arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1209.4556nucl-th
收藏

核物质中的手征四体相互作用

Chiral four-body interactions in nuclear matter

N. Kaiser

摘要:

对核物质和中子物质中手征四核子相互作用进行了探索性研究。与手征$4π$ -顶点和手征NN $3π$ -顶点相结合的π介子交换所产生的首阶项被发现是非常小的。对于密度高达$ρ=0.4\,$ fm $^{-3}$的粒子,它们对每个粒子能量的吸引力贡献保持在$0.6\,$ MeV以下。我们还考虑了由π介子交换和核子的双重$Δ$同量异位素激发引起的四核子相互作用。对于大多数封闭的四回路图,在四个费米球上发生的积分可以解析地求解,或者简化为易于管理的单参数或双参数积分。在对交替符号的3-环、2-环和1-环图的个别大贡献求和之后,人们得到在核物质饱和密度$ρ_0=0.16\,$ fm $^{-3}$处$2.35\,$ MeV对每个粒子能量的中等贡献。曲线$\bar E(ρ)$随密度迅速上升,约为$ρ$的三次方。在纯中子物质中,类似的手征四体相互作用在相同的密度$ρ_n$下导致大约一半强的排斥作用。计算结果表明,长程多核子力,特别是由质量间隙为$293\,$ MeV的强耦合$πN Δ$ -系统提供的力,对核物质和中子物质的物态方程仍然起着重要的作用.

英文摘要:

An exploratory study of chiral four-nucleon interactions in nuclear and neutron matter is performed. The leading-order terms arising from pion-exchange in combination with the chiral $4π$-vertex and the chiral NN$3π$-vertex are found to be very small. Their attractive contribution to the energy per particle stays below $0.6\,$MeV in magnitude for densities up to $ρ=0.4\,$fm$^{-3}$. We consider also the four-nucleon interaction induced by pion-exchange and twofold $Δ$-isobar excitation of nucleons. For most of the closed four-loop diagrams the occurring integrals over four Fermi spheres can either be solved analytically or reduced to easily manageable one- or two-parameter integrals. After summing the individually large contributions from 3-ring, 2-ring and 1-ring diagrams of alternating signs, one obtains at nuclear matter saturation density $ρ_0=0.16\,$fm$^{-3}$ a moderate contribution of $2.35\,$MeV to the energy per particle. The curve $\bar E(ρ)$ rises rapidly with density, approximately with the third power of $ρ$. In pure neutron matter the analogous chiral four-body interactions lead, at the same density $ρ_n$, to a repulsive contribution that is about half as strong. The present calculation indicates that long-range multi-nucleon forces, in particular those provided by the strongly coupled $πN Δ$-system with its small mass-gap of $293\,$MeV, can still play an appreciable role for the equation of state of nuclear and neutron matter.

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。

↑