Nuclear Structure in Chiral Quark Models Nuclear Force and Many-Body Problem

研究工作沿着以下三条路线进行：第一，在平均场近似下，利用基于QCD的有效夸克理论研究重子的内部夸克结构。我们发现在最简单的Nambu-Jona-Lasinio（NJL）模型中不存在稳定的孤子解。如果我们将模型推广到味SU（3），瞬子诱导的6-Fermi相互作用对稳定孤子对坍缩起主要作用。这样，我们就可以在同一模型中描述介子和重子。其次，我们精确求解了NJL模型中的相对论性3夸克Faddeev方程，包括J=0和J=2两体通道。这是本研究最重要的成果。我们已经表明，与原来的NJL拉格朗日不能得到一个束缚态，我们已经给出的形式的拉格朗日，其中一个可以描述的π介子在Bethe-Salpeter框架，和核子和δ的Faddeev框架。我们用Faddeev方程的解来描述核子的静态性质，发现在夸克-双夸克结合能较小的情况下，朴素夸克-双夸克模型的结果更接近于精确的结果。第三，在相对论介子-核子理论框架下研究了核和中子物质的物态方程。利用1/N展开式，我们证明了高阶关联项对软化状态方程的重要性。我们发现相对论性状态方程的软化在很宽的温度和密度范围内都成立。

The research was carried out along the following three lines : First, we used effective quark theories based on QCD to investigate the internal quark structure of baryons in the mean field approximation. We found that in the simplest Nambu-Jona-Lasinio (NJL) model there exist no stable soliton solutions. If we extend the model to flavor SU(3), the instanton induced 6-Fermi interaction plays the dominant role to stabilize the soliton against collapse. In this way we could describe both meons and baryons within the same model. We also investigated the chiral sigma model, and developed a method to eliminate the Landau-ghost from the soliton.Second, we solved the relativistic 3-quark Faddeev equation in the NJL model exactly, including the J=0 and J=2 two body channels. This is the most important achievement of the present research. We have shown that with the original NJL Lagrangian one cannot obtain a bound state, and we have given the form of the Lagrangian by which one can describe the pion in the Bethe-Salpeter framework, and nucleon and delta in the Faddeev framework. We used the solution of the Faddeev equation to describe static properties of the nucleon, and found that the results of the naive quark-diquark model are close to the exact ones provided that the quark-diquark binding energy is small.Third, we investigated the equation of state of nuclear and neutron matter in the framework of relativistic meson-nucleon theory. Using the 1/N expansion, we have shown the importance of the higher order correlation terms to soften the equation of state. We have found that the softening of the relativistic equation of state holds over a wide range of temperatures and densities.