Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism

We present finite-temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean-field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature increases. We find that the nuclear potential surface diffuseness is the main driver for the pseudospin splittings and that it increases as the temperature grows. We conclude that pseudospin symmetry is better realized when the nuclear temperature increases. The results confirm the findings of previous works using relativistic mean field theory at $T=0$, namely that the correlation between the pseudospin splitting and the parameters of the Woods-Saxon potentials implies that pseudospin symmetry is a dynamical symmetry in nuclei. We show that the dynamical nature of the pseudospin symmetry remains when the temperature is considered in a realistic calculation of the tin isotopes, such as that of the Dirac-Hartree-Bogoliubov formalism.

Figure 1

Nuclear potentials as a function of the radial distance for the tin isotope chain. In the top panels, the meson potentials for (a) neutrons and (b) protons with the Coulomb potential are displayed for ${}^{100}\mathrm{Sn}$ (full lines) and ${}^{150}\mathrm{Sn}$ (dashed lines). In the bottom panels, the potentials (c) $V_n\left(r\right)$ for neutrons and (d) $V_p\left(r\right)$ for protons are shown from $A=100$ to $A=170$.

Figure 2

Nuclear potentials of the nucleus ${}^{100}\mathrm{Sn}$ as a function of the radial distance with temperatures varying from $T=0$ to $T=8$ MeV. The left column represents our FTDHB calculations for (a) ${\mathrm{\Sigma }}_c\left(r\right)$, (c) $V_n\left(r\right)$, and (e) $V_p\left(r\right)$. The right column shows our fit with a Woods-Saxon shape of the (b) ${\mathrm{\Sigma }}_c\left(r\right)$, (d) $V_n\left(r\right)$, and (f) $V_p\left(r\right)$, together with the Woods-Saxon parameters depth $V_0$ (in MeV), radius $R$ (in fm), and surface diffuseness $a$ (in fm).

Figure 3

The Woods-Saxon potential parameters for the (a) depth $|{\mathrm{\Sigma }}_{0,c}|$ in (MeV), (b) radius $R_c$ (in fm), and (c) diffusivity $a_c$ (in fm) vs temperature for tin isotope chain.

Figure 4

The Woods-Saxon parameters (a) $|{\mathrm{\Sigma }}_c|R_c^2$ and (b) diffusivity $a_c$ divided by their respective values at $T=0$ vs temperature for the tin isotope chain.

Figure 5

Energy splitting for several pseudospin doublets of ${}^{150}\mathrm{Sn}$ for (a) neutrons and (b) protons for temperatures varying from $T=0$ up to $T=8$ MeV.