Date of Award

Spring 1962

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)



First Advisor

Lee, Kiuck

Second Advisor

Berners, Edgar D.

Third Advisor

Greene, J. B.


This paper consists of part of a research project under Dr. K. Lee, sponsored by the National Science foundation. It is generally considered that heavy nuclei might be deformed assymetrically. However this problem has not been thoroughly investigated due to mathematical complexity in solving wave equations for the assymetric potential. A rather simpler case of spheroidal deformation has been investigated by Nilsson. To investigate the question of the stability of a pear-shaped deformation, it is first necessary to evaluate the energy levels of individual particles in such deformation. This has been achieved following Nilsson's approach using IBM 7074 digital computer. In order to adopt Nilsson's representation, it was necessary to transform the potential energy used by Lee and Inglis in terms of spherical polar coordinate system. It is further necessary to obtain a relationship between the deformation parameters p and 6 (the former used by Lee and Inglis and later used by Nilsson) since the results are very sensitive with respect to these parameters. These transformations are made in Chapter I. In Chapter II matrix elements necessary in this project are derived. In Chapter IV the explicit expressions of the Clebsch- Gordon coefficients for higher angular momentum quantum numbers are derived . De tailed aspects of the computer programs are described in Chapter V .