Exact Solwtion of Few-Body Systems and Its applications

在物理学中，我们已经发展了许多针对少体系统的高精度计算方法。这些方法包括基于高斯基的耦合重排通道变分方法、随机变分方法、Faddeev-Yakubovsky方法、耦合离散连续通道方法等。这些方法已经被应用于各种有趣和重要的问题。主要结果如下：(1)用变形的辅助库仑势Faddeev方程计算了低于三体分裂阈值的三核子散射态。(2)用高斯基耦合通道变分方法计算了反质子氦原子的准稳态，并很好地解释了激光实验数据，精度达到6位有效数字。(3)我们发展了四体计算方法，并将其应用于A=4，7，13的轻超核的结构研究中。我们弄清楚了能级结构之间的关系和自旋相关的YN力。(4)通过精确求解三核子中间态，(5)我们预言了一个新的正电子分子能级，在Ex=4.9 eV时，L=1，它不会衰变到两个正电子，而是通过发射e1光子衰变到地面。将Faddeev-Yakubovsky方法应用于2H(d，p)~3H和2H(d，n)~3He的四体反应，得到了较好的计算结果。

We have developed a lot of high-precision calculational methods for few-body systems in physics. the methods include the gaussian-basis coupled-rearrangement-channel variational method, the stochastic variational method, Faddeev-Yakubovsky method, the coupled-discretized continuum channel method, and so on The methods have been applied to various interesting and important problems. some of the results are as following :(1) We showed usefulness of the deformed Faddeev equation with the auxial Coulomb potential in the calculation of the three-nucleon scattering states below the three-body breakup threshold.(2) We calculated the quasi-stable states of the antiprotonic helium atoms with the use of Gaussian basis coupled channel variational method and explained very successfully the laser experimental data with the accuracy of 6 significant figures.(3) We developed the four-body calculational method and applied it to the structure study of light hypernuclei with A=4,7 and 13. We made clear the relation between the energy-level structure and the spin-dependent YN forces.(4) By solving exactly the three-nucleon intermediate states, we made clear the mechanism of non-mesonic decay of the hypertritons.(5) We predicted a new level of positronium molecule with L=1 at Ex=4.9 eV which dose not decay to two positroniums but decays to the ground atate by emitting E1 photon. If the E1 transition is ovserved, it will be an evidence of the molecule.(6) We applied the Faddeev-Yakubovsky method to the four-body reaction 2H (d, p) 3H and 2H (d, n) 3He and obatined a good results with the paris potential.