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arXiv 2410.03356nucl-th
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强化版平均场近似:氘核的精确描述

Mean-field approximation on steroids: exact description of the deuteron

B. Bally, A. Scalesi, V. Somà, L. Zurek, T. Duguet

AI总结:

本文证明氘核可在基于平均场的框架内被精确描述,通过非正交Bogoliubov态的低维线性组合以低于百分之一的精度重现其基态性质,并指出质子-中子配对与变分前粒子数恢复是关键要素。

摘要:

本文证明,氘核,即由单个质子和单个中子组成的最轻束缚核系统,可以在基于平均场的框架内被精确描述。尽管乍看似乎矛盾,但氘核的基态结合能、磁偶极矩、电四极矩和均方根质子半径,确实通过非正交 Bogoliubov 态的低维线性组合以低于百分之一的精度被重现,即采用一种数值成本随 $n_{\ ext{dim}}^4$ 扩展的方法,其中 $n_{\ ext{dim}}$ 是单体 Hilbert 空间基的维度。通过进一步将系统置于谐振阱中,${}^{3}S_1$ 通道中的中子-质子散射长度和有效范围也被精确重现。为实现此任务,(i) 通过在 Bogoliubov 变换中混合质子和中子单粒子态来引入质子-中子配对,以及 (ii) 在变分前恢复质子和中子数,被证明是必不可少的要素。这一出人意料的结果对于如何随核质量变化最高效地捕获必要关联,以及对于确保基于手征或无π有效场理论的轻核以外多体计算实现逐阶可重整性的可能性,均具有深远意义。在此背景下,本研究近期将扩展至 $^{3}$H 和 $^{3,4}$He,以及无π有效场理论的领先阶。

英文摘要:

The present article demonstrates that the deuteron, i.e. the lightest bound nuclear system made of a single proton and a single neutron, can be accurately described within a mean-field-based framework. Although paradoxical at first glance, the deuteron ground-state binding energy, magnetic dipole moment, electric quadrupole moment and root-mean-square proton radius are indeed reproduced with sub-percent accuracy via a low-dimensional linear combination of non-orthogonal Bogoliubov states, i.e. with a method whose numerical cost scales as $n_{\text{dim}}^4$, where $n_{\text{dim}}$ is the dimension of the basis of the one-body Hilbert space. By further putting the system into a harmonic trap, the neutron-proton scattering length and effective range in the ${}^{3}S_1$ channel are also accurately reproduced. To achieve this task, (i) the inclusion of proton-neutron pairing through the mixing of proton and neutron single-particle states in the Bogoliubov transformation and (ii) the restoration of proton and neutron numbers before variation are shown to be mandatory ingredients. This unexpected result has implications regarding the most efficient way to capture necessary correlations as a function of nuclear mass and regarding the possibility to ensure order-by-order renormalizability of many-body calculations based on chiral or pionless effective field theories beyond light nuclei. In this context, the present study will be extended to $^{3}$H and $^{3,4}$He in the near future as well as to the leading order of pionless effective field theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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