Exact Solwtion of Few-Body Systems and Its applications

在物理学中，我们已经发展了许多高精度的少体系统计算方法。这些方法包括高斯基耦合重排通道变分法、随机变分法、Faddeev-Yakubovsky方法、耦合离散通道法等。结果表明：（1）在计算三体破裂阈值以下的三核子散射态时，变形Faddeev方程和辅助库仑势是有效的。(2)本文用高斯基耦合道变分法计算了反质子氦原子的准稳态，并成功地解释了激光实验数据，精度达到6位数。(3)本文发展了四体计算方法，并将其应用于A= 4，7和13的轻超核的结构研究。明确了能级结构与自旋相关的YN力之间的关系。(4)通过对三核子中间态的精确求解，我们明确了超介子的非介子衰变机制。(5)我们预言了在Ex= 4.9eV处，L=1的正电子素分子的一个新能级，它不衰变为两个正电子素，而是通过发射E1光子衰变到基态。如果能观察到E1跃迁，则可作为分子的证据。(6)本文将Faddeev-Yakubovsky方法应用于四体反应2 H（d，p）3 H和2 H（d，n）3 He，在巴黎势下得到了较好的结果。

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.