On the Microscopic and Macroscopic Aspects of Nuclear Structure With Applications to Superheavy Nuclei

The thesis is concerned with the relation between a microscopic approach and a macroscopic approach to the study of the nuclear binding energy as a function of neutron number, proton number and nuclear deformations. First of all we give a general discussion of the potential energy of a system which can be divided into a bulk region and a thin skin layer. We find that this energy can be written down in the usual liquid drop type of expression, i.e., in terms of the volume, the surface area and other macroscopic properties of the system. The discussion is illustrated by a study of noninteracting particles in an orthorhombic potential well with zero potential inside and infinite potential outside. The total energy is calculated both exactly (a microscopic approach) and also from a liquid drop type of expression (a macroscopic approach). It turns out that the latter approach reproduces the smooth average of the exact results very well. We next make a digression to study the saddle point shapes of a charged conducting drop on a pure liquid drop model. We compare the properties of a conducting drop with those of a drop whose charges are distributed uniformly throughout its volume. The latter is the usual model employed in the study of nuclear fission. We also determined some of the more important symmetric saddle point shapes. In the last part of the thesis we generalize a method due to Strutinski to synthesize a microscopic approach (the Nilsson model) and a macroscopic approach (the liquid drop model). The results are applied to realistic nuclei. The possible occurrence of shape isomers comes as a natural consequence of the present calculation. Their trends as a function of neutron and proton members are discussed and the results are tabulated. We also work out the stabilities of the predicted superheavy nuclei with proton number around 114 and neutron number around 184 and 196. Some of these nuclei appear to have extremely long life times. The possible experimental production of these superheavy nuclei are also discussed