The temperature dependent level density parameter plays an important role in the study of shape transitions in hot rotating nuclei. It can be investigated by mean field theories such as Hartree - Fock method and the Landau theory of phase transitions, but these theories ignore the statistical thermal fluctuations. For a nucleus with finite number of particles, such fluctuations on level density parameter can be large. The aim of this work is to obtain the level density parameter for 88Mo and 90Mo. The level density parameters for the considered nuclei are evaluated by finding the thermo dynamical functions using cranked Nilsson – Strutinsky prescription. The ensemble average of the entropy that depends on β,γ are calculated by the Landau theory of shape transitions. The thermal averaged values of β,γ then yields the required entropy. Now the value a and <a> gives the level density parameter calculated at equilibrium configuration (β0,γ0) without and with thermal fluctuations respectively. The results obtained for the level density parameter as a function of temperature and angular momentum for the case of 88Mo and 90Mo nuclei shows that the change in level density obtained as a function of temperature is more than that obtained as a function of angular momentum. The results obtained are also in conformity with the marked temperature dependence of the level density parameter observed experimentally.

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