Shape evolutions of $^{72,74}$Kr with temperature in the covariant density functional theory

The rich phenomena of deformations in neutron-deficient krypton isotopes such as the shape evolution with neutron number and the shape coexistence attract the interests of nuclear physicists for decades. It will be interesting to study such shape phenomena using a novel way, i.e., by thermally exciting the nucleus. So in this work, we develop the finite temperature covariant density functional theory for axially deformed nuclei with the treatment of pairing correlations by BCS approach, and apply this approach for the study of shape evolutions in $^{72,74}$Kr with increasing temperatures. For $^{72}$Kr, with temperature increasing, the nucleus firstly experiences a relatively quick weakening in oblate deformation at temperature $T \sim0.9$ MeV, and then changes from oblate to spherical at $T \sim2.1$ MeV. For $^{74}$Kr, its global minimum locates at quadroupole deformation $\beta_2 \sim -0.14$ and abruptly changes to spherical at $T\sim 1.7$ MeV. The proton pairing transition occurs at critical temperature 0.6 MeV following the rule $T_c =0.6 \Delta_p (0)$ where $\Delta_p(0)$ is the proton pairing gap at zero temperature. The signatures of the above pairing transition and shape changes can be found in the curve of the specific heat. The single-particle level evolutions with the temperature are presented.