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

本研究主要沿着以下三个方向进行：首先，我们利用基于QCD的有效夸克理论研究了平均场近似下重子的内部夸克结构。我们发现在最简单的Nambu-Jona-Lasinio （NJL）模型中不存在稳定孤子解。如果我们将模型扩展到flavor SU(3)，则瞬时子诱导的6-费米相互作用在稳定孤子防止坍缩方面起主导作用。用这种方法，我们可以在同一个模型中描述介子和重子。我们还研究了手性σ模型，并提出了一种消除朗道鬼影的方法。其次，我们精确地求解了NJL模型中的相对论性3夸克Faddeev方程，包括J=0和J=2两个体道。这是本研究最重要的成果。我们已经证明了用NJL的原始拉格朗日不能得到束缚态，并且我们给出了拉格朗日的形式，人们可以用它来描述贝特-萨尔彼得框架中的介子，以及法迪夫框架中的核子和delta。我们使用Faddeev方程的解来描述核子的静态性质，发现在夸克-夸克结合能较小的情况下，朴素夸克-二夸克模型的结果与精确的结果接近。第三，我们在相对论介子-核子理论的框架下研究了核与中子物质的状态方程。利用1/N展开，我们证明了高阶相关项对软化状态方程的重要性。我们已经发现，相对论状态方程的软化在很大的温度和密度范围内保持不变。

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.