Proportional-Counter Selection of Cloud-Chamber Events Citation Rouse, Carl Albert (1956) Proportional-Counter Selection of Cloud-Chamber Events. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8D6S-QT11. https://resolver.caltech.edu/CaltechETD:etd-06242004-144822 Abstract The 48" magnet-cloud chamber has been controlled by a gated proportional counter and photographs taken of 5313 expansions have been analyzed. The proportional counter was found to (1) select events of lower energy than penetrating shower detectors; and (2) select at a much lower hourly rate interactions in which V-particles were produced. However, the V-particles detected appeared on the average to be of lower energy, hence, could be measured with maximum cloud-chamber accuracy. The µ-meson-induced electron showers detected by the proportional counter have been analyzed. Experimental and theoretical frequencies were obtained for the production of showers with a minimum of 40, 100, and 200 electrons. The frequencies for showers of 100 and 200 electrons were found to be the most reliable. These experimental frequencies are 1.6 +0.8 -0.4 x 10 -6 per second and 0.44 ± 0.21 x 10 -6 per second, respectively. The corresponding theoretical values computed from collision and bremsstrahlung probabilities for spin ½ µ-mesons of 10 x 10 -6 per second and 3.5 x 10 -6 per second reflect the uncertainties of cascade shower theory. Two V-particles of particular interest were photographed. One, event 47202, appears to be strong evidence for the existence of the neutral τ-particle with the decay scheme, τ° → π⁺ + π⁻ + π° + Q ~ 78 Mev. The second V-particle, event 46944, was a negatively charged K-particle that is consistent -- from ionization momentum measurements and decay dynamics -- with the decay scheme, θ⁻ → π⁻ + π°, P* = 206 Mev/c. The measured P* for the event is 207 ± 10 Mev/c. With other events that could be consistent with the θ⁻, this event helps to establish the existence of this K-particle. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Mathematics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Mathematics Thesis Availability: Public (worldwide access) Research Advisor(s): Anderson, Carl D. (advisor) Cowan, Eugene W. (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1956 Funders: Funding Agency Grant Number Caltech UNSPECIFIED Office of Naval Research (ONR) UNSPECIFIED Record Number: CaltechETD:etd-06242004-144822 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-06242004-144822 DOI: 10.7907/8D6S-QT11 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 2714 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 28 Jun 2004 Last Modified: 13 Jul 2023 23:57 Thesis Files PDF - Final Version See Usage Policy. 2MB Repository Staff Only: item control page

PROPORTIONAL-COUNTER SELECTION OF CLOUD-CHAMBER EVENTS Thesis by Carl Albert Rouse In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1956 ACKNOWLEDGEMENTS The autho1° wishes to acknowledge those who have made this thesis possible. With deep and sincere pleasure, the author wishes to express his thanks to Professor Carl D. Anderson and Professor Eugene W. Cowan for their continuing interest, inspiration and guidance. Their many fruitful suggestions concerning every phase of this work are largely responsible for the success of the experiment. The author is also very grateful to Drs. Robert B. Leighton, Victor A. J. van Lint, George H. Trilling, Arnold A. Strassenburg, John D. Sorrels, Don Pickerell, Messrs. John Kadyk, Robert Luttermoser, Gerry Neugebauer, Fred Fuselier, Edward Williams, Bruce Dean and Robert Blocker for the part each had in the design, construction and operation of the 48" magnet-cloud chamber; construction of the proportional counter; and helping the author understand the associated electronic circuits. The cooperation and productivity of everyone associated with the Cosmic Ray Laboratory left the author with a deep sense of pride in having been a part of the group. In addition to Drs. Anderson and Cowan, the author wishes to thank Drs. Leighton, Trilling, and Robert F. Christy for several stimulating discussions concerning various parts of the data obtained during the experiment. Finally, for direct and indirect financial aid, the author is indebted to the California Institute of Techr.ology for the awarding of the Paul E. Lloyd Fellowship; the physics department for part-time employment and a Graduate Assistantship; Mrs. Margaret Fleming who very kindly allowed the author to occupy her patio house (and use her swimming pool) during the greater part of his stay at the institute; and to the Office of Naval Research for their financial support of the research. ABSTRACT The 48 rr magnet-cloud chamber has been controlled by a gated proportional counter and photographs taken of 5313 expansions have been analyzed. The proportional counter was found to (1) select events of lower energy than penetrating shower detectors; and (2) select at a much lower hourly rate interactions in which V-particles were produced. However, the V-particles detected appeared on the average to be of lower energy, hence, could be measured with maximum cloud-chamber accuracy. The p-meson-induced electron showers detected by the proportional counter have been analyzed. Experimental and theoretical frequencies were obtained for the production of showers with a minimum of 40, 100, and 200 electrons. The frequencies for showers of 100 and 200 electrons were found to be the most reliable. These experimental frequencies are 6 l.6~g:~ x 10- 6 per second and 0.44 ± 0.21 x 10- per second, respectively. The corresponding theoretical values computed from collision and bremsstrahlung probabilities for spin 1 2 p-mesons of 10 x 10 -6 per second and 3.5 x 10 -6 per second reflect the uncertainties of cascade shower theory. Two V-particles of particular interest were photographed. One, event 47202, appears to be strong evidence for the existence of the neutral T-particle with the decay scheme, 'l:"0 -w++w+ n° + Q-78 Mev. The second V-particle, event 46944, was a negatively charged K-particle that is consistent--from ionizationmomentum measurements and decay dynamics--with the decay scheme, G -rr-- + rr 0 , P* = 206 Mev /c. the event is 207 ± 10 Mev/c. The measured P* for With other events that could be consistent with the Q-, this event helps to establish the existence of this K-particle. TABLE OF CONTENTS Page . .. . . . . . . . . . . . . . . I. INTRODUCTION II. PROPORTIONAL-COUNTER SELECTION WITH THE ~-8" MAGNET-CLOUD CHAMBER • . . . . . . A. APPARATUS B. RESULTS c. III. • • • • . . • SUMMARY AND CONCLUSIONS 4 4 •...... • 1 • • 6 .••..• 12 . . . . 15 PENETRATING SHOWER DETECTION . . 15 15 IV. COMPARISON OF PROPORTIONAL COUNTER AND PENETRATING SHOWER SELECTION . . . • . . . 17 V. µ-MESON INDUCED ELECTRON SHOWERS 20 A. B. A. B. C. D. E. VI. B. C. 31 . . . 33 MEASUREMENTS AND ANALYSIS CONCLUSIONS . • . . .... .......... INTRODUCTION . • . . . • MEASUREMENTS AND ANALYSIS SUMMARY AND CONCLUSIONS . .. .. .. ... . . . . .. . . . APPENDIX A . . .. . . . .. . 20 20 25 34 34 34 43 44 44 44 48 APPENDIX APPENDIX B IX. . . . . . . . . . . . . . . . . . INTRODUCTION . • . • . . . . . . . . . . CHARGED K-PARTICLE A. VIII. INTRODUCTION. . . . . . • . . . • EXPERIMENTAL RESULTS. . . . . THEORETICAL DISCUSSION . • . DISCUSSION OF RESULTS • • . . . . SUMMARY AND CONCLUSIONS CONCERNING µ-MESON ELECTRON SHOWERS. . . . • NEUTRAL K-PARTICLE A. B. C. VII. INTRODUCTION . . . • • . RESULTS . . • . . . . . REFERENCES 49 51 59 I. INTRODUCTION There are two basic ways in which expansion-type cloud chambers may be operated: (a) random selection of events (1,2,3) or (b) controlled selection of events (1,4,5}. With random expansions it is difficult to make the sensitive time of the chamber greater than 1/lOOOth to l/200th of the total time of operation even with short recycling times, large volumes, and long sensitive times. The advantage of a ran- domly operated cloud chamber is its lack of bias on the observed events. The two main disadvantages are (a) the low efficiency for the selection of interesting events and (b) the low accuracy of measurements when the event does not immediately precede the time when the chamber is photographed. Thus, the present need for large numbers of interesting events with accurate measurements makes some form of cloud chamber control necessary. Control of the chamber has been done by various forms of particle detectors in various arrangements about the cloud chamber. The detectors have been arranged externally, internally or in a combination external-internal array. The particular geometry used necessarily introduces a bias toward particular types of events in the set of photographs obtained. There is also a bias due to the rigor of selec- tion used, i.e., the types and amounts of absorber used and the numbers of detectors required in coincidence and/or -2- anti-coincidence in order to record the event. Hence, in designing a cloud-chamber experiment, the 'counter' geometry and •counter' coincidence--anti-coincidence is chosen to give the most efficient collection of the events under investigation. The particle detectors used for cloud-chamber control have taken several forms. Geiger counters (6,7,8), scintil- lation counters (9), fast ion chambers (10,11), Cerenkov detectors (12,13,14), rr-µ decay detectors (15), neutron counters (16,17,18), and proportional counters (19,20,21) have been used in various manners and with varying degrees of success. Of these the Geiger-counter selection has been by far the most productive. Nevertheless, the particles of interest observed in the high-energy interactions selected by penetrating shower detectors usually have high momenta in the laboratory system of' reference. Hence, identifica- tion of the particles through accurate ionization-momentum measurements and observation of decay modes is difficult with the magnetic fields and chamber sizes available. The bias of penetrating-shower detectors thus passes low-momenta and perhaps other types of events that are, or could be, of interest. With this in mind, other investigators have tried the above mentioned Cerenkov detectors, scintillation counters, neutron counters, rT-µ decay detectors, skeleton proportional counters (19), and standard thin-walled, gasfilled proportional counters in an attempt to photograph -3low-energy events or other events of interest. After operat- ing a thin-walled proportional counter in a six-inch magnetcloud chamber (20), it was decided to build one for the 43,r magnet-cloud chamber. The events obtained with the 48 11 chamber are analyzed below and compared with a sample of · events detected with the same apparatus triggered with penetrating shower detection. Of particular interest is the analysis of µ-meson-induced electron showers and a neutral K-particle and a charged K-particle that decay in the chamber. -4- II. PROPORTIONAL-COUNTER SELECTION WITH THE 43n MAGNET-CLOUD CHAMBER A. APPARATUS The 48 11 magnet-cloud chamber has been described in the theses of Drs. Victor A. J. van Lint (22) and George H. Trilling (23). The electronic circuits for the proportional counter were basically those used by Drs. M. L. Merritt (20) and R. C. Jopson (21). Consequently it is only necessary to briefly describe the proportional counter and the chamber geometry used during the present experiment. The proportional counter was of the thin-walled gasfilled type, being constructed of .010-in. brass and filled to 44 psi (absolute pressure) Argon and 0,5 psi CO 2 . Sup- porting ribs maintained the rectangular shape of the counter. The counter was 1 in. thick, 3 in. wide, and 10 in. long with a 1-mil tungsten wire placed along the 10-in. axis acting as the anode. A schematic drawing of the chamber geometry is shown in Fig. 1. Note particularly the location of the propor- tional counter between the middle and bottom cloud chambers. The expansion of the chamber was controlled by a coincidence of any one of six Geiger counters in the shielded counter tray between the top chamber and the middle chamber and a proportional-counter pulse of a size corresponding to a particle of about four times minimum ionization. This ~---- - --Absorber - Cloud Chamber (Ch 12) · · ~ ~ ,- ---- ~ / # ~ M S 4 - - - - S h i e l d e d Counter Tray------™1 Lens Axes I I ---- ---- --Cloud Chamber-- --- -- - (Ch 3) i --- I -----Proportional Counter --Front View Fir:. 1. --- -- - -c::::J -Cloud Chamber -- -- - - (Ch 4) -~t__ _ Approx. scale: 1:8 Side View Scher:1a tlc dia;~ram of the cloud-chamber geometry. I V! I -6ionization is that of about four 1 Mev/c electrons, a 67 Mev/c 1f-meson, or a 230 Mev/c K-particle. (The cloud cham- bers will henceforth be referred to, from top to bottom, as Ch 12, Ch 3, and Ch 4.) Because of the difficulty of accurately determining the minimum pulse height necessary · to trip the chamber, the circu:.t adjustments were chosen as a function of the picture-taking rate. A rate of about three pictures per hour was found to be optimum for this investigation. After each expansion, a three-minute hold time permitted the chambers to return to equilibrium. The photography, thermostating, and measurement techniques were the same as described by van Lint (22). B. RESULTS Tables I through IV summarize the events selected dur- ing the last 1476 hours of operation. A total of 4203 pic- tures were taken at an over-all average rate of 2.9 per hour. Faster and slower rates were used for two rolls of film. However, this produced no significant changes in the hourly rates for the various events. Tables II, III, and IV expand on items listed in Table I. In Table I, Showers' and 1 1 Stars 1 , 'Penetrating Showers', 1 Mixed Showers' are self-explanatory. Electron 1 Stopping or Stars' are events in which a track is visible in Ch 3 above the proportional counter but not visible in Ch 4 below the counter. Observation in Ch 4 would have been possible if there were no intervening absorber. If the momentum of -7these tracks were ~200 Mev/c, the event was listed as a 1 Probable Star• in Table III. The •µ-meson-induced electron showers' are events in which a single track was observed in Ch 12 and associated with it an electron shower produced in the lead and observed in Ch 3. Fig. 3 is the photograph of a large electron shower produced by a µ-meson. (Cf. Section V.) Table IV separates the 1 Miscellaneous 1 events. From an examination of this Table the difficulties of proportionalcounter operation are evident. The high percentage of single tracks tripping the chamber was probably due to a combination of reasons. Fluctuation in the ionization of the track (20) while passing through the proportional counter; knock-on electrons occurring within the proportional counter; and amplifier noise or 110 volt line transients occurring during the gate time and added to a "minimum-ionizing 1' pulse from the proportional counter appear to be the most probable causes. Included in the 1 Accidental 1 pictures were all pictures in which no visible particle was observed passing through the proportional counter. In many of these pictures, elec- trons were seen coming from the back pistons of Ch 3 or Ch 4, hence not all of the accidentals were due to noise or pulseheight variations. Corrections in the amplifier circuit re- duced the number of accidentals from as high as 65 per cent in one preliminary roll to an average of 10 per cent in later -8Table I. Summaries of events obtained with proportionalcounter and penetrating-shower detection. Event Proportional-counter selection* No. % /hr Penetrating-shower selection** No. % /hr Decaying Vparticles 11*** 0.28 0.009 20 3.0 0.13 Stars 231 5.5 0.185 23 3.4 0.15 Stopping or Stars 160 3.8 0.13 12 1.8 o. 078 Penetrating showers 26 0.62 0.021 90 13.3 0.59 Electron showers 440 10.5 0.35 26 3.8 0.17 µ-meson-induced electron showers 92 2.2 0,074 5 0.74 0,033 Mixed showers 105 2.5 0.084 13 1.9 0.085 Pictures with at least one track with I~ 1. 7 I 0 272 6.5 0.22 75 11.0 o.49 Miscellaneous 2965 70.0 2.4 548 81.0 3.6 * Sensitive time: 1250 hrs. ** Sensitive time: 153 hrs. *** Does not include events 46944 and 47202. -9- Table II. Type Vparticle Decaying V-particles. Proportional-counter selection No. /hr % Penetrating-shower selection No. /hr % X 4 36 0.0032 4 20 0.026 go 1 0~- 0.0008 4 20 0.026 1 5 0.0065 v+ V 2 18 0.0016 2 10 0.013 Vo 4 36 0.0032 9 45 0.059 Totals 11 lOO 0.009 20 100 0.13 -10-. Table III. Stars detected during proportionalcounter selection. Origin No. Proportional counter 124 41.0 0.10 Absorber between Ch 12 and Ch 3 77 25.5 0.062 Absorber between Ch 3 and Ch 4 (outside ~roportional counter) 18 6.o 0.014 Absorber above Ch 12 12 4. O. 0.01 Probable stars (tracks stopping in proportional counter) 71 23.5 0.057 Totals 302 100.0 0.265 /hr -11- Table IV. :Miscellaneous events detected during proportional-counter selection. d of' ;O - Event No. misc. Singles 1861 Doubles r/o of total /hr 62.8 42.0 1.5 202 6.8 4.8 Cl. 16 'I1riples 22 o.8 0,5 0.018 Knock-on electrons from proportional counter 147 5.c Accidentals 625 21.0 14.8 0.5c Blank 75 2.5 1.8 0.06 Chamber did not expand 33 1. 1 o.8 0.026 100.0 70.0 2.37 Totals 0.12 -12rolls. Such a reduction was necessary for the success of the experiment. Table II lists the decaying V-particles observed in the cloud chambers during the experiment. Four of the V-particles were produced in stars originating in the pro·portional counter, as shown in the photograph, Fig. 2. This represents about one V-particle per 50 to 60 such stars if the 71 1 Probable Stars 1 of Table III are included, or, one V-particle per 30 to 40 proportional-counter stars if the •Probable Stars' are not included. In addition, approxi- mately 10 or more tracks from the stars appeared to be consistent with non-decaying charged K-particles. Several of them could possibly have been stopped had there been plates in Ch 4. Of the V-particles observed during the entire ex- periment the most interesting are events 47202 and. 46944, which are discussed in Sections VI and VII, respectively. The first appears to be strong evidence for the existence of the C. --r:0 , and the second is an excellent case of a 8-. SUMMARY AND CONCLUSIONS The following observations and conclusions were drawn from the present experiment: 1. Events 46944, 47202, 51035, and others; p-meson- induced electron showers; and several low-angle penetrating showers show that gated proportional-counter control of an expansion cloud chamber selects interesting events that are -13- Fig . 2 . counter' star . Event 51035 . /\? dmitted from a 'proportional This penetrating shower is outside the solid angle of the penetrating - shower detector . -14passed or detected with less certainty by penetrating shower detectors. 2. In the 124 •proportional-counter• stars, only about four contained more than five high-energy tracks within a small angle. This seems to indicate that proportional counters do select low-energy interactions. A complete analysis, however, has not been made. 3. Plates below the proportional counter would in- crease the observation of interesting events by stopping the long-lived, low-energy, unstable particles produced in the 1 proportional-counter 1 stars. -15- III. A. PENETRATING-SHOWER DETECTION INTRODUCTION Cloud-chamber geometry for penetrating-shower detec- tion is that shown in references (22) and (23). It is the same as that shown in Fig. 1 except for the following three changes: (a) Shielded Geiger-counter tray used above Ch 12. (b) A lead absorber 1-5/8 in. thick placed between Ch 3 and Ch 4 in place of the proportional counter. (c) Shielded Geiger-counter tray placed below Ch 4. The characteristics of penetrating-shower detectors are well known. Hence, this section is not meant to be an exhaustive study of a large number of pictures. Only 677 pictures from three recent rolls of film were surveyed in order to get some numbers for a qualitative comparison with the proportional-counter results discussed above. B. RESULTS The 677 pictures were taken during a sensitive time of 153 hours with an average picture-taking rate of 4.4 per hour. The chamber was triggered by either of two types of coincidences: 0-2-2 or 2-2-1. This means that any simul- taneous pulses occurring from O (or 2) counters in the top counter tray, 2 (or 2) or more counters in the middle tray, -16and 2 (or 1) or more counters in the bottom tray will cause the event to be photographed. The results are listed in Tables I and II along with the proportional-counter results. Only the V-particles are discussed in detail since the events of interest in Tables III and IV do not apply to penetrating-shower detection. In Table I, the events listed carry the same meaning as described above in Section II, Part B, except for as 1 1 Miscellaneous. 1 The 548 pictures classed Miscellaneous 1 in penetrating-shower detection are all pictures in which there is no evidence of a shower--penetrating, mixed, or electron. The events, however, cannot be classified as accurately as the proportional-counter events in Table IV with respect to the efficiency of the detecting technique. It is interesting to notice that two of the 20 V-particles and about 30 to 50 per cent of the stars and stopping particles were observed in pictures in which there was no visible evidence of a shower. -17- IV. COMPARISON OF PROPORTIONAL-COUNTER AND PENETRATING-SHOWER SELECTION From the hourly rates listed in Table I, one can draw the following conclusions: 1. Penetratiµg-shower detection is much more effi- cient as a detector of decaying V-particles. Nevertheless, events like 46944, 47202, and 51035 indicate that proportionalcounter selection has a better chance per V-particle of detecting cases that can be measured with maximum·accuracy. 2, Stars are observed with about the same frequency. However, in Table III note that almost half of the stars detected during proportional-counter selection were produced in the much smaller amount of absorber immediately above, within, or immediately below the proportional counter. Using the value of 6.7 grams per square centimeter, a star frequency of about 0.016 stars per cubic centimeter per day is obtained. The 110 grams per square centimeter in the two lead absorbers within the cloud chamber used during penetrating-shower selection result in a frequency of observation of about 0.00048 stars per cubic centimeter per day. (Stopping tracks were not included in the calculations.) 3. Penetrating showers are detected with greater ef- ficiency with penet~ating-shower detectors, although the gated-proportional counter has a better chance of detecting low-angle penetrating .showers. In addition to event 47202, -18there were two other events in which such low-angle shower secondaries produced interactions in the bottom of Ch 12, from which tracks consistent in mass with K-particles traversed the height of the chamber. Such events produced in ' plates below a proportional counter would probably have been accompanied by a decay above the counter. 4. Electron showers are detected with greater effi- ciency with proportional counters. 5, Mixed showers are detected with about equal effi- ciency. 6. µ-meson-induced electron showers are d~tected with greater efficiency with proportional-counter selection. 7, More of the events photographed with penetrating- shower selection have at least one track with ionization greater than about 1.7 times minimum ionization visible in the chamber volume. 8. About ten per cent more events of those photo- graphed with penetrating shower selection were triggered by events other than showers, stars or stopping particles, such as single particles. From the experiment, it was concluded that: 1. Gated proportional counters require more attention than Geiger counters, but, it was found that after the amplifier-noise and line-transient problems were reduced, the apparatus operated with a relatively high degree of stability. In fact, during the last half of the experiment, the major source of the maintenance problems was not the proportional -19counter and its circuits, but the rest of the cloud-chamber apparatus. 2. Gated proportional counters used in magnet-cloud chamber geometry similar to that of this experiment, can best be used under the following conditions: (a) With good 110-volt line filtering. (b) With large proportional-counter area and with two or more anodes within the sensitive volume of the proportional counter. (c) In parallel with penetrating-shower detectors. -20- V. A. µ-MESON INDUCED ELECTRON SHOWERS INTRODUCTION The most extensiye investigation of electromagnetic inter- actions of µ-mesons has been the experiments by M. Schein and P. S. Gill (24) on "bursts" detected in shielded ionization chambers. R. F. Christy and_S. Kusaka (25) did the theoreti- cal analysis of the results. references (31) and (32). Other experiments are given in Similar events were ob.served in the 48 11 magnet-cloud chamber with proportional-counter control. Fig. 3 shows an example of a µ-meson-induced electron shower containing 200 or more electrons. Cloud-chamber data of such events have the advantage over previous ionization-chamber measurements in that effects of stars and air showers are not included. B. EXPERIMENTAL RESULTS Table V lists the relative sizes and frequencies of the 92 showers reported in Table I. In Table V, ,g, is the mini- mum number of electrons observed in the shower and is the number of showers with Sor more electrons. 1 N(S) 1 The common logarithm (written in this section as 'log 1 ) of these values is plotted in Fig. 4 in a graph of log N(S) vs log S. The slope of this graph beyond 8=40 is consistent with that obtained by Schein and Gill (24). The decreased -21- Fig. 3 , Event 48668 . µ -meson- induced electron shower . About 200 or more electrons are visible in the middle cloud chamber . -22- Table V. Frequencies of µ-meson-induced electron showers. Frequency (/hr) s* N(S)** 10 92 + 6.5 - 0.074 15 65 + 5.4 - 0.052 20 56 + - 5.0 0.045 25 46 + - 4.5 0.037 30 41 + 4.3 - 0.033 40 31 + 3.7 - 0.025 50 21 + 3.1 0.017 60 15 + - 2.6 0.012 70 10 + 2.1 - 0.0080 100 7 + - 1.8 0.0056 200 2 + - 0.95 0.0016 * Minimum number of electrons observed in the shower. ** Number of showers with Sor more electrons. -23! I I I I ' I I' I I l I I i i I ---i 40 -----·--+- -t i) z 1 ,.___ 10 ___,1,_ ___.,_ 20 _.__.......J.._.......J.._....__-1...--1--1........1.-..1....-----iL---L-"'_ 30 60 40 80 s Fig. 4. Graph of log N(S) VB. log S. 100 200 _..j 300 -24slope below S = 40 probably reflects a decreasing efficiency of detection more than anything else. The frequencies at which the showers for particular values of S were observed during the sensitive time of 4.5 x 10- 6 seconds are as follows: s N(S) N(S)/sec (x 10- 6 ) 40 31 +- 3.7 6.8 + o.8 100 7 +- 1.8 1.6 + o.4 - 200 2 + 0.95 o.44+ 0.21 The primaries of all the showers passed through an area of 690 square centimeters at a distance of 39 centimeters above the proportional counter. The horizontal area of the propor- tional counter is 190 square centimeters. These quantities do not exactly define the exact total solid angle but from the pictures it was decided that they give a fair approximation. After considering the theory of such showers these experimental results will be discussed in more detail~ -25C. THEORETICAL DISCUSSION The theoretical frequency for the production of electron showers of S electrons by electromagnetic interaction of µ-mesons in ten radiation lengths of lead is given by (cf. Christy (25)): where separate integrations are carried out for the contributions of collision and radiation processes to the frequency and where E 0 µ-meson energy in Bev. Er Energy of knock-on electron or energy of radiated photon in Bev. t Depth of absorber in radiation lengths. Radiation length in gram per cm 2 8 dE N(E )dE :::: 15 • Number of µ-mesons per second with 0 0 0 E~ energy E 0 in dE admitted in the solid angle of ~he experimental geometry (28). X 0 Probability per gram per cm 2 that a µ-meson of energy E0 will produce a knock-on electron of energy E 1 in dE 1 • Probability per gram per cm 2 that a µ-meson of energy E0 will radiate a photon of energy Et in dE'. P(E' ,t,S) Probability that a knock-on electron or photon of energy E 1 at depth twill produce a shower of Sor more electrons at depth t = 10. -262 /(E 0 + 11) is the maximum transferable eHergy by a µ-meson of energy E0 • E max E El Minimum energy of a knock-on electron or photon that will produce a shower of S electrons at depth t = 10. 1 . min Energy of a µ-meson whose maximum transferable energy is the minimum energy of a knock-on electron or photon that will produce a shower of S electrons at a depth t = 10, or, a µ-meson whose E 1 ma x = E 1 min •• <pco, and 'YraJ m for a particle Christy and Kusaka computed of mass m, of spin 0, ½, and 1 and of "normal 11 magnetic moment. The forms of the above probabilities for particles of spin½ and mass m given by Rossi (26) and used here with the same notation are l(E 0 ,E 1 )dE 1 col = and {(E 0 ,E 1 )dE 1 rad = 4c(NZ A 2 2 Er 2 (1 ~ln ( 2 3h 2E 0 In C e dE 1 1 + (1- E•) 2 - -(1 - -E'] 32 E0 Eo r2 (me) e m rn }J)- ~ , 2 2 where C = trNZre /A = 0.150Z/A cm /gm and rn = 1.38 x 10- 13 A3 cm= 0.49 reA¼ , re= electron radius. interest, For the energies of /J= 1. The probability P(E 1 ,t,S) was obtained by the use of Rossi shower curves (27) shown in Fig. 5. An example of the 6 t--------+----+------;------t-----i-----+-----;------+---~--~ ---t- --- --- 5 ------+-- i 4 ----+----+----+ --·-·- - ··---- --------+------~ log S =:2.5 -10 lzl Cl) ~ 3 ' lQg,S ~ 2.0 r--+---k J\) --.J I log S ~ l.~ ,-1 2 t-------+---- -+----+- I ----+-- ·--~--- ------1-- - · - - · - + - - - - - - + - · · - ·--· ·-1 ---·· I 11----- i -----+------+------+----l-----c+-, . i I ii 0 Fig. 2 1 0 5. 3 6 4 5 t {radiation length) 7 8 log!' vs t~ for different values of S (cf. reference (27)}. 0 9 10 -28method will be given by finding the probability for the production of 100-electron showers by knock-on electrons or photons of 7.5 Bev energy. Fig. 6 shows the graph of P(E 1 ,t,S) vs t obtained by the following approximate method. The ten radiation-length absorber is divided into five cells of two radiation lengths, each cell centered about t = 1,3,5, 7, and 9. Consider now Fig. 5. For showers of 100 electrons, the curve labeled log S = 2 is the curve of interest. Only 1 small fluctuations in S--order of magnitude 3 2 --are assumed. Using the critical energy e 0 = 0.0076 Bev, ~og (E 1 /e 0 ) is 2.99, for E 1 = 7.5 Bev. The critical energy, e 0 , is the collision loss per radiation length of electrons of energy e 0 • The next step is to note where the value of log (E 1 /e 0 ) lies with respect to the curve, log S = 2, at the various values of tr (tr= 10-t). log (Er/e 0 ) For the knock-on occurring at t = 3T the value of = 2.99 is noted in Fig. 5 at tr = 7, since tr • 7 is now equivalent tot= 10 in the absorber. The value lies essentially on the curve, hence the probability for this cell is 0.5 since half of the time S would be greater than 100 and half of the time, less. Fort= 5 in the absorber; at tr = 5 in Fig. 5 the value of log (E 1 /e 0 ) lies above the curve, hence the probability is 1.0 for this cell. For the other cells, the value of log (E 1 /e 0 ) lies below the curve, hence the value of P(Er,t,.s) is zero for these cells. Consequently, the outline of the shaded area in Fig. 6 represents the ap- P(B• • t.S) l.Or-------r-------------,-....,....----.------, 0.51----------1~r-r~~~-A----t-----1 0 0 1 2 3 4 5 6 7 8 9 t (radiation length) Fig. 6. Graph of P(E•,t,S) vs t, for B• = 7.5 Bev and S = 100 electrons. 10 t I\J \0 I -30- = 7.5 Bev and S = 100. proximate function P(E•,t;S} for E• The probability functions for other values of E 1 were obtained in a like manner. Because of the nature of P(E•,t;S), Eq. (1) had to be integrated numerically. N(S)/sec::::xol1 Eq. (1) then becomes I N(Eo} pcol ~~af' At (E 0 , E1 ) P (E,, t, S) At AE I dE 0 rad where the summation is carried out over 6t, 6E'>, and between the limits of integration given in Eq. (1). dE 0 An upper limit of 200 Bev was used in the summation over E0 since the contribution to the frequencies beyond this is negligible. Using reasonable values of E 1 and E0 , approximate theoretical frequencies were obtained as follows (with the experimental values repeated beside them for comparison): s Experimental frequen/s (x 10-6 sec) +- o.4 100 1.6 200 o.44 +- 0.21 40 6.9 + 1.7 Theoretical frequegcy (x 10- /sec) Ratio of theoretical to experimental frequency 10 6 3.5 8 68 10 -30AIn an attempt to account for the large discrepancies between the experimental and theoretical frequencies, two factors were varied independently to test the effect on the theoretical values. First, the value of the critical energy, e 0 , was raised to 10 Mev and the calculations carried through for showers of 100 or more electrons. This reduced the above theoretical frequency about 40 per cent to about 6.x 10- 6 per second. Next, with e 0 still equal to 7.6 Mev, it was assumed that the observed showers of 100 or more electrons corresponded to calculated showers of 200 or more electrons. This would be the theoretical frequency for the 200-electron showers above, i.e., 3.5 x 10 -6 per second. This is about a 6 5 per cent re- duction in this theoretical frequency. Physically, this assumption is based on the loss of electrons in the absorber by scattering and perhaps other causes. The experiments of W. Blocker et al. (33) indicate that this loss due to backsea ttering is about 41 per cent of the calculated number of electrons. Consequently, varying both factors at once could conceivably reduce the theoretical number to about 2-3 x 10- 6 per second. Another uncertainty is the size and position of the shower maximum in lead. Belenky (34) shows that these quanti- ties are smaller than those used in the Rossi shower curves. This change would decrease the theoretical frequencies further a few per cent. -30BFinally, the final uncertainty considered is the amount of the fluctuations in the size of the showers. The fluctu- 1 ations are believed to range anywhere from S2 to S-1 (29). Larger fluctuations than those assumed in this analysis would cause an increase in the theoretical frequency due mainly to the contributions by fluctuations below E'min and Eomin* The actual value is probably somewhere between the values above. -31D. DISCUSSION OF RESULTS The major sources of error in the experimental results are as follows: 1. Knowledge of the µ-meson spectrum. The best values available to the author of the vertical intensities ofµmesons of various energies were obtained by the use of two graphs listed by J. G. Wilson (28). One graph is a range-- energy relation for p-mesons in terms of range through earth, in meters of water. The second graph is that of the vertical intensity of the hard component of cosmic radiation as a function of depth through earth. 2. Poor statistics for S = 100 and S = 200. 3. Decreased efficiency of detection for the smaller electron showers. A momentum of about 50 to 60 Mev/c is needed for an electron leaving the lead absorber above Ch 3 in a vertical direction to reach the proportional counter. Without materialization of photons in the brass absorber above the proportional counter, the detection of the event would depend on the possible causes for single tracks tripping the chamber discussed in Section II, Part B, above. 4. Difficulty of observing every electron that enters Ch 3, particularly in large showers. This error will always be in one direction, viz., to give a value of S that is actually smaller than the minimum number of electrons in the class of showers. Therefore, the error in the experimental -32-6 shower frequency for S = 100 should perhaps be 1. 6+0 _0 : 8 4 x 10 per second rather than as given on page 24. The major factors influencing the accuracy of the theoretically derived cross-sections are: 1. Knowledge of the µ-meson spectrum as above. 2. Complexity of the theoretical analysis of cascade electron showers (cf. Rossi (29)). 3. The uncertainties of cascade shower theory. 4. The effect of a magnetic field on the development of a cascade electron shower. The exact analysis of this would be quite complex, but the effect is believed to be small. 5. The accuracy of the probability function, P(E',t,S). Its accuracy depends on (2) through (4) above and the finite size of the cells used. -33E. SUMMARY AND CONCLUSIONS CONCERNING µ-MESON ELECTRON SHOWERS. The following conclusions can be made about µ-meson- induced electron showers: 1. Cloud chambers controlled by proportional counters afford a better method for the study of µ-meson electromagnetic interactions than ionization chambers. 2. The large discrepancy between the experimental and theoretical shower frequencies appear to reflect the uncertainties in shower theoryJ particularly the critical energy, loss of electrons due to scattering, size and position of the shower maximumJ and fluctuations in the sizes of the showers. VI. A. NEUTRAL K-PARTICLE INTRODUCTION The decay in Ch 12 of a neutral K-particle--event 47202--is shown in Fig. 7. The cloud chamber was ':;rig- cered by the low-angle penetratinc shower visible in the lower-left corner of the chamber. The axis of the shower is down to the right and toward tre piston of the chamber. There appears to be an almost equa1 proba-oili ty of triggering the chamber by either penetrating-shower detection or gated-proportional-co~nter control, but perhaps a greater probability should be given to the proportional counter because of the direction of the shower axis. The V-particle appears to have oeen produced in the interaction in the bot~on of Ch 12, we11 defined by the three heavily ionizing tracks seen originatinc on the botto:n left side of the chambe:>. the arrow at B. 1 This apparent origin is indicateci. by 0 1 in ~he :igure. MEASUREMENTS Al;D ANALYSIS In Fj_g. 7, the positive track is indicated by the arrow at 1 A 1 and the negative track, by the arrow at 1 31• The momentum of the positive was deter:nined tc be lCl + 3 Mev/c and that of the ne[::ative track, <;3.6 ±- 3 Mev/c., with an included angle of 61.8°. The ionization estinates ~or each -35- Fig. 7. Event 47202. Decay of a neutral K-particle that appears to be strong evidence for the existence of a neutral T -particle with the decay scheme, t lT - + lTo + Q ~ 78 Mev. 0 - n+ + track range from 1.8 to 3 times minimum ionization, I 0 , with the most probable values of ionization, I, given by 2.5 I 0 • In order to get the most probable masses of the particles, a comparison of the expected values of ionization for P lT-mesons and µ-mesons of momenta P+ = 101 Mev/c and = S4 Mev/c are made as follows: p+ p 101 Mev/c 94 ~~ TT-meson 2.3 Io 2.5 Io µ-meson 1.7 Io 1.8 I'0 Differences in ionization of 20 per cent or more should be discernible, but no difference that large is apparent. Further, by comparison with the identified, 520 Mev/c proton track with the most probable ionization of 3.0 I 0 --the nearly vertical track on the left in Fig. 7--the ionization of the above tracks could not be lower than 2 I 0 • Consequently, from ionization-momentum measurements, both particles are probably of TT-meson mass. Their masses are certainly not as light as that of an electron. Nevertheless, the dynamics of the decay were carried out considering three possible combinations of charged particles, viz., (rr\rr-), (rr•,p- ), and (µ+,u-). On the basis of a two-body decay, the three Q-values are obtained as follows: -37Q(TT+ ,TT-) = 17.2 + 2.5 Mev (1) Q(lT+,µ-) = 19.9 + 2.5 Mev (2) Q(µ+,TT-) = 25.2 + 3.0 Mev (3) The resultant momentum, P0 , of the two visible tracks is 167 ± 4 Mev/c. All three of the above Q-values are very different from that of the nomal 9° decay, hence, the event is of the anomalous type reported by van Lint (22) and others. Three possible decay schemes that could explain the event are: 8 anom o gO anom lf + + ,-ll - where Y is a neutrino. +V + Ql , ( 4) , (5) (6) The highly probable origin can be used in an attempt to determine which decay scheme is the most probable. With an origin it is possible to simplify the analysis of a three-body decay to that of a two-body decay by considering the two visible tracks as a single particle of momentum equal to the vector sum of the momenta of the visible particles and of mass equal to the sum of the masses of the visible decay products plus the Q-value ob- -38tained on the basis of a two-body decay. This method simpli- fies and completes the analysis of cascade three-body decays discussed by van Lint (22). (See Appendix A.) Applying this method of analysis to event 47202, the masses of the 'combined' particles are, using relationships · ( 1) through ( 6), 111-rrrr = 2m" + 17 = 297 Mev , m-rrµ = m,r + mµ + 20 = 266 Mev , mµlT = mp. + fin' + 25 = 271 Mev , with a laboratory momentum of If the vector representing the line of flight of the K0 particle is called LOF, then the angle between~ and LOF is from which the transverse momentum is given by . 40.2° = 108 + 3 Mev/c PoT = P0 sine and the longitudinal momentum is given by P0 L = P0 cosine 40.2° = 127 + 3 Mev/c • Only the analysis of the in detail. r decay will be discussed First, a minimum Q-value is obtained by assuming -39that the transverse momentum is equal to the center-of-mass momentum, Pb, or POT= p~ = 108 Mev/c, Next, a ir 0 is assumed to be emitted with a momentum in the center-of-mass system equal and opposite to that of the m,Tlr , or, -P* Tl'" = - -P*0 Now the total energy of both particles in the center-of-mass system equals the minimum value for the rest mass of the parent particle and is given by The minimum Q-value is then given by ~in = 489 - 2mTT '""' In,,o = 7 4 Mev . In the decay of a is 78 Mev. t 0 of mass 493 Mev, the expected Q-value This implies that if the neutral particle in event 47202 is indeed of ffo mass, it is emitted at nearly right angles to the line of flight in the center-of-mass system--the most probable region of emission (22). If, now an initial mass of 493 Mevis assumed, I;,.! becomes 112 Mev/c. Using Trilling 1 s formula (23) for ~ ~ = PoL E!r ! Emr ro: ~ m-z + R2 ~n OT ,---. , m2PoL +E:Wn-z = O. 4 O nrr ~T ¥/J, -40from which JS= 0.37 and 't = 1.08 and = 197 Mev/c • The time of flight is given by = 1.9 x 10- 9 seconds . t = c P-ro Finally, the minimum ,a for the event is = 0. 37 . rSmin = Obviously, the event, relative to the visible origin, is very consistent with the assumption of the decay Table VI lists the above quantities together with those for the decay schemes (5) and (6). Evidently, if we disre- gard ionization estimates, the dynamics can be consistent with all three decay schemes. The production dynamics, how- ever, would favor the lowest value of proceeds as follows. ;S. The argument If no large fraction of the momentum of the primary production particle is absorbed by the nucleus, the velocity of a particle in the Laboratory System becomes increasingly smaller as the laboratory angle of emission becomes larger. Consider the relationship for the labora- -41- Table VI. Summaries of three possible three-body decay schemes for event 47202. · :Q,-value ( two-body decay) (Mev) 17 ± 2.5 19.9 ± 2.5 25.2 ± 3.0 Combined 1 mass (Mev) 297 266 . 271 Minimum Q-value (Mev) 74 150 154 P* (Mev/c) 112 175 173 G* (Degrees) 90 142 141 o.4o 1.02 0.98 0.37 0.72 0.70 1.08 1.42 1.40 /Jmin 0.37 o.43 o.4o P(of K0 )(Mev/c) 197 504 485 Time of flight (x 10- 9 seconds) 1.9 0.54 0.56 1 (*) All values of Yf are single-valued. -42tory momentum of a particle 1 i 1 as a function of the labora- tory angle of emission, 8i, given by (30) ' where it is seen that for fixed~ and ~i*, Pi is a decreasing function of ei. In an interaction in which the velocity of the particle in the center-of-mass system (~f) is equal to the velocity of the center of mass, the limiting laboratory angle of emission is 90° with a laboratory momentum equal to zero. The degree to which this is applicable to event 47202 depends on the fraction of the momentum absorbed by the nucleus in which the V-particle was produced. The magnitude of the probability that a large fraction of this momentum is absorbed by the nucleus can be ascertained from the total number of identified ~-particles produced in the absorbers between the cloud chambers during previous experiments. Of about 100 such particles observed, only about six were seen moving backward in the laboratory system. * Hence, the probability that the nucleus will absorb a large fraction * It can be shown that in a nucleon-nucleon or TT-nucleon collision, a product particle with mass greater than nucleon mass would not be seen traveling backward in the Laboratory. System. See Appendix B. -43Now, the K0 under con- of the momentum is less than .06. sideration appears to have been emitted at nearly right angles to the shower axis, hence, has the largest probability of having the lowest of the three possible values of~- C. CONCLUSIONS The following conclusions can be drawn concerning event 47202: 1. The masses of either particle observed in the decay of the particle shown in Fig. 7 is certainly no~ as light as the mass of an electron. 2. The analysis of event 47202 presents the strongest evidence known to the author for the existence of a neutral "t'-particle with the decay scheme + 3. Tr 0 , Tf O + Q ~ 78 Mev Because of the lack of observable evidence of the other possible decay schemes cannot be ruled out ab- solutely. A few more events of the quality of event 47202 (or better) are needed to firmly establish the existence of the --c-0 • -44- VII. A. CHARGED K-PARTICLE INTRODUCTION One of the three negatively charged V-particles de- tected during the proportional-counter operation.of the 48u magnet-cloud chamber is shown in Fig. 8. The particle entered the visible region of Ch 12 from the l&ft-rear as indicated by the arrow at 1 A 1 in the figure. It traversed about two-thirds of the chamber width and decayed near the rear-to-front center of the chamber. The visible secondary left the chamber as indicated by the arrow in the figure at 1 B1 • The chamber was triggered by low-energy particles that apparently came from the same interaction in which the particle of interest was produced. It appears that the event would have certainly been passed by the penetrating-shower detector. B. MEASUREMENTS AND ANALYSIS The momentum of the primary was dete:r:>mined to be 521 + 40 Mev/c, and that of the seconday, 191 + 7 Mev/c. The ionization of the primary is estimated to be about 1.5 times minimum ionization. The ionization of the secondary is estimated to be less than that of the primary and about 1.3 or 1.4 times minimum ionization. Now, the ionization -45- Fig . 8. Event 46944. Decay of a negatively charged V-particle that is consistent wlth the decay, g- --lT - -t lT 0 , P* = 206 Mev/c. P* for the event= 207 + 10 Mev/c. -46of a 520 Mev/c proton is 3.0 I 0 and that of a 520 Mev/c K-particle is 1.5 I 0 • Hence, the mass of the primary is certainly not greater than the mass of a proton. Further, the ionization of a 191 Mev/c lT-meson is 1.25 I 0 ., and that of a 191 Mev/c p-meson is 1.1 I 0 • Consequently, the visible secondary is probably of ~-meson mass. The laboratory angle of emission of the rr-meson is 62.2°. From this, a transverse momentum, PT, of 169 + 6 Mev/c and a longitudinal momentum, PL(~), of 89 ± 3 Mev/c are obtained. The apparent length of the primary track is about 27 centimeters, hence, the time of flight 'is greater than 9 x 10- 10 seconds. Using the primary momentum of 521 Mev/c and a mass of 493 Mev., the velocity of the Center of Mass is given ~Y /J= P/W = 0.725 + 0.056 where W is the total energy of the particle. From ft, (6 = 1 . 05 + O. 08 and ~ = 1.45 + 0.11 . Transformation of PL(rr) to the center of mass system gives -47- and with PT determined above, Computation of the error in P* by the relationships given in reference {23) gives a P* ~P* of ±IOMev/c., or., = 207 + 10 Mev/c . The expected P* in the decay is 206 Mev/c. Further., if the secondary of ev~nt 46944 is assumed to be a p meson., a P* of 198 ± 10 Mev/c is obtained. This value is inconsistent with the expected value of P* of about 239 Mev/c for the decay K~ --F +?+? C. SUMMARY AND CONCLUSIONS The following conclusions can be made concerning event 46944: 1. The mass of the primary is certainly not greater than the mass of a proton and most probably equal to the mass of a K-particle. 2. The event is inconsistent with the decay Kp- - ru- +?. +?. , because of the difference of the measured and e~pected P* of aoout four probable errors. 3. The event shows excellent consistency with the decay Q 4. - - Tr + Tfo + Q _, 218 Mev . With the cases reported by Trilling (23) in his study of charged V-particles and the others obtained in this laboratory since his report was written, the excellent case reported here helps to establish the existence of the G-. -49- VIII. APPENDIX APPENDIX A FURTHER COMMENTS ON CASCADE THREE-BODY DECAYS Consider the decay of a particle of mass mi that decays into two particles with masses m0 and m1 . Further, assume the particle m0 immediately decays into two more particles with masses m2 and m . 3 The cascade can be repre- sented by the relationships as follows using the definition of a Q-value: Qio = mi - ml - mo L- m2 + m3 . The second decay can also be written as or, substituting in and rearranging the above relationships, and -50Let m2 and m represent two measurable charged particles. 3 Then Q is obtained from measurements on particles 2 and 3. 23 With an assumed mass for m1 and an origin, a minimum Q-value can be obtained after a minimum value for the mass of the primary particle, m , is determined from the relationship i With this, ID.,:, '- -51- APPENDIX B LIMITING LABORATORY ANGLE OF EMISSION OF HYPERONS After it was noticed that only a small fraction of the observed neutral V-particles where seen moving backward in the laboratory system, the question of the production dynamics necessary for this was thought to be of interest. Fig. 9 represents the collision of a particle of mass mi and momentum P1 with a particle at rest of mass m0 • The particle of interest will be the product particle of mass m and laboratory momentum, Pm. M represents The second particle of 1 mass 1 the sum of the masses of all the particles ex- cept the particle of interest plus the 11 particles (e.g., mass m0 in Appendix A). sultant momenta. Q-value 11 for these PM is their re- The laboratory angle of emission of par- ticle mis represented by Qm--the other quantity of interest. The problem can now be restated as follows: For m :> m0 , under what conditions will gm> 90°? Consider, now, the transformation of the longitudinal component of the center-of-mass momentum of particle m given by ( 1) where, of course, Wm is the total energy of the particle. CENTER OF MASS SYSTEM LABORATORY SYSTEM . m pm mi 0/ 0 ---------· pi m < Q* ··-,,m '" mi ,Qm \ • """""nptr- _, ~ m 0 P*0 o M M I Total momentum = P --~ --PA -- ""' P1 0 w I +fPA + 2 P*2 = ( W* 2 + .M 2 - m2) _ M2 m 2w' W* = f:2 + m2, W =iW* Fig. 9. "' ,v = {Pf + mi + m --- = -Pi Velocity of center or mass =;3 Total energy = W = \.;7 Schematlc diagrams of a two-particle collision. M2, -53Calling the direction of Pi the positive direction, PmL will be negative--which will be the case when mis emitted backward in the laboratory system--when P~L is negative, and when jYP;LJ) ~pw;. The minimum value of P~ for which this could be true occurs when P:L = P;. Conse- quently, the problem reduced to that of finding the condition under which 1'P*m >'YAW* r m or ( 2) The problem can be made more general by the analysis of the conditions under which >, Qm < 90° 15w; <~ P*m =, Gm = 90° <, gm > 90° Squaring Eq. (3), or (3) -54transposing (4) Using the relationship for Pi given in Fig. 9 and using W =YW*, Wand W* being the total energy in the laboratory system and center-of-mass system, respectively, Eq. (4) becomes Now, using ~= (Pi/W) = (P/W), 0y2 = W2 /(w 2 - P2) , and after going through the algebra, ~,em <00° =,em= 90° >, em ) '!JOO. Substituting into Eq. 2 2 2 2 M - m = A, and mi - m0 = C, (6) -55- ( 7) or, multiplying by -1, "7,0m <. '30o =,em= 000 ~,em )'~00. (8) For M = m1 and m = m0 , i.e., C = A, f(W ••.. ) = 0, hence, no value of the energy for particle mi will produce a laboratory angle of emission greater than 90° for a particle equal in mass to the mass of the target particle. For other combinations of particle masses, things get more complex. Before proceeding with the analysis, an ex- pression for the threshold energy in which particles of mass This energy is the Mand m can be produced will be derived. energy in the center of mass system for which W* = M + m = w/~ w2 = ~2(M + m)2 = w2 w2 - p2 (M + m) 2 .from which (9) = Returning to the analysis for arbitrary masses, Eq. (8), by completing the square, becomes --zr where m I m0 • 0 ;\ 2 (10) 2 m - m0 Now, for application to the production of -particles in lf.meson-nucleon collisions, let mi = 0.140 Bev, m0 = 0.940 Bev, and m = 1.107 Bev. As a function of Wand M, Eq. (10) then becomes 2 2 2 2 f(W,M) = [W - 1.380 (0.361 - M )] - 2.635 (0.361 - M ). (11) Eq. (11) represents a parabola which opens out in the direction of the positive f-axis. For M = O, 0.361, and 1.00 Bev, Eq. (11) becomes f(W,M = 0) = (W - 0.497) 2 - 0.343, (12) -57- f(W, M = 0.361) = w2 , (13) and = (W + 0.881) 2 - 1.074. f(W, M = 1.00) (14) The corresponding values of the threshold energy are given by (15) Wn (M = o) = 1.11 Bev, WTh (M = 0.361) = 2.00 Bev , (16) 2 . 88 Bev , (17) and WTh ( M = 1 . 00) = respectively. From Eqs. ( 12), ( 13), and ( 14) the maximum values of W for which f(W) = 0 are 1.052, zero, and 0.211 Bev. These values are less than the threshold energies given by Eqs. (15), (16), and (17), hence, it appears that f(VJ,M) > O for values of W above threshold. To test the function for large values of M, consider the values of W which make f(W,M) =Oas determined from Eq. (11), or, -58- W(f = 0) = 2 (1.380 + 1.62) (0.361 - M) . (18) From Eq . ( 9) , as M- o0 , (19) Consequently, the threshold energy is always gre~ter than the value of the energy, W, for which f(W,M) = o. Hence, 0 for a 7T-meson-nucleon collision, a /\ -particle produced in the interaction would not be seen moving backward in the laboratory system. A similar analysis carried out for a nucleon-nucleon collision led to the same conclusion. Therefore, the observation of A.0 -particles moving backward in the laboratory system implies that the nucleus in which the particle was produced absorbed a large fraction of the momentum of the primary production particle. -59IX. 1. REFERENCES L. Janossy, Cosmic Rays, 2nd Ed., Oxford At the Clavendon Press (1950). 2. E. J. Williams and G. E. Roberts, Nature, 145, 102 ( 1940). 3. A. Lovati, A. Mura, C. Succi, and G. Tagliaferri, Nuovo Cim., 12, No. 4, 526-38, (1954). 4. P. M. s. Blackett and G. P. S. Occhialini, Proc. Roy. Soc., Al39, 699 (1933). 5. P. M. S. Blackett, Proc. Roy. Soc., Al46, 281 (1934). 6. B. 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