Low-Energy Theorems for Neutron–Proton Scattering in $\chi $EFT Using a Perturbative Power Counting

IF 1.7 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Few-Body Systems Pub Date : 2024-06-25 DOI:10.1007/s00601-024-01938-w

Oliver Thim

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Abstract

Low-energy theorems (LETs) for effective-range parameters in nucleon-nucleon scattering encode properties of the long-range part of the nuclear force. We compute LETs for S-wave neutron–proton scattering using chiral effective field theory with a modified version of Weinberg power counting. Corrections to the leading order amplitude are included in distorted-wave perturbation theory and we incorporate contributions up to the third order in the power counting. We find that LETs in the $^1S_0$ and $^3S_1$ partial waves agree well with empirical effective-range parameters. At the same time, phase shifts up to laboratory scattering energies of about 100 MeV can be reproduced. We show that it is important to consider the pion mass splitting in the one-pion exchange potential in the $^1S_0$ partial wave while the effect is negligible in the $^3S_1$ partial wave. We conclude that pion exchanges, as treated in this power counting, accurately describe the long-range part of the S-wave nuclear interaction.

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使用惯性功率计数的 $$\chi $$ EFT 中中子-质子散射低能定理

核子-核子散射中有效范围参数的低能定理（LET）编码了核力长程部分的特性。我们利用手性有效场理论和改进版温伯格功率计数计算 S 波中子-质子散射的 LET。对前导阶振幅的修正包含在畸变波扰动理论中，我们在功率计数中包含了高达三阶的贡献。我们发现局部波（(^1S_0\)和（(^3S_1\)）的LET与经验有效范围参数吻合得很好。同时，实验室散射能量高达约 100 MeV 的相移也可以再现。我们表明，在 $^1S_0$ 部分波中，考虑一离子交换势中的先驱质量分裂是很重要的，而在$^3S_1$ 部分波中，这种影响可以忽略不计。我们的结论是，这种幂级数处理的先驱交换准确地描述了 S 波核相互作用的长程部分。

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来源期刊

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures. Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal. The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).

Low-Energy Theorems for Neutron–Proton Scattering in \(\chi \)EFT Using a Perturbative Power Counting

Abstract