Author

Carl K. Ross

Date of Award

7-1973

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Supervisor

Dr. R. K. Bhaduri

Abstract

Although the Strutinsky method has been widely used in calculating the nuclear deformation energy, it contains various ambiguities which may affect the accuracy and reliability of the calculations. In particular, the smoothing procedure for extracting the smooth density of states used in calculating the shell correction to the deformation energy has no firm theoretical basis. As a means of testing this smoothing procedure, an alternative method for obtaining that part of the exact density of states which depends only on the overall features of the distribution of single-particle states is proposed. This approach utilizes a high temperature expansion of the exact single-particle partition function, and it is used to calculate the shell correction for three different spectra for which the partition function is known analytically at high temperatures. The shell corrections calculated by the partition function method are compared with the corresponding results from the Strutinsky method, and they are found to be in reasonable agreement.

When the Strutinsky method is applied to potential wells of finite depth, the shell correction is found to be highly dependent on the parameters in the smoothing procedure. Lin suggested that this ambiguity might be removed by including the effects of the continuum resonances, but his calculations indicated that they are of little importance. The possible effects of the continuum on the smooth density of states are re-examined, and it is pointed out that resonances much higher in the continuum than those considered by Lin can influence the shell correction. When Lin's calculation is repeated including these higher resonances, a reasonably unique shell correction is obtained.

A third ambiguity in the Strutinsky method has been pointed out by Kelson and Shoshani, who suggest that it violates the conservation of angular momentum. They estimate that if the effects of angular momentum conservation are explicitly included, the fission barriers of superheavy nuclei may be lowered by as much as 2.5 MeV over existing calculations. An examination of the basis of the Strutinsky method shows however, that the correction as suggested by Kelson and Shoshani is inappropriate, and that for all practical purposes angular momentum conservation is properly included in the Strutinsky method.

The final chapter discusses the possible effects of shell structure in the deformation energy on the rotational bands of deformed nuclei. A two-particle rotor is taken to be a rough approximation to a deformed rotating nucleus, and for an appropriate two-body potential the rotor is shown to display backbending behaviour similar to that observed for rare-earth nuclei. This indicates that centrifugal stretching may be an important mechanism in giving rise to backbending, and the possible effects of stretching in more realistic calculations is discussed.

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