Abstract
Nogami's method is extended to finite temperatureT. The effect of quantum and statistical fluctuations for the particle number in the finite temperature BCS model on the excitation energy, entropy, specific heat, level density and level density parameter is calculated in hot58Ni nucleus. The calculations have been performed with the finite temperature BCS gap and statistical average gap due to the finiteness of nucleus. In the finite temperature RPA the contribution of dipole and quadrupole vibrational modes to the specific heat and the increase of level density is calculated.
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