核物质的低能有效场论研究

doi:10.3969/j.issn.1000-5641.202022007

摘要/Abstract

摘要：

采用低能有效场论分析了核物质和零温费米系统; 通过严格求解¹S₀分波Bethe-Goldstone方程(Bethe-Goldstone Equation, BGE), 得到了闭合形式的Brückner G矩阵, 并完成了其非微扰重整化. 在对理论参数的值进行选取之后, 完全了在Brückner G矩阵框架下, 分析包括密度背景中的配对问题以及费米系统单粒子能量在内的物理性质. 此外还将本文的框架和结果与其他文献进行了比较.

关键词: 有效场论, Brückner G矩阵, 重整化, 有限密度

Abstract:

In this study, the low-energy effective field theory approach is used to analyze nuclear matter and a zero-temperature Fermi system. By solving the Bethe-Goldstone equation (BGE) in the ¹S₀ channel, we obtain the closed-form Brückner G matrix and derive its renormalized non-perturbative form. Upon selecting values for relevant parameters, a number of physical issues are analyzed with the Brückner G matrix, such as pairing and single particle energy of a Fermi system in the density background. Lastly, the framework and results are compared with those published in the literature.

Key words: effective field theory, Brückner G matrix, renormalization, finite density

中图分类号:

O412.3

潘廷纬, 杨继锋. 核物质的低能有效场论研究[J]. 华东师范大学学报（自然科学版）, 2021, 2021(1): 82-91.

Tingwei PAN, Jifeng YANG. Low-energy effective field theory study of nuclear matter[J]. Journal of East China Normal University(Natural Science), 2021, 2021(1): 82-91.

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参考文献 21

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p_F/fm^–1	k_p/fm^–1
p_F/fm^–1	x = +0.20	x = –0.20	x = +0.05	x = –0.05
0.02	0.019993	0.095892	0.287473	0.599659
0.10	0.019993	0.095883	0.287139	0.599531
0.30	0.019993	0.095889	0.287364	0.599622
0.60	0.019993	0.095887	0.287282	0.599591

p_F/fm^–1	k_p/fm^–1
p_F/fm^–1	x = +0.20	x = –0.20	x = +0.05	x = –0.05
0.02	0.019993	0.095848	0.292220
0.10	0.019993	0.095815	0.290605
0.30	0.019993	0.095837	0.291721
0.60	0.019993	0.095829	0.291325

p_F/fm^–1	(E/A)₁/MeV				(E/A)₂/MeV
p_F/fm^–1	x = +0.20	x = –0.20	x = +0.05	x = –0.05	(E/A)₂/MeV
0.02	0.004272	0.07010	0.47441	1.39254	0.004334
0.10	0.004272	0.07005	0.46638	1.33538	0.082810
0.30	0.004272	0.07009	0.47179	1.37403	0.610010
0.50	0.004272	0.07007	0.46980	1.35990	1.584170

p_F/fm^–1	(E/A)₁/MeV				(E/A)₂/MeV
p_F/fm^–1	x = +0.20	x = –0.20	x = +0.05	x = –0.05	(E/A)₂/MeV
0.02	0.004272	0.06959	0.42301	1.21512	0.004334
0.10	0.004272	0.06940	0.38721	0.95924	0.082810
0.30	0.004272	0.06953	0.41158	1.13564	0.610010
0.50	0.004272	0.06948	0.40276	1.07292	1.584170
注: 取 ${\varLambda _{ {J_0} } }$ = 35 MeV时, 一部分p_F取值的Brückner G 矩阵没有极点, 所以灰色部分是一般积分所得的结果

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