arXiv 2104.054742021-04nucl-th

在Chiral有效场论中Hartree-Fock计算中的截断效应

Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory

Université de Bordeaux（波尔多大学）；Université de Strasbourg（斯特拉斯堡大学）

M. Sánchez Sánchez, Dao Duy Duc, L. Bonneau

备注：: Resubmitted to Physical Review C. Thoroughly revised version
发表信息：: Phys. Rev. C 107, 064307 (2023)
DOI：: 10.1103/PhysRevC.107.064307

AI总结：

研究在Chiral有效场论中使用大于核子质量的截断对核体性质的影响，通过Hartree-Fock方法计算氧核基态性质，发现截断效应表现为对吸引奇点部分波的反常项和深层束缚态修正的敏感性，高截断会消除Hartree-Fock近似中的束缚态解。

摘要：

我们探讨在Chiral有效场论中使用大于核子质量的截断对核体性质的影响，通过Hartree-Fock方法在由平面波构成的立方基组中计算氧核基态性质。发现截断效应以两种方式表现：对吸引奇点部分波的反常项（与相应低能常数的符号相关）和对深层束缚态的修正（在足够高的截断下）。实际上，后者会剥夺Hartree-Fock近似在核中产生束缚态解的能力。我们得出结论，当使用Nogga-Timmermans-van Kolck的功率计数（截断高于核子质量）的领先阶Chiral势时，无法产生无反常束缚态效应的自洽均场，无法作为超越均场方法的参考态。对于产生吸引的^3S_1接触势的高截断，最多只能在均场解中纳入对反常束缚态的部分修正。剩余的修正必须加到残余相互作用中，超出Hartree-Fock近似。实际上，在^3D_2通道中，可能实现一个完整的修正，能量位移的规模为或略大于2021年Phys. Rev. C 103, 054304推荐的规模。

英文摘要：

We explore the effects on nuclear bulk properties of using regularization cutoffs larger than the nucleon mass within the chiral effective field theory with a power counting that ensures order-by-order renormalization in the two-nucleon system. To do so we calculate ground-state properties of the $^{16}$O nucleus in the Hartree--Fock approach in a basis made up of plane waves confined in a cube. We find that regularization cutoff effects manifest themselves in two distinct ways: a strong sensitivity to the the counter-terms in attractive singular partial waves (related to the sign of the corresponding low-energy constant) and to the correction for spurious deeply bound states (for high enough cutoffs). In fact the latter happens to deprive the Hartree--Fock approximation of yielding bound solutions in nuclei. We conclude that, when using a leading-order chiral potential in the Nogga--Timmermans--van Kolck's power counting (with a regularization cutoff higher than the nucleon mass), one cannot produce a selfconsistent mean field free of spurious bound-state effects that can serve as a reference state for beyond-mean-field methods. For high regularization cutoffs which yield an attractive $^3S_1$ contact potential, one can at best incorporate in the mean-field solution a partial correction for spurious bound states. Then the remaining correction has to be added to the residual interaction in a treatment beyond the Hartree--Fock approximation. In fact a ``full'' correction in the $^3D_2$ channel, with energy shifts of the order of or somewhat larger than those recommended in Phys. Rev. C 103, 054304 (2021), is possible.

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