Thermal properties of zinc isotopes in the static path approximation

Employing a quadrupole-quadrupole interaction Hamiltonian in the so-called static path approximation, which is based on path integration in the space of single-particle potential fields, we have calculated the excitation energy, level density, and level density parameter of some of the zinc isotopes with neutron numbers, N=34, 40, 44, and 46 at finite temperatures, T≤2.0 MeV. Using a cranking Hamiltonian (with rotation about the X axis) in the same approach we have also studied the behavior of the moment of inertia as a function of rotational frequency (ω) and temperature for ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, taking it as an illustrative example. At low temperature (T≊0.5 MeV) the effect of rotation alignment is seen at ω≊1.0 MeV whereas at T≊2.0 MeV the moment of inertia becomes almost independent of ω, indicative of a rigid body behavior.