Low-energy effective field theory study of nuclear matter
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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.
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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
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图 2 取
${\varLambda _{{J_0}}}$ = 138 MeV, x = 0.2时, 极点位置kp与pF的关系Fig. 2 Relationship between the poles kp and pF, with
${\varLambda _{{J_0}}}$ = 138 MeV, x = 0.2
图 3 取
${\varLambda _{{J_0}}}$ = 35 MeV, x = 0.2时, 极点位置kp与pF的关系Fig. 3 Relationship between the poles kp and pF, with
${\varLambda _{{J_0}}}$ = 35 MeV, x = 0.2
图 4
${\varLambda _{{J_0}}}$ = 138 MeV, x = 0.2, pF = 0.3 fm–1时的G-k图Fig. 4 Graph of G-k with
${\varLambda _{{J_0}}}$ = 138 MeV, x = 0.2, pF = 0.3 fm–1
图 8
${\varLambda _{{J_0}}}$ = 35 MeV, x = 0.2, pF = 0.5 fm–1时的G-k图Fig. 8 Graph of G-k with
${\varLambda _{{J_0}}}$ = 35 MeV, x = 0.2, pF = 0.5 fm–1
图 5
${\varLambda _{{J_0}}}$ = 35 MeV, x = 0.2, pF = 0.3 fm–1时的G-k图Fig. 5 Graph of G-k with
${\Lambda _{{J_0}}}$ = 35 MeV, x = 0.2, pF = 0.3 fm–1
图 6
${\varLambda _{{J_0}}}$ = 138 MeV, x = 0.2, pF = 0.5 fm–1时的G-k图Fig. 6 Graph of G-k with
${\varLambda _{{J_0}}}$ = 138 MeV, x = 0.2, pF = 0.5 fm–1表 1
${\varLambda _{{J_0}}}$ = 138 MeV, Brückner G矩阵的一些极点位置kpTab. 1 Some poles kp of Brückner G matrix with
${\varLambda _{{J_0}}}$ = 138 MeVpF/fm–1 kp/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 
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表 2
${\varLambda _{{J_0}}}$ = 35 MeV, Brückner G矩阵的一些极点位置kpTab. 2 Some poles kp
of Brückner G matrix with ${\varLambda _{{J_0}}}$ = 35 MeVpF/fm–1 kp/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
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表 3
${\varLambda _{{J_0}}}$ = 138 MeV, 单粒子能量, (E/A)1表示(1)方法的数值结果, (E/A)2表示(2)方法的结果Tab. 3 Single particle energy with
${\varLambda _{{J_0}}}$ = 138 MeV, (E/A)1 represents the numerical result of method (1), (E/A)2 represents the result of method (2)pF/fm–1 (E/A)1/MeV (E/A)2/MeV x = +0.20 x = –0.20 x = +0.05 x = –0.05 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
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表 4
${\varLambda _{{J_0}}}$ = 35 MeV, 单粒子能量, (E/A)1表示(1)方法的数值结果, (E/A)2表示(2)方法的结果Tab. 4 Single particle energy with
${\varLambda _{{J_0}}}$ = 35 MeV, (E/A)1 represents the numerical result of method (1), (E/A)2 represents the result of method (2)pF/fm–1 (E/A)1/MeV (E/A)2/MeV x = +0.20 x = –0.20 x = +0.05 x = –0.05 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pF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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