Neutral uranium (U I) is a very difficult atom for theoretical calculations due to a large number of valence electrons, six, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can treat efficiently valence-core correlations and relativistic effects, but because the formalism was developed for Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for +6 charge of such a potential. Much more efficient is relativistic configuration-interaction (RCI) approach which uses relatively accurate starting DHF potential that includes some valence electrons to make the valence electron Hamiltonian diagonally dominated for some states. Here we report calculations of U I hyperfine constants of several low-energy states using the RCI method with the starting potential that includes four f valence electrons. With this starting potential, it is possible to use the single-configuration approximation or small basis sets to obtain quite accurate results for hyperfine structure constants. In fact, by scaling nuclear magnetic moment, the agreement for 5 levels was within 5%, and a new magnetic moment can be recommended 0.43(2). When two states are mixed, it is difficult to predict exact mixing fractions, so in this case, we proposed a method in which the mixing fraction is found by optimization of one parameter in MPBT correction to obtain correct g-factors. The resulting hyperfine constants are significantly improved. Finally, CI-MBPT approach was also tested, with some success for low-energy states, with the limited basis set. The methods investigated here can be further developed to include more extensive data sets to improve accuracy and can be applied to other atoms and for calculations of other properties, for example, relevant to fundamental symmetry tests.

中文翻译：

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UI超精细常数的相对论构型相互作用和多体摄动理论计算

中性铀（UI）由于大量的价电子，六个价电子，强大的价-价和价-核相关性，高态密度和相对论效应而成为理论计算中非常困难的原子。构形相互作用多体摄动理论（CI-MBPT）可以有效地处理价核相关性和相对论效应，但是由于形式主义是针对不包含价电子的狄拉克-哈特里-福克（DHF）起始电势开发的，因此相当大需要CI空间来补偿这种电位的+6电荷。相对论配置-相互作用（RCI）方法效率更高，它使用相对准确的起始DHF电位，该电位包括一些价电子，以使价电子哈密顿量对角地占据某些状态。在这里，我们报告了使用RCI方法计算的几种低能态的UI超精细常数的计算，其起始电势包括四个价电子。有了这种起始潜力，就有可能使用单构型近似值或小的基集来获得非常精确的超精细结构常数结果。实际上，通过缩放核磁矩，5个级别的一致性在5％以内，可以建议使用新的磁矩0.43（2）。当两种状态混合时，很难预测精确的混合分数，因此，在这种情况下，我们提出了一种方法，其中通过优化MPBT校正中的一个参数以获得正确的g因子来找到混合分数。所得的超精细常数得到显着改善。最后，还对CI-MBPT方法进行了测试，在有限的基础条件下，对于低能状态取得了一些成功。此处研究的方法可以进一步开发，以包括更广泛的数据集以提高准确性，并且可以应用于其他原子，以及用于其他性质的计算，例如与基本对称性测试有关的性质。