Nuclear state densities are important inputs to statistical models of compound-nucleus reactions. State densities are often calculated with self-consistent mean-field approximations that do not include important correlations and must be augmented with empirical collective enhancement factors. Here, we benchmark the static-path plus random-phase approximation (SPA + RPA) to the state density in a chain of samarium isotopes ${}^{148\text{–}155}\mathrm{Sm}$ against exact results (up to statistical errors) obtained with the shell-model Monte Carlo (SMMC) method. The SPA + RPA method incorporates all static fluctuations beyond the mean field together with small-amplitude quantal fluctuations around each static fluctuation. Using a pairing plus quadrupole interaction, we show that the SPA + RPA state densities agree well with the exact SMMC densities for both the even- and odd-mass isotopes. For the even-mass isotopes, we also compare our results with mean-field state densities calculated with the finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation. We find that the SPA + RPA repairs the deficiencies of the mean-field approximation associated with broken rotational symmetry in deformed nuclei and with the violation of particle-number conservation in the pairing condensate. In particular, in deformed nuclei the SPA + RPA reproduces the rotational enhancement of the state density relative to the mean-field state density.

中文翻译：

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静态路径中重核的状态密度加上随机相位近似

核态密度是复合核反应统计模型的重要输入。状态密度通常使用自洽平均场近似计算，不包括重要的相关性，并且必须通过经验集体增强因子进行增强。在这里，我们将静态路径加随机相位近似 (SPA + RPA) 与钐同位素链中的状态密度进行了基准测试${}^{148\text{——}155}\mathrm{SM}$与使用壳模型蒙特卡罗 (SMMC) 方法获得的精确结果（最多统计误差）进行对比。SPA + RPA 方法结合了平均场之外的所有静态波动以及每个静态波动周围的小幅度量子波动。使用配对加四极杆相互作用，我们表明 SPA + RPA 状态密度与偶数和奇数质量同位素的确切 SMMC 密度非常吻合。对于偶数质量同位素，我们还将我们的结果与使用有限温度 Hartree-Fock-Bogoliubov (HFB) 近似计算的平均场态密度进行比较。我们发现 SPA + RPA 修复了与变形核的旋转对称性破坏和配对凝聚物中粒子数守恒的违反相关的平均场近似的缺陷。特别是，