEMENT - 3 9 -exposure the film is developed in Kodak D19 solution for fifteen minutes. This process of over-development increases the contrast between tracks and background. A stop-bath (Kodak SB-5) is used between developing and fixing. The whole development procedure can be carried out very efficiently in a Kodak Day-Light tank for 3 5 num. film. Pictures of electron tracks have been successfully taken at f 3*5 and f 4 with the Exacta camera. The latter stop is the better, because of the increased depth of focus. 2 . Some Observations With a y-ray Source a. Experimental Arrangement A schematic diagram of the experimental arrangement i s shown in Plate 10. The filtered and collimated TT-ray beam from the The" source enters the chamber perpendicularly to the axis of the camera, and parallel to the flash lamps. It passes through the centre of the chamber, and iemerges out the other side which is protected by three inches of lead shield-ing. If i t i s found that back scattering i s serious at low energies, a "tiinnel" type of absorber can be easily constructed. A picture of the cloud chamber apparatus i s shown in Plate 11, with the coils, camera, stand, mirrors, and a flash lamp. The control panel i s to the right of the cloud chamber table. In the foreground is the lead shielding which houses the source and collimator. The overhead pipes carrying the PLATE 11 CLOUD CHAMBER APPARATUS -40-cooling water for the magnet coils and chamber base are visible in the background. The alignment of the source and. functioning of the chamber were fi r s t extensively studied tdth 60 cm. of air in the chamber. The vapour used was two parts of ethyl alcohol to one part of water. Since no Xenon has been available to date, the operation of the chamber has been checked and pre-liminary pictures have been taken with Argon as the gas. The operation of the chamber should be quite similar, since both Xenon and Argon are monatomic gases. The Argon used was at 55 cm. pressure. An alcohol mixture of two parts of normal propyl alcohol to one part of water has been found to give good tracks. The Argon and alcohol were admitted into the chamber, using the procedure described under "Operation of the chamber". b« Pictures Plates 12 and 13 show the electrons obtained from the ThC" beam filtered by a 1/4" plug of brass, with and without a magnetic field. Although there probably are several pairs in Plate 12, the great number of events make3 their determi-nation difficult. (In these and the following pictures, the negatives have not been "touched up", as i s often done for publication purposes). Note the great number of Compton electrons knocked out of the chamber wall. There are approxi-Plate 12 , B>600 gauss irlate 13 No Pield Plate 14 H-480 Gauss -41-mately as many diffuse as sharp tracks. This ratio i s a function of the sensitive time of the chamber. If i t i s found that there are too many diffuse tracks formed in Xenon, there i s provision in the control circuit for shuttering the source, . (This will certainly be done with the (p,}T ) radiation). There i s a certain amount of background light in the chamber, internally reflected from the chamber walls, velvet, and top glass plate. This cannot be entirely eliminated with a chamber as small as the one used. The lamps must be correctly aligned to reduce the background as far as possible. In order to cut down the radiation, the brass plug was replaced by a 3/4" lead plug. Plates 14 and 15 show the electrons obtained under these conditions. The great number of events has been considerably reduced, A typical pair is shown tm. the cantre of the chamber, in Plate 14, This picture was taken with a magnetic field of 480 gauss across the chamber. It will be necessary to have a thin window in the chamber wall to lessen the number of Compton electrons knocked out. Thifc.Beryllium f o i l will be best (not available to date). To test the effect of a window, the chamber was dismantled, and a half-inch hole was drilled in the plexiglass cylinder, to within 3/64" of the inside edge. The source was then lined -42-up with this window. Plate 16 shows a picture taken with a 3/4" filtering lead plug. The number of Comptons has been considerably reduced. Plate 16 Electron Tracks. H =480 gauss -43 APPENDIX Continuously Sensitive Cloud Chamber There has recently been renewed interest in the type of cloud clamber which i s continuously sensitive. Besides being useful for providing an exceptionally vivid demonstration of charged particles, such a chamber would have obvious advantages which would make i t extremely impor-tant as a research instrument. Very few moving parts would be required, so that mechanical difficulties would be greatly lessened. (See for instance, Section IV - 2). In addition, the elimination of the "dead time" of a conventional expan-sion chamber would allow the more rapid accumulation of date. The f i r s t attempt to develop such a chamber was made by Vollrath^' in 1936, using chemical methods. Vollrath found that when HCI vapour and vapour were allowed to diffuse together, the mixture obtained was supersaturated with regard to both components. This sort of chamber was good for demonstration purposes only. The type of continuously active chamber now being examined in several laboratories was fi r s t investigated by A. Langsdorf4^. This chamber attains a continuous super-saturation by the principle of diffusion of vapour through Plate 17 TRAY OF WATER ///////// s / CARDBOARD SATURATED WITH METHANOL GLASS CYLINDER -DRY ICE DIFFUSION CLOUD CHAMBER -44-a strong temperature gradient. Vapour evaporating from a warm surface will reach a region of supersaturation near a cold surface. Tracks will form along the paths of ionizing particles in this region. I have briefly investigated this type of chamber for possible demonstration purposes. One model i s shown in Plate 17. A brass plate 1/4" thick is placed on a block of dry ice. A piece of black velvet on this plate makes a good background for viewing tracks. A glass cylinder 6" in length and diameter forms the chamber proper. Packing card-board soaked in mgthyl hydrate i s placed on the cylinder, and another brass plate on this. A tray of warm water on the upper plate keeps i t at room temperature. Under these ,0 , Qonditions, there i s a temperature gradient of 6 /cm. across the chamber. Tracks from a polonium alpha source were observed by shining the beam of a projection lamp into the chamber, perpendicular to the observer's line of vision. For the fir s t fifteen minutes a dense cloud of droplets formed, until a steady state was reached and a l l the dust particles were deposited. Then tracks were observed in a half-inch high region just above the bottom plate. It was found neces-sary to put an electric field of 1000 volts between the two plates, in order to increase the number of events. The -45-electric field helps remove some of the old ions which affect the background. Tracks formed continuously for about an hour, but throughout this period there was a background of droplets which would hamper photography. Any small leaks of air into the chamber caused turbulence and affected the tracks. "Frost" forming on the outside of the cylinder near the base had to be wiped away every few minutes, so that the tracks could be observed. A chamber of half the height (3") showed essen-t i a l l y the same characteristics. It was hoped that a larger chamber would be less affected by convection currents from the walls. A plexiglass cylinder 12" high and 12" in diameter was constructed. However, no tracks could be obtained with this larger chamber, probably because i t was not made very leak-tight. The preliminary experiments indicate that i t should not be too difficult to make a diffusion type chamber which can be used for demonstrations. The main requisites are that the chamber be leak-tight and that the temperature gradient be made uniform by using a fairly large chamber. Although a l l labora-tories^"*^ 2investigating the continuously active cloud chambers have had to cope with the same difficulties mentioned above, i t seems certain that i t w i l l soon become a useful research in-strument. Indeed, the nice tracks obtained by Cowan^at the California Institute of Technology indicate that for many pur-poses, i t may eventually supercede present day expansion chambers. i -46-BIBLIOGRAPHY For the theory of pair production, I recommend the following references: 1. Bethe and Heitler, Proc. Roy. Soc. 146A, S3, 1934 2. W. Heitler, Quantum Theory of Radiation, Oxford University Press, London, 1949 3. Jost, Luttinger and Slotniek, Phys. Rev. 80, 189, 1950 The last reference gives a recent treatment of the pair production process employing Feynman's method, which i s equivalent to the Born Approximation. The experimental work on pair production i s covered thoroughly in the List of References. A good starting point for cloud chamber work is the article: 4. Das Gupta and Ghosh, Rev. Mod. Phys, 18, 225, 1946 -47-LIST OF REFERENCES 1. Perrin, Comptes Rendus 197, 1100, 1933 2. Plesset and Oppenheimer, Phys. Rev. 44, 53, 1933 3. Bethe and Heitler, Proc. Roy. Soc. 146A, 83, 1934 4. Bethe, Proc. Camb. Phil. Soc. 30, 539, 1934 5. Jost, Luttinger, and Slotnick, Phys. Rev. 80, 189, 1950 6. Jaeger and Hulme, Proc. Roy. Soc. 153A, 443, 1935 7. Alichanow, Alichanian and Kosodaew, Nature 136, 475, 1935 8. Wheeler and Lamb, Phys. Rev. 55, 858, 1939 9. Heitler, Quantum Theory of Radiation. Oxford University Press, London, 1949, second edition, p 198 10. Crane and Halpern, Phys. Rev. 55, 838, 1939 11. Borsellino, Nuovo Cent., 4, 112, 1947 12. Phillips and Kruger, Phys. Rev. 76, 1471, 1949 13. Watson, Phys. Rev. 72, 1060, 1947 14. Gaerttner and Yeater, Phys. Rev. 78, 621, 1950 15. Wentzel, Ann. d. Phys. 69, 335, 1922 16. Klarmann and Bothe, Zeits. f. Phys. 101, 489, 1936 17. Miwa and Kozima, Proc. Physico-Math. Soc. Japan 19, 757, 1937 18. Simons and Zuber, Proc. Roy. Soc. 159A, 383, 1937 19. Zuber, Helv. Phys. Acta. 11, 207, 1938 20. Groshev, J. Phys. U.S.S.R. V, 115, 1941 21. Roy, Proc. Phys. Soc. 62, 499, 1949 22. Chadwick, Blackett and Occhialini, Proc. Roy. Soc. 144A, 235,. 1934 -48-23. de Benedietti, C. R. 200, 1389, 1935 24. Davisspn and Evans, M. I.T. Technical Report No.37, 1950 25. Walker, Phys. Rev. 76, 527, 1?49 26. Koch and Carter, Phys. Rev. 77, I65, 1950 27. Modesitt and Koch, Phys, Rev. 77, 175, 1950 28. Rosenbaum, Phys. Rev. 78, 628, 1950. 29. Lawson, Phys. Rev. 75, .433,.1949. 30. Powell, Hartsough and H i l l , Phys. Rev. 81, 213, 1951 31. Adams, Phys. Rev. 74, 1707,,1948 32. Wolfson, Phys. Rev. 78, 176, 1950 33. Tabids of Electronic Functions, Federal Works Agency, W.P.A. for the City of New York, ,1941 34. Ho Zah-Wei, Phys. Rev. 70,.224, 1946 35. Fowler and Lauritsen, Phys. Rev. 76, 314, 194? 36. Bethe, Phys, Rev. 69, 689, 1946 37. Bethe, Phys. Rev. 70, 821, 1946 38. Bothe, Handbuch der Physik, Verlag Julius Springer, Berlin, 1933, Vol. 22, II, p 1 39. Williams, Proc. Roy. Soc. 169A, 531, 1939 and Phys. Rev. 58, 292, 1940 40. Goudsmit and Saunderson, Phys. Rev, 58, 36, 1940 41. Moliere, Zeits. f. Naturforsch. 3a, 78, 1948 42. Snyder and Scott, Phys. Rev. 76, 220, 1949 43. Groetzinger, Berger and Ribe, Phys. Rev. 77, 584, 1950 44. Parry, M.A. Thesis, University of B.C., April 1949 45. Strong, Procedures in Experimental Physics, Prentice Hall, New York, 1949, p 171 1 -49-46. Emanuel, Exacta Guide, Transatlantic Arts, New York,~1945 47. Vollrath, R.S.I. 7, 409, 1936 48. Langsdorf, R.S.I. 10, 91, 1939 49. Needels and Nielsen, R.S.I. 21, 976, 1950 50. Cowan, R.S.I. 21, 991, 1950 51. Fowler, Mil l e r , Shutt and Thorndike, Phys. Rev. 81, 324, 1951 52. Nexson, Weddle and Nielson, Phys. Rev. 81, 325, 1951 


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