Gamow-Teller excitations at finite temperature: Competition between pairing and temperature effects

The relativistic and nonrelativistic finite temperature proton-neutron quasiparticle random phase approximation (FT-PNQRPA) methods are developed to study the interplay of the pairing and temperature effects on the Gamow-Teller excitations in open-shell nuclei, as well as to explore the model dependence of the results by using two rather different frameworks for effective nuclear interactions. The Skyrme-type functional SkM* is employed in the nonrelativistic framework, while the density-dependent meson-exchange interaction DD-ME2 is implemented in the relativistic approach. Both the isoscalar and isovector pairing interactions are taken into account within the FT-PNQRPA. Model calculations show that below the critical temperatures the Gamow-Teller excitations display a sensitivity to both the finite temperature and pairing effects, and this demonstrates the necessity for implementing both in the theoretical framework. The established FT-PNQRPA opens perspectives for the future complete and consistent description of astrophysically relevant weak interaction processes in nuclei at finite temperature such as $\beta$ decays, electron capture, and neutrino-nucleus reactions.

Figure 1

Left panel: The ${\mathrm{GT}}^{-}$ strength for ${}^{42}\mathrm{Ca}$ calculated using the SkM* interaction at $T=0$, 0.5, 0.7, 0.87, and 0.9 MeV. The isoscalar pairing strength is varied as $V_0^{\mathrm{is}}=0$, 330, 660, and 726 MeV ${\mathrm{fm}}^3$ (see text for explanation). Right panel: The same but for the DD-ME2 interaction in the particle-hole channel and the finite range isoscalar pairing. The isoscalar pairing strength is varied as $G_0^{\mathrm{is}}=0$, 100, 200, and 220 MeV. The excitation energies are calculated with respect to the ground state of the parent nucleus. The excited states are smoothed with a Lorentzian of width $\mathrm{\Gamma }=1$ MeV. The vertical gray lines are drawn to guide the eye.

Figure 2

The centroid energies ($m_1/m_0$) (upper panels) and the total sum of the ${\mathrm{GT}}^{-}$ strengths (lower panels) for the excited states below 10 MeV as a function of temperature for ${}^{42}\mathrm{Ca}$. The calculations are performed using the SkM* (left panels) and DD-ME2 functionals (right panels) and by varying the isoscalar pairing strength.

Figure 3

The same as in Fig. 1, but for ${}^{46}\mathrm{Ti}$.

Figure 4

The same as in Fig. 2, but for ${}^{46}\mathrm{Ti}$.

Figure 5

The same as in Fig. 1, but for ${}^{118}\mathrm{Sn}$.

Figure 6

Schematic representation of the charge-exchange excitation in the $\mathrm{\Delta }{T}_z=-1$ (upper panel) and $\mathrm{\Delta }{T}_z=1$ (lower panel) channels. $E_{\mathrm{RPA}}^{*}$ denotes the RPA excitation energy, $E_t^{*}$ and $E_d^{*}$ are the excitation energies with respect to the target and the daughter ground states, respectively. The mass and binding energy differences between the daughter and target nucleus are given by $\mathrm{\Delta }M=M_d-M_t$ and $\mathrm{\Delta }B=B_t-B_d$, respectively. $\mathrm{\Delta }np$ represents the neutron-proton mass difference.