INTRODUCTION. The present work is mainly concerned with the comprehensive analysis of nuclear binding energies and the

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1 1 $ $ INTRODUCTION One of the main objectives of the study of nuclear physics is the understanding of the "Structure of Nuclei". This includes all aspects of the motion of the nucleons, their paths in space, their momenta^the correlations between them, the energies binding them to each other. Although considerable progress has been made in recent years knowledge of the nuclear forces is still in an early stage. It is therefore, not possible to develop a theory of nuclear structure based on the present knowledge of nuclear forces. In the absence of a detailed theory of nuclear structure, one tries to obtain a consistent picture of the nuclear structure through the close study of various experimental data by means of emperical laws. The laws, thus obtained, give some informations about the structure of the nucleus. A most basic property of a nucleus is its binding energy. This Is brought about by the specific nuclear forces, counteracted partially by the Coulomb repulsion between the protons. Hence, an analysis of nuclear binding energies sheds light on the nature of nuclear forces. The present work is mainly concerned with the comprehensive analysis of nuclear binding energies and the

2 systematic of nuclear energy characteristics. The sequence of the -work is given below s Chapter I presents a critical review of different nuclidic mass equations formulated to account for the sys- tematics of the nuclidic masses or binding energies. First two sections of chapter II are dealt with the analysis of nuclear binding energies. The deviations of nuclear binding energies from a smooth relation are closely associated with the nuclear structure. The deviations of nuclear binding energies from a quadratic equation have been resolved into two periodic curves F(Z) and F(I) which determine the periodicity in the structural development of the nuclei and also the relative stability of the nuclei. It has been found that the minima of the F(Z) curve correspond to magic numbers, except for the proton nufeber 50. On this basis, a strong binding toasffgy has also been observed near Z = 40 and Z ss 58. The binding energies of the set of nuclei of a particular odd mass number, as well as those for the even even nuclei or even mass number are determined by a relation of the following approximate form E = Eq + p ( N - N0)2 where N0 is the optimum neutron number for the given mass

3 number and p is the neutron-proton exchange energy. This relationship however, does not hold for all the nuclei of a given mass number. In this work p and N are allowed to vary frith N. bod agreement with the experimental values has been obtained. In section three of this chapter, we have established a correlation between nuclear excitation and formation energies. The neutron-proton exchange energy p has been found similar.to the expected change for the general process of excitation energy. We have considered the 1st and 3rd excitation energies for the strongly bound odd and even mass nuclei. The observed similarity of all the excitation energies with the p values may be regarded to be of significance. Fourth section deals with the A - binding energies of hyper nuclei. It is considered that the A - binding energy of a hyper nucleus is related closely to the maximum binding energy E* of a nucleus with the same nucleon number as the particle number in the A - hyper nucleus. The binding energies of hypernuclei are expressed by the relation of the form = E*Asexpf- o ln(a) + ^3 where En(A) is the ground state energy per nucleon uncorrected by coulomb and asymmetry energy. The emperical relation suggests a statistical approach to nucleonic interactions. Chapter III

4 is concerned with the nuclear radii and the isobaric analysis of total beta decay energies. Guided by the results of high energy electron scattering and on the basis of energy equivalence of mirror nuclei, we have obtained an emperical relationship for the nuclear radius in terms of nucledn number. This relation has been used to calculate the isotope shift for different isotopes. A general improvement of the theoretical values is obtained. In section three, we have modified the Bethe-Welzaacker relation for nuclear binding energy. The expression, obtained for nuclear radius, is used to calculate the Coulomb energies. The asymmetry term contains a coefficient which is close to the coefficient considered necessary in the Bethe-Weizsacker relation. With this modification of Coulomb energy term, we have established a relation for nuclear binding energy which does not contain the surface tension correction term proportional 2/ to A '3. The deviations are found to be systematic. In the last section of this chapter, a new approach Is made for the analysis of total beta decay energies which are «determined directly from the parameters required to determine the isobaric parabolas. Isobaric parabolas are determined by / the combination of Coulomb and asymmetry energy terms'. The binding energies of all nuclei are determined In terms of a

5 & # I smooth function -f(a) in association with a Coulomb energy term Uc, determined by the variable parameter R(A), the equivalent radius for spherical charfee distribution and an asymmetry term Ua, determined by the correction factor C(A) associated with (N-Z)2/A. The deviations from the experimental values are generally small. Coulomb energies, calculated directly by the analysis of nuclear binding energies are in fair agreement with the coulomb energies determined from the nuclear charge distribution obtained by Hofstadter,.The values of R(A) and C(A) obtained from the analysis of nuclear binding energies, determine the parabolic parameters b and 2^, necessary for the determination of beta-disintegration energies. Shell effects on the parameter b, the line of beta stability and the pairing energies are discussed in detail. Chapter IV deals with the systematics of nucleon pairing and separation energies. It has been found that the nucleon pairing energies in general increase with the Increase of the total angular momentum J of the orbit in which pair is present, but the increase in the value is apparently slower than predicted by Mayer5 s theory. There are however exceptions. Expressions for neutron and proton pairing energies are obtained which show the dependence of pairing energies on the nucleon number as well as. on J. We get in general a lower value of the

6 6 I proton pairing energies than the neutron pairing energies. In the last two sections of this chapter^ a correlation between nuclear separation energies for even even nuclei and the angular momentum J of the preceding odd nucleon has been established. On the basis of shell model, one would expect a linear variation of nuclein separation energies for the nuclei obtained from one another by adding pairs of nucleons. This is not strictly correct. "We have seen that the neutron separation energies (S^ for even even nuclei with same J and for a fixed isotope and the proton separation energies (Sp) for even even nuclei with same J and for the same-isotone, lie on a straight line. Shell effects on the slopes of the isotopic S^ and isotonic Sp lines have been discussed. In the final chapter, we have used asymmetric rotator model to calculate the axial asymmetry of light even even nuclei. It Is observed that except for Mg (24), Si(28) and Fe(56), the above model is not applicable to determine the axial asymmetry of light even even nuclei. The results that we have obtained in the present work are given in the form of tables and graphs.