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 $^{56,68}$Ni and $^{56}$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.

中文翻译：

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核壳结构的温度演化和动力核子有效质量

我们在有限温度下研究中等质量原子核中的费米子 Matsubara Green 函数。具有粒子-振动-耦合 (PVC) 起源动力学核的单费米子戴森方程是在狄拉克旋量的基础上制定和求解的，该方程通过介子-核子协变能量密度函数最小化正则势。在能量相关自能的领先近似中考虑了超过平均场的 PVC 相关性，并获得了费米子传播子的有限温度戴森方程的完整解。在这种方法中，我们研究了与核坍缩超新星相关的核系统 $^{56,68}$Ni 和 $^{56}$Fe 的单粒子状态的碎裂及其随温度的演变。与能量相关的，或动态的，