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arXiv 0906.2349nucl-th
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有限密度核系统手征有效场论的非微扰方法

Non-perturbative methods for a chiral effective field theory of finite density nuclear systems

A. Lacour, J. A. Oller, U. -G. Meißner

摘要:

最近,我们发展了一种新的手征功率计数方案,用于以核子和π介子为自由度的核物质的有效场论[1]。它允许考虑到本地以及π介子介导的多核子相互作用的系统扩展。在本研究中,我们应用这种功率计数的π介子自能和能量密度的核和中子物质在次领先秩序的评价。为了在实际计算中实现这种功率计数,我们在这里开发了一种基于酉手征微扰理论的非微扰方法,用于执行所需的计算。我们明确地表明,在介质中的核子-核子相互作用的介子自能的贡献,这一顺序取消。对称核和中子物质的能量密度的主要趋势已经在次领先的顺序再现。此外,一个准确的描述中子物质状态方程,与复杂的多体计算相比,通过改变其预期值附近的减法常数只有轻微的。对称核物质的情况需要引入额外的微调减法常数,将高阶贡献的影响参数化。这样,经验饱和点和核物质的不可压缩性被很好地再现,而每个核子的能量作为密度的函数与文献中的复杂计算密切一致。

英文摘要:

Recently we have developed a novel chiral power counting scheme for an effective field theory of nuclear matter with nucleons and pions as degrees of freedom [1]. It allows for a systematic expansion taking into account both local as well as pion-mediated multi-nucleon interactions. We apply this power counting in the present study to the evaluation of the pion self-energy and the energy density in nuclear and neutron matter at next-to-leading order. To implement this power counting in actual calculations we develop here a non-perturbative method based on Unitary Chiral Perturbation Theory for performing the required resummations. We show explicitly that the contributions to the pion self-energy with in-medium nucleon-nucleon interactions to this order cancel. The main trends for the energy density of symmetric nuclear and neutron matter are already reproduced at next-to-leading order. In addition, an accurate description of the neutron matter equation of state, as compared with sophisticated many-body calculations, is obtained by varying only slightly a subtraction constant around its expected value. The case of symmetric nuclear matter requires the introduction of an additional fine-tuned subtraction constant, parameterizing the effects from higher order contributions. With that, the empirical saturation point and the nuclear matter incompressiblity are well reproduced while the energy per nucleon as a function of density closely agrees with sophisticated calculations in the literature.

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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