Temperature evolution of the nuclear shell structure and the dynamical nucleon effective mass

We study the fermionic Matsubara Green functions in medium-mass nuclei at finite temperature. The single-fermion Dyson equation with the dynamical kernel of the particle-vibration-coupling (PVC) origin is formulated and solved in the basis of Dirac spinors, which minimize the grand canonical potential with the meson-nucleon covariant energy density functional. The PVC correlations beyond mean field are taken into account in the leading approximation for the energy-dependent self-energy, and the full solution of the finite-temperature Dyson equation is obtained for the fermionic propagators. Within this approach, we investigate the fragmentation of the single-particle states and its evolution with temperature for the nuclear systems ${}^{56,68}\mathrm{Ni}$ and ${}^{56}\mathrm{Fe}$ relevant for the core-collapse supernova. The energy-dependent, or dynamical, nucleon effective mass is extracted from the PVC self-energy at various temperatures.

Figure 1

Single-particle states in ${}^{68}\mathrm{Ni}$ at zero and finite temperatures calculated in the RMF approximation.

Figure 2

The dominant fragments of the single-particle states in ${}^{68}\mathrm{Ni}$ at zero and finite temperatures calculated in the $\mathrm{RMF}+\mathrm{PVC}$ approximation.

Figure 3

Temperature evolution of the neutron pairing gap (top) and the neutron single-quasiparticle states (bottom) around the Fermi surface in ${}^{68}\mathrm{Ni}$. The dashed line indicates the chemical potential.

Figure 4

Temperature evolution of the neutron ${1\mathrm{f}}_{7/2}$ state in ${}^{68}\mathrm{Ni}$. Blue bars represent the spectral strength distributions (spectroscopic factors) of the fragmented state calculated within the thermal “$\mathrm{RMF}+\mathrm{PVC}$” approach. The red bar corresponds to the pure RMF state, and the dashed green line indicates the chemical potential.

Figure 5

Same as in Fig. 4, but for the neutron ${3\mathrm{d}}_{3/2}$ state in ${}^{68}\mathrm{Ni}$.

Figure 6

Same as in Fig. 4, but for the proton ${1\mathrm{d}}_{3/2}$ state in ${}^{68}\mathrm{Ni}$.

Figure 7

Same as in Fig. 4, but for the proton ${1\mathrm{g}}_{9/2}$ state in ${}^{68}\mathrm{Ni}$.

Figure 8

The single-particle states in ${}^{56}\mathrm{Fe}$ at zero and finite temperatures calculated in the RMF approximation.

Figure 9

The dominant fragments of the single-particle states in ${}^{56}\mathrm{Fe}$ at zero and finite temperatures calculated in the $\mathrm{RMF}+\mathrm{PVC}$ approximation.

Figure 10

Neutron (blue) and proton (red) dynamical effective masses in ${}^{56}\mathrm{Ni}$ (left) and ${}^{68}\mathrm{Ni}$ (right) computed with the imaginary parts of the energy variable $\mathrm{\Delta }=2\mathrm{MeV}$ (dashed curves) and $\mathrm{\Delta }=5\mathrm{MeV}$ (solid curves) at $T=0$. The dynamical effective masses are averaged over the single-particle states within 40-MeV energy window around the neutron and proton Fermi surfaces, respectively.

Figure 11

The dynamical effective masses of neutrons and protons in ${}^{56}\mathrm{Fe}$ calculated with (solid curves) and without (dashed curves) pairing correlations at zero temperature. The value $\mathrm{\Delta }=5\mathrm{MeV}$ was used for the imaginary part of the energy variable. The symbol ${\mathrm{\Delta }}_p$ stands for the superfluid pairing gap.

Figure 12

Temperature evolution of the nucleon dynamical effective masses in ${}^{56,68}\mathrm{Ni}$ calculated with $\mathrm{\Delta }=5\mathrm{MeV}$.