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A Modified Nuclear Model for Binding Energy of Nuclei And A MODIFIED NUCLEAR MODEL FOR BINDING ENERGY OF NUCLEI AND THE ISLAND OF STABILITY BY KENNETH KIPCHUMBA SIRMA A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS, UNIVERSITY OF ELDORET, KENYA. MAY, 2021 ii DECLARATION Declaration by the Candidate I declare that this is my original and personal work and has not been presented for a degree in any other university. This thesis is not to be reproduced without the prior written permission of the author and/or University of Eldoret. Kenneth Kipchumba Sirma ______________________________ _______________________ SC/PHD/002/15 Date Approval by Supervisors This thesis has been submitted for examination with our approval as University Supervisors. ______________________________ _______________________ Prof. Kapil M. Khanna Date Department of Physics University of Eldoret, Kenya. ______________________________ _______________________ Dr. Samuel L. Chelimo Date Physics Department University of Eldoret, Kenya. iii DEDICATION To my beloved mum Grace for her unconditional love, advice and support. To our children Gael and Abby you are blessings. My wife Jacinta, for her love and care. iv ABSTRACT A new nuclear model of quantifying binding energy of nuclei is proposed. The nucleus is assumed to be composed of two regions; the inner core region and surface region. The inner core is assumed to be composed of Z proton-neutron pairs (Z=N) and the surface region is composed of the unpaired neutrons for a nucleus in which N>Z. The interaction between the core and neutrons in the surface region is assumed to be such that it leads to an average potential Vo in which each neutron in the surface region can move. Knowing the experimental values for the binding energy of nuclei, this average interaction potential Vo has been calculated for light, medium, heavy nuclei and Super heavy elements. Vo varies for isotopes, Isobars and Isotones. For isotopes the value of Vo decreases as the nuclei surface region neutron number (N) increases. A decrease in Vo is quite large when the neutron number increases by unity in light nuclei compared to heavy nuclei. For isotones, the value of Vo increases with an increase in proton number (Z). This is evident for both light nuclei and heavy nuclei. For Isobars, all elements ranging from light to SHE, Vo increases with decreasing A-2Z. The value of Vo is calculated for 254 234 295 super heavy nuclei or elements (SHE or SHN) starting from 92U to 118 Ei. The calculated values of the interaction potential Vo range from 671.688 MeV for to the value 267 938.961 MeV for . However, a very high value of 1022.206 MeV is noted for 110 Ds . Definite variations in Vo are obtained for Isotones, Isotopes and Isobars. For Isotones, the value of Vo increases while there is an increase in proton number (Z increases). For isotopes, Vo value decreases while number of neutrons in neutron skin region increases. For isobars, Vo value increases while proton number (Z) increases. This trend in variation of Vo is evident across all the nuclides, the obtained values of Vo are within the expected theoretical values, also the variation of Vo is in agreement with “Woods-Saxon potential”. v TABLE OF CONTENTS DECLARATION ................................................................................................................ ii DEDICATION ................................................................................................................... iii ABSTRACT ....................................................................................................................... iv TABLE OF CONTENTS .................................................................................................... v LIST OF TABLES ........................................................................................................... viii LIST OF FIGURES ........................................................................................................... ix LIST OF SYMBOLS .......................................................................................................... x ACKNOWLEDGEMENT ................................................................................................ xii CHAPTER ONE ............................................................................................................... 1 INTRODUCTION............................................................................................................. 1 1.1 Composition of Nuclei and Nuclear forces ............................................................... 1 1.1.1 Phenomena of pairing in finite and infinite nuclear system .............................. 1 1.1.2 Limits of stability ............................................................................................... 4 1.2 Statement of the problem .......................................................................................... 5 1.3 Research Objectives .................................................................................................. 6 1.3.1 General Objective ............................................................................................... 6 1.3.2 Specific Objectives ............................................................................................. 6 1.4 Justification of study ................................................................................................. 6 1.5 Significance ............................................................................................................... 7 CHAPTER TWO .............................................................................................................. 8 LITERATURE REVIEW ................................................................................................ 8 2.1 Background Information ........................................................................................... 8 2.2 Binding energy of the nucleus ................................................................................. 10 2.3 Semi-Empirical Mass formula (SEMF) .................................................................. 11 2.3.1 Volume Energy ................................................................................................. 12 2.3.2 Surface Energy ................................................................................................. 13 2.3.3 Coulomb Energy ............................................................................................... 13 2.3.4 Asymmetry Energy ........................................................................................... 14 2.3.5 Pairing Energy .................................................................................................. 14 vi 2.4 Separation Energy ................................................................................................... 14 2.5 Super Heavy Elements (SHE) and Island of stability ............................................. 16 2.6 Neutron Dripline ..................................................................................................... 20 2.7 Coulomb Energy ..................................................................................................... 20 2.8 Isotopes.................................................................................................................... 21 2.9 Isotones.................................................................................................................... 22 2.10 Isobars ................................................................................................................... 22 CHAPTER THREE ........................................................................................................ 24 METHODOLOGY ......................................................................................................... 24 3.1 Theory ..................................................................................................................... 24 3.2 Calculation of p and Btot ....................................................................................... 24 3.3 Derivation for Vo ..................................................................................................... 26 3.4 Super Heavy Nuclei (SHN) ..................................................................................... 28 CHAPTER FOUR ........................................................................................................... 31 RESULTS AND DISCUSSIONS ................................................................................... 31 4.1 Results ..................................................................................................................... 31 4.2 Discussions .............................................................................................................. 32 4.2.1 Light Nuclei.......................................................................................................... 32 4.2.1.1 Isotopes .......................................................................................................... 32 4.2.1.2 Isotones .......................................................................................................... 33 4.2.1.3 Isobars ............................................................................................................ 35 4.2.2. Medium Nuclei .................................................................................................... 36 4.2.2.1 Isotopes .........................................................................................................
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