A fully microscopic model for the description of nuclear level density (NLD) in spherical nuclei is proposed. The model is derived by combining the partition function of the exact pairing solution plus the independent-particle model at finite temperature (EP+IPM) with that obtained by using the collective vibrational states calculated from the self-consistent Hartree-Fock mean field with MSk3 interaction plus the exact pairing and random-phases approximation (SC-HFEPRPA). Two important factors are taken into account in a fully microscopic way, namely the spin cut-off and vibrational enhancement factors are, respectively, calculated using the statistical thermodynamics and partition function of the SC-HFEPRPA without any fitting parameters. The numerical test for two spherical $^{60}$Ni and $^{90}$Zr nuclei shows that the collective vibrational enhancement is mostly dominated by the quadrupole and octupole excitations. This is the first microscopic model confirming such an effect, which was phenomenologically predicted long time ago and widely employed in several NLD models. In addition, the influence of collective vibrational enhancement on nuclear thermodynamic quantities such as excitation energy, specific heat capacity and entropy is also studied by using the proposed model.

中文翻译：

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球核总能级密度的完全微观模型

提出了一种用于描述球形核中核能级密度 (NLD) 的完全微观模型。该模型是通过将精确配对解的配分函数加上有限温度下的独立粒子模型 (EP+IPM) 与使用自洽的 Hartree-Fock 平均场和 MSk3 计算的集体振动态相结合而推导出来的相互作用加上精确配对和随机相位近似（SC-HFEPRPA）。以完全微观的方式考虑了两个重要因素，即自旋截止和振动增强因子分别使用统计热力学和 SC-HFEPRPA 的分配函数计算，没有任何拟合参数。对两个球形 $^{60}$Ni 和 $^{90}$Zr 核的数值测试表明，集体振动增强主要由四极和八极激发主导。这是第一个证实这种效应的微观模型，这是很久以前的现象学预测并广泛应用于几个 NLD 模型中。此外，还利用所提出的模型研究了集体振动增强对激发能、比热容和熵等核热力学量的影响。