APPLICATION OF SEMI-CLASSICAL METHODS TO DEFORMED AND SUPERDEFORMED NUCLEAR SYSTEMS

Abstract

The present thesis aims at bringing the latest discoveries in nuclear physics and the new developments in semiclassical physics closer together. The low energy domain of nuclear physics has been replete with exciting observations of superdeformed (SD) bands in a number of pockets of the chart of nuclides beginning with the first discovery of a discrete high spin SD band in 152Dy in 1986 [1]. Since then a large number of SD bands have been seen in A=80,130,150,190 mass regions [2]. On the experimental side, the observation of these weakly populated and very low intensity structures represents a triumph of the modern detector arrays and data analysis capabilities of modern computing systems. It has also led to the emergence of what we may term as ultra-weak spectroscopy. Theoretically, one expected the observation of these structures on the basis of potential energy surface calculations based on Strutinsky method which lays emphasis on the role of shell structure near the Fermi energy in stabilising specific configurations at specific shapes [3-5]. A detailed compilation of these results as applicable to SD shapes may be found in the reference [6]. Experimental discovery of SD bands thus also implies a growing confidence in the predictive capabilities of the present theoretical methods in nuclear physics. Large deformations and high angular momenta, which are intertwined themes, have now become commonplace in nuclear physics [71. Superdeformed, structures like fission isomers were already known in 1970 [8]. There is however an important difference between SD structures and fission isomers; while the former are essentially observed at high spins, the fission isomers are observed at low spins. Moreover the SD bands display characteristics which make these structures look very simple yet very hard to understand. Physics over the past decades, has also been witness to a resurgence in the study of non-linear features and application of semiclassical methods to quantal systems. Semiclassical techniques, first ushered in by Bohr, Sommerfeld, Einstein etc. were abandoned after the advent of quantum theory [9,10]. These have now been found to be of immense help and use in unraveling the nature of truth underlying the various phenomena exhibited by corn- plex quantum and semi-quantum (mesoscopic) systems. The study of chaotic dynamics in hamiltonian systems has become a growing discipline during the recent years. These studies are now being carried out in nuclei also with an emphasis on order-to-chaos transition in the classical dynamics of a particle in various shapes of cavities [11,12]. While earlier studies of chaos in nuclei have concentrated on statistical approaches [13], semiclassical methods have now begun to play a very important role. Developments like the periodic orbit theory [91 have brought to fore the deep connection between classical motion and quantal shell struc-ture. Effects like superdeformation at high spin are directly linked to quantal fluctuations which tend to stabilise shapes having axes ratio 2 :.1,3 : 1, etc. The fact that these are very feeble and weak structures suggests that small nonlinear terms have a role to play in stabilising these structures with specific configurations.