Temperature-dependent shell effects in 16O and 40Ca with a realistic effective Hamiltonian.

Abstract

Finite temperature properties of $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ are evaluated self-consistently, with a realistic effective Hamiltonian. Resulting thermodynamic functions such as the free energy are analyzed to extract their smooth thermal dependence and the thermal dependence of the shell effects. The temperature dependence of single particle energies is large compared to results obtained with phenomenological Hamiltonians. Gaps between shell centroids decrease uniformly with increasing temperature. However, the spin-orbit splitting decreases even faster, so that the shell gap follows a pattern of an initial increase with temperature followed by an eventual decrease to zero at high $T$. This thermal blocking of the Hartree-Fock spin-orbit potential is associated with the thermal sensitivity of surface properties. The approximation of thermal occupation of the $T=0$ spectrum is also invalidated and the self-consistent treatment is necessary to obtain physical quantities such as the level density parameter as a function of $T$.