Thermal response of states of approximate angular momentum in the finite temperature restricted Hartree-Fock approximation

The thermal response of states of approximate angular momentum in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ with $J^{\pi }$ ${=8\mathrm{}}^{+}$ has been calculated in the finite temperature restricted Hartree-Fock approximation. Full angular momentum projection has been circumvented by the use of constraints on the total angular momentum J${^}^2$ and the z component J${^}_z$. States with an abnormal occupation of the single particle orbitals at T=0 exhibit a discontinuity in the thermal response of their variational energy.