Abstract
The shape transitions of nuclei at high excitation energy and the role of thermal fluctuations on the shape parameters is examined. Landau theory of phase transitions is used to determine the shape evolution with temperature and spin. The constants in the Landau expression for free energy are obtained by the free energy surfaces calculated using the finite temperature version of the cranked Nilsson - Strutinsky shell correction method. Paring is not included in the study. We report that the ground state of the considered 197Tl nucleus is prolate. At high spin the nucleus persist in the same shape with much elongation. But at high temperature and spin a spherical to prolate shape transition leading to triaxial is obtained. It is seen that with thermal fluctuations the averaged shapes for the above nuclei at different temperatures and spins are mostly triaxial which are quite different from the most probable prolate or oblate shapes.