Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1964 The ompC ound Elastic Scattering of 3.15 Mev Neutrons by Calcium-40. Zorawar Khangura Singh Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Singh, Zorawar Khangura, "The ompoundC Elastic Scattering of 3.15 Mev Neutrons by Calcium-40." (1964). LSU Historical Dissertations and Theses. 999. https://digitalcommons.lsu.edu/gradschool_disstheses/999 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. TJhis dissertation has been 65—3398 microfilmed exactly as received SINGH, Zorawar Khangura, 1928- THE COMPOUND ELASTIC SCATTERING OF 3.15 MEV NEUTRONS BY CALCIUM-40. Louisiana State University, Ph.D., 1964 Physics, nuclear Please Note: Name in vita is Zorawar Singh Khangura. University Microfilms, Inc., Ann Arbor, Michigan THE COMPOUND ELASTIC SCATTERING OF 3.15 MEV NEUTRONS BT CALCIUM-40 A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Physios by Zorawar Khangura Singh B.A., The Punjab University, 1950 M.So., The M.U. Aligarh, 1954 B.T., The Punjab University, 1957 August, 1964 ACKNCJWLBDfflfSNT Thtt author wishes to express hie gratitude to Dr« Dorr C* Ralph for his valuable suggestions and critical discussions on this work* He also wishes to thank Carol J* Spahn and James Benham for their assistance and support in the Van de Graaff laboratory* ii TABLE OF CONTENTS Page ACKNOWLEDGMENT, • • ........... 11 TABLE OF CONTENTS....................................... .............................. ................... I l l LIST OF TABLES................................................................................................. v LIST OF FIGURES,.. ............. vi ABSTRACT........................................................................................................... r i i CHAPTER I . INTRODUCTION 1.1 The Bohr Rypothesis of Compound N ucleus....... ............ 1 1.2 The Optical Model .............................................. 2 1.3 Shape-elastic and Compound-elastic Scattering........ 4 1.4 Measurement of Compound-elastic S cattering ....................... 5 I I . EXPERIMENTAL APPARATUS 2.1 Introduction ........................ • • • • .............................. 8 2.2 The Pulsed Neutron Source.•••••••.••• ............................. 8 2.3 Neutron Produolng Target.. •••• 9 2.4 Scattering Samples •••••• ....................... 12 2.5 Neutron Detector ................... 12 2.6 The Experimental E lectronics............ ................••••• 14 2.7 Neutron Monitor ......... • • • • • • • ......... 18 2.8 Performance of the Tiae-of-Flight Spectrometer••••••• 19 I I I . THE EXPERIMENTAL PROCEDURE 3*1 Introduction.. ......... 22 3.2 Effective Energy of Neutrons Produced from a Gas Target.....e.•••••••• .............. ••••• ......................... 22 3.3 Measurement of Angular D istributions ............................ 25 3*4 Separation of Elastically Scattered Neutrons . in the Time Spectra..................... 29 3*5 The Calculation of the Angular Distribution.••••••••• 29 IV. CONCLUSIONS 4*1 The Differential Elastic Cross Section. ....................... 40 • i l l CHAPTER Page 4*2 Compound-elastic Cross Sectio n ...... ................ 42 SELECTED BIBLIOGRAPHY................................................................................... 44 APPENDIX 1. Flux Calculations ....... .................................................. 46 2. Attenuation Factor...........*..*.. .................. ••••••••• 48 3. Fortran for K_. ........ ••••...•• ...................... 48 4* Fortran for ?Ea?fr(Qg«r.En) ... ••••• 49 5. Table for D(d,n)He3 Cross Se c t i o n ......... ...................... 54 VITA..................................................................................................................... 55 C iv LIST OF TABLES Table Page I. Neutron Energy Distribution in the Gas Cell .................. 27 II. Differential Cross Sections. .............. 38 III . D(d,n)He^ Cross Sections ...................... 54 V LIST OF FIGURES Figure Page 1 Level Sehoaes of Caloiue^O and Potaseium-39 .................. 7 2 Pulsed Neutron Source ••••••• 10 3 Gas Target Assembly ................................ •••••••••••••• 11 4 S oatterers ................ 13 5 Experimental Geometry. ................... 15 6 Block Diagram of Time-of-Flight C irc u itry .... •••••• 16 7 Tunnel Diode Discrim inator.•••••• .................................. •••••••«. 17 S Monitor Ciouitry ................................. • • • • • .......... 20 9 Monitor Shield .................................................... ................................ 21 10 D(dfn)He3 Reaction Cross Section vs ............. 26 11 Unconnected Time-of-Flight Spectrum of Calcium-40.•••••••• 30 12 Time-of-Flight Spectra of Calcium-40 and Potassium-39 with Background Subtracted .................. •••••••• 31 13 Direct Beam Time Spectrum in the Forward D irection. •••••• • 32 14 Polyethylene and Caloium-40 Speotra a t Low Bias Setting. •• 35 15 The Differential Elastic Cross Sections of Ca-40 and K-39* 36 16 The Differential Compound-Elastic Scattering Cross Section of Caloium-40 ................ •••••••••• •••• 37 17 Flux Calculations ................ ••••• 50 vi ABSTRACT An attempt has been made to measure the differential compound elastic scattering of neutrons of energy 3*15 Mev by calcium -40 using a method based on the dissimilarity between the energy level schemes of potassium-39 and calcium-40, and based further on the assumption that shape elastic scattering of neutrons from these two nuclei is essentially the same. Since potassium-39 w ill exhibit very small compound elastic scattering compared to calcium-40 the difference in differential elastic scattering cross sections of these two nuclei will represent, to a close approximation, differential compound elastic scattering by calcium-40. The measured compound e la stic cross section of calcium-40 appears larger a t angles below 50° and sm aller above 1 1 0 ° than pre­ dicted by Hauser-Feshbach theory. The experimental data curve agrees fa irly well with theory between 50° and 1 1 0 ° • The measured total compound elastic cross section is 1. 0 &0.05 barns and th at found by theory is 1.0 barn. The detailed fit betweon the measured and computed differential compound elastic cross section is not good. This may due in part to the choice of single level parameters used in the theoretical calculations. That the general magnitude of the compound elastic cross sections is correct, is supported by the good agreement of the total cross sections. The assymmetry of the d iffe re n tia l compound ela stic cross section presumably resu lts from a breakdown of the assumption of identical shape elastic scattering in the calcium-40 and potassium-39. vii CHAPTER I INTRODUCTION 1*1 The Bohr Hypothesis of Compound Nucleus In 1936 N. Bohr suggested that nuclear reactions take place in two stages:^ first, the formation of a compound nucleus; and second, the subsequent decay of this compound nucleus. The cross section for a particular nuclear reaction may then be expressed as the product of two factors; first the cross section for the formation of the compound nucleus—*a quantity, for fast neutrons, always close to the geometrical area—and second, a quantity which measures the probability that the compound nucleus decays in the mode in question. The creation of the compound nucleus implies that the compound nucleus has an independent existence and that lasts for time long compared with the duration of the co llisio n . As pointed out by Bohr, in a ll probability, i t s lifetim e w ill be long enough fo r i t to lose all memory of its mode of formation when finally it is relieved of its excess energy by the emission of another particle. Immediately following the instant of collision this energy is rapidly shared out among tho constituents of the nucleus, thus the average energy of any one of them is insufficient to enable that particle to leave the nucleus and the compound nucleus finally emits a particle only when ^Neils Bohr, "Neutron Capture and Nuclear Constitution," Nature. CXXXVII (1936), 344. 1 2 6h« improbable event ooours that a large fraction of the energy of axoitation ia again conoantratad in ona oonatituant. The mode of decay o dapanda only on the angular momentum and tha energy and ita binding energy to tha compound nucleus• This is called Bohr Hypothesis. To calculate the probability of a particular reaction it is necessary to make an additional assumption. Tha siapiest ia to assume th at -the amission of tha different constituents of the nucleus, neutrons, - protons and more complex bodies likeoC -partioles, may be treated on an equal footing and that the probability of evasion of a specified par­ ticle may be calculated on. a statistical basis. 1 .2 The Optical Model Instead of considering the individual collisions which the incident particle must make within the nucleus it is possible to consider, alternatively, the interaction of that particle with the nucleus as a