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A Study of the Methods of Meson Mass Determination A

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A Study of the Methods of Meson Mass Determination A A STUDY OF THE METHODS OF MESON MASS DETERMINATION A THESIS Presented to the Faculty of the Division of Graduate Studies Georgia Institute of Technology In Partial Fulfillment of the Requirements for the Degree Master of Science in Physics by Gilbert Carl Knollman June 1950 r 642 ii A STUDY OF THE METHODS OF MESA f- MASS DETERMINATION Approved: ra■•■•■■■■■■•■ Date Approved by Chairman /227 1 9. c-n iii ACKNOWLEDGMENTS I wish to express my sincerest thanks to Doctor L. D. Wyly for his valuable assistance in preparing this work. I would also like to thank my wife, Hilda, for her aid in proofreading the material. iv • TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION 1 Statement of the Problem 1 Discussion of the Problem 3 Definition of Terms and Symbols Used . s 9 II. MESON HISTORY" 12 III. GENERAL APPARATUS EMPLOYED IN MESON MASS MEASURE- ENTS 19 IV. GENERAL Mi, THOD3 OF MEASURING RAN CE, CURVATURE, AND SPECIFIC IONIZATION 37 V. DIRECT METHODS OF MESON MASS DETERMINATION. 46 Elastic Collision 46 VI. INDIRECT METHODS OP MESON MASS DETERMINATION. 58 Range and Curvature 58 Momentum Loss 73 Ionization and Curvature 98 Method A: Primary Ionization of Slow Electrons and Curva- ture 98 Method B: Probable Ionization and Curvature 106 Ionization and Rahge 111 VII. PHOTOGRAPHIC PLATE METHODS OF MESON MASS DETERMI- NATION 119 Coulumb Scattering 125 Grain Counting 133 Magnetic Deflection 140 VIII. OTHR MSPHODS OF MESON MASS DETERMINATION . 152 TABLE OF CONTENTS (continued) ♦ CHAPTER PAGE Neutron-Proton Exchange Force . 152 Deflection in Combined Electric and Magnetic Fields 152 Disintegration 155 Photographic Technique 155 Cloud-Chamber Technique 160 Meso-States 162 IX. DISCUSSION 165 General Causes of Inaccurate Mass Determi- nation 165 Experimental Errors Involved in the Methods 173 General Criticisms of the Methods 192 X. SUMMARY AND CONCLUSIONS 195 3IBLIOGRAPHY 202 APPENDIX I: BASIC EQ:6ATTONS 223 APPENDIX II: SPECIFIC IONIZATION [.S A FUNCTION OF THE VELOCITY OF A PARTICLE 225 APPENDIX III: RANGE AS A FUNCTION OF THE VELOCITY OP A PARTICLE 230 APP NDIX IV: EOMETRTCAL DETERMINATION OF THE AVERAGE COULOMB SCATTERING ANGLE OF A MpSON IN PASSING THR)UCH ,N EMULSION 232 APPENDIX V: M AS TREmZNT OP RECOIL ELECTR,N TRACKS OF CONSIDERABLE CURVATURE 235 APPENDIX VI: THE DIPER2 - TIAL COLLISION PROBABILITY . 240 vi LIST OF TABLES TABLE PAGE S I. MESON MASSFS FROM THE ELASTIC COLLISION METHOD . 55 II. MESON MASSES FROM THE RANGE AND CURVATURE METHOD 67 III. MESON MASSES USING RANGE AND CURVATURE RELATIONSHIPS OF MP1ONS V1D PROTONS 69 IV.VALUES OF d (11/0 )/dx IN LEAD AS A FUNCTION OF 010. -p2)qa 77 V. MESON MASSES FROM THE MC:q1NTUM LOSS METHOD . 95 VI. MESON MASSES FROM THE IONIZATION AND CURVATURE METHOD 112 VII. MESON MASSES FROM THE IONIZATION AND RANGE METHOD 118 VIII. MESON MASSES FROM THE COULOMB SCATTERING METHOD. 134 IX. MESON MASSES FROM THE GRAIN COUNTING METHOD. 141 X. M-SON MASSES FROM THE MAGNETIC DEFLECTION METHOD 151 XI. VALUES OF -41E/tint AS FUNCTIONS 017,9/(1 ..1g 2 )/a . 228 vii LIST OF FIGURES FIGURES PAGE 1. NOMOGRAPH GIVING MASS OF A PARTICLE IN TERMS OF SEVERAL VARIABLES 5 2. PHOTOGRAPH OF A PARTICLE OF MASS INTFRMEDIATE BETWEEN THAT OF A PROTON AND THAT OF AN ELECTRON. 16 3. APPARATUS TO MEASURE THE IONIZATION PRODUCED BY MESONS 20 4. A GEIGER-M6LLER COUNTING TUBE 22 5. DETAIL OF A WILSON CLOUD CHAMRER 28 6. PHOTOGRAPHS OF TWO MESONS IN A CLOUD CHAMBER. 30 7. TRACK OF A MESON IN A PHOTOGRAPHIC EMULSION . 36 8, AN ARRMGEMENT FOR QUICK MEASUREMENT OF THE RADIUS OF CURVATURE OF A PARTICLE 41 9. ENERGY TRANSFERRED TO ELECTRONS AS A FUNCTION OF THE MOMENTUM OP PRIMARY PARTICLES 48 10a. MESON UNDERGOING AN ELASTIC COLLISION IN A CLOUD MISER 49 10b. DIAGRAM OP AN ELASTIC COLLISION OF A MESON WITH AN ELECTRON 49 11. dE/dx Hp /(Mba sk )„ R/(M/me ) AND Hp /R PLOTTED AS A FUNITIONPA/ O(1 - d82 ) 11 60 12. A7-PARATUS FOR TiP: STUDY OF RANGE AND CURVATURE OP MESONS 63 13, PHOTOGRAPH OF A MESON FROM WHICH RANGE AND CURVA- TURE DATA HAVE BEEN OBTAINED 64 14. PHOTOGRAPH OF A MESON OF UNUSUALLY LOW MASS AS OBTAINED BY THE RANGE AND CURVATURE METHOD OF MASS DETERMINATION 66 15, MESON TRACK ON PHOTOGRAPHIC PLATES 71 16. d(H/r))/dx PLOTTED AS A FUNCTION OF /(1 -(3 2 ) '/4. 78 17. GRAPHICAL PLOT OF Tr E CALCULATE RELATION BETWEEN RANGE AND MOMENTUM FOR HYDROGEN AND HELIUM NUCLEI AND MESONS 81 • v i ii LIST OF FIGURES (oontinued) FIGURES PAGE 18. SCHEMATIC DIAGRAM OF TWO SIMULTANEOUSLY OPERATED CLOUD CHAMBERS TO MEASURE MOMENTUM AND RANGE OF MESONS 83 19. ARRANGEMENT OF APPARATUS FOR MESON MASS MEASURE- MENT BY THE METHOD OF MOMENTUM LOSS 85 20. PHOTOGRAPH OF A MESON STOPPING IN LEAD 87 21a. GRAPH OP RANGE AND Hp FOR MESONS OBSERVED BY W. B. FRETTER 90 21b. GRAPH OF ACCURATE RANGE AND Hp FOR THE MESONS OF FIG. 21a 90 22. PHOTOGRAPHS OF A NEGATIVE AND A POSITIVE MESON AS OBTAINED BY R. B. BRODE 91 23. STEREOSCOPIC PHOTOGRAPHS OF A NEGATIVE MESON STOPPING IN THE GAS OF A CLOUD CHAMBER 92 24. MESON MASS MEASUREMENTS OF RETALLACK AND BRODE USING THE MOMENTUM LOSS METHOD 94 25. WEIGHTED MASS SPECTRUM OF MESON MASS VALUES OF SEVERAL OBSERVERS USING THE MOMENTUM LOSS METHOD. 97 26. DIAGRAM OF A LARGE RANDOMLY OPERATED CLOUD CHAM- BER 103 27. PHOTOGRAPHS ILLUSTRATING THE DIFFERENCE IN IONIZA- TION BETWEEN MESONS AND ELECTRONS 105 28. SPECIFIC IONIZATION VERSUS Hp FOR MESONS 108 29. PHOTOGRAPH OF A HEAVILY IONIZING MESON TRACK EN- ABLING MASS DETERMINATION BY THE IONIZATION AND CURVATURE METHOD 110 30a. THEORETICAL COLLISION LOSS AS A FUNCTION OF vio FOR AIR AND LEAD 115 30b. THEORETICAL RANGE DIVIDED BY MASS NUMB:PR FOR AIR AND LEAD 115 31a. METHOD OF MEASURING ANGULAR DEVIATIONS OF MESONS 131 • ix LIST OF FIGURES (continued) FIGURES PAGE 31b. REPRODUCTION OF A SECTION OF DRAWING MADE ON A TYPICAL MESON TRACK TO DETERMINE MESON MASS BY COULOMB SCATTERING 131 32a. GRAPH OF TRACKS OF PROTONS AND)A-MESONS IN A PHOTOGRAPHIC PLATE 139 32b, PHOTOMICROGRA?H OF THE PRODUCTION OF A SECONDARY MESON IN'A PITOTOGRAPHIC EMULSION 139 33. DIAGRAMS OF EXPERIMENTAL ARRANGEMENT OF APPARATUS FOR MESON MASS DETERMINATION BY MAGNETIC DEFLEC- TION METHOD 146 34. PHOTOGRAPH OF A pC-MESON 148 35. RADIUS OF CURVATURE VERSUS RESIDUAL RANGE FOR MESONS IN A PHOTOGRAPHIC EMULSION 149 36. DISINTEGRATION OF A NUCLEUS BY A MESON AS OB- SERVED IN A PHOTOGRAPHIC PLATE . 157 37. STEREOSCOPIC PHOTOGRAPHS OF THE TRANSFORMATION OF A MESON INTO TWO LIGHT PARTICLES 163 38. VARIATION IN MESON MASS AS A FUNCTION OF RADIUS OF CURVATURE FOR A MASS 200 mi 178 39. THE RELATIONSHIP BETWEEN MOMENTUM AND RANGE FOR DIFFERENT VALUES OF MESON MASS TO OBTAIN THE ER- ROR IN MASS DUE TO AN ERROR IN Hp 186 40. DIAGRAM FOR THE DETERMINATION OF THE AVERAGE COULOMB SCATTERING ANGLE OF A MVSON IN PASSING THROUGH A PHOTOGRAPHIC EMULSION 233 41. FIGURE ILLUSTRATING MASS DETERMINATION BY THE METHOD OP PLASTIC COLLISION FOR ELECTRON TRACKS OF CONSIDERABLE CURVATURE 237 4 A STUDY OF THE METHODS OF MESON MASS DFTERMINATION CHAPTER I INTRODUCTION Statement,of the problem' The term "cosmic rays" is somewhat over twenty years old, and the branch of physics with which it deals first began to open up about 1910. Prior to that year not a trace of evidence had appeared that any rays of a penetrating power greater than that of the r-rays of radium existed, much less that rays entered the earth from outside its atmosphere. In studying radioactivity by electroscopes it was no- ticed that with no emitting source present, any charged else- troscope would always exhibit a residual rate of discharge. The conclusion was drawn that some very penetrating radiation was arriving continuously from outside. Balloon flights into the atmosphere established the fact that a radiation, called cosmic rays, was constantly bombarding the earth, the primary radiation consisting of high energy proton'. In the upper- most layers of the atmosphere, some of the protons interact with the air nuclei to give mesons in groups of five to ten generated in a single act. Each meson observed near the surface of the earth was 4 2 found to be short-lived (the half-life later approximated as about 2.3 millionths of a second), probably decaying into either a positive or negative electron and a neutrino. Since cosmic-ray particles are moving with velocities approaching that of light, the relativistic time contraction extends the lifetime in the observer's frame of reference to several hundred microsecondsi, thereby enabling the mesons to be de- tected at sea level. The discovery of these particles at once initiated research as to their nature, that is, their charge and mass. A variety of results for the meson mass has been presented to date. It is the purpose of this thesis therefore (1) to ex- amine the existing methods of meson mass measurement; (2) to investigate the experimental errors and inaccuracies of each method; and (3) to determine the possibility of unique meson masses from the many values obtained utilizing the several methods. It is hoped that the present study will lead to more advantageous methods for future determination of the meson mass and its uniqueness, thereby indicating not only more about cosmic rays but also the answers to some interesting problems in high energy nuclear physics raised by the meson-producing process. Although the actual mechanism of meson production is unknown, the meson is involved in nuclear reactions and particularly in the disintegrations of nuclei.
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