原子核结团效应研究和推广的Skyrme模型

This project concerns the development of a Skyrme-type model for applications to nuclear physics and nuclear clusters. Unlike conventional nuclear theory, it is based on a first-principles effective field theory which is the chiral Lagrangian with higher-order derivative corrections and higher-order corrections to the potential. Baryons are identified with the solitons in the field theory and the nuclear spectra are obtained from semi-classical quantization of spin and isospin rotational modes as well as vibrational modes. Although the calculations are based on numerical methods, they require much less computational power than lattice QCD and it is straightforward to consider dynamical problems of, for instance, scattering and decay, in real-time formalism. Another advantage is the possibility for the model to describe nuclear clusters, which is a challenge for mean field models. Finally, a main advantage over data-driven nuclear theory models, is that our model has a very small number of parameters, i.e. about 3-5 parameters, of which 2 are already fixed by pion physics. The model is still under development and some progress has already been made by the principal investigator of the project, which deals with the overall binding energies of the nuclei. Further steps that needs to be carried out to arrive at a high-precision model for nuclear physics are the following. The sixth-order derivative term (higher-order correction term), has been known recently to be essential for fluid-like properties of nuclei; special techniques for this term will however be needed. Isospin-breaking effects should be studied further and Coulomb interactions should also be taken into account, especially for larger nuclei. The project will require a new medium-sized computer and cutting-edge numerical methods and the results are expected to become comparable and competitive with other nuclear models. Finally, we hope to make predictions for nuclear cluster states that will be interesting for IMP's experiments to search for.

本项目旨在研究Skyrme模型在核物理及原子核结团中的应用。该模型从第一性原理出发，以有效场论为基础，通过向手征拉氏量添加高阶微分项及高阶势能项修正项来研究原子核。本项目在计算量和计算机性能需求上都低于格点QCD，但能更好地描述动力学过程，比如散射和衰变。该模型可以描述核结团，而包括壳层模型的很多其它模型都对此无能为力。该模型最大的优势是，该理论中只包含3-5个参数，其中2个已由π介子物理确定，自由参数很少。该模型已经在计算原子核的总结合能方面获得了很大进展。已知六阶微分项（及更高阶修正项）对描述原子核类液体性质十分关键，因此为了提高模型精度，我们需要找到处理这些高阶项的特殊技巧。同样需要考虑同位旋破缺及库伦作用的贡献，特别是对重原子核而言。本项目需要一个中型计算机工作站和尖端数值计算方法。本项目可以预言原子核性质，并利用近物所实验装置对其进行进一步研究。

量子色动力学（QCD）中最轻的自由度是介子，人们很久之前就已经知道它们的低能有效理论在大 N 下可以简化为 Skyrme 模型。 该模型具有经典的孤子解，其对应于 QCD 中的重子。 然而，将这一事实和现实世界（N=3 QCD）唯象地联系起来到目前为止是不可能的，原因有如下几个。 首先，从 QCD 中很难提取出由更高能量和其他介子引起的小 N 修正和更高阶修正。 其次，该系统本质上是量子力学的，而现有工具在很大程度上受限于经典场论。 该项目旨在开始挑战这两个问题。..首先，我们系统地研究了 Skyrme 模型在更高能量和包括更大质量介子时可能出现的扩展类型。 我们以几个原则为指导，其中包括原子核的稳定性和实际的结合能。 我们表明，先前的尝试会导致非球对称形变下的普遍的不稳定性，并引入了没有此类不稳定性的高阶校正。 我们还发现包含 omega 介子会大大改善对结合能的拟合。 我们系统地找到了 Skyrmions 的数值解，实际上我们发现的解比半个世纪以来对这些孤子的研究发现的解还多，我们还将这些解应用在核结构的研究，重点是原子核团簇。..在量子方面，我们发明了一种新的形式，称为线性化的孤子微扰理论。 它是对旧的集体坐标形式的改进，集体坐标形式依赖于一个正则变换，而人们已经知道该正则变换与正规化不兼容，这导致了一些著名的错误答案。 此外，线性化的孤子微扰理论比集体坐标更易于使用，它允许我们解决了许多此前被视为开放问题的问题。 特别是，在玩具模型中，我们得到了对质量、形状因子、衰变率和散射振幅的两圈修正，所有这些都远远超出了使用集体坐标能够达到的水平。 在某些情况下，我们能够将我们的结果与使用可积性和经典场论获得的结果进行比较，且它们总是一致的。