非置换对称全同粒子的调和超球基
The harmonic hyperspherical basis for identical particles without permutational symmetry
摘要：
用超球谐基描述了$A$ -体系统的束缚态。这里提出的方法是基于超球谐函数的势能表示。使用这种表示，基本元素之间的矩阵元素是简单的，和势能是在一个紧凑的形式，非常适合于数值实现。基既不是对称的，也不是反对称的，就像在全同粒子的情况下所要求的那样;然而，在哈密顿矩阵对角化之后，本征向量反映了其中存在的对称性，并且物理状态的识别是可能的，正如在特定情况下所示的那样。我们考虑的应用程序，原子，分子和核少体系统中的对称性破缺项存在于哈密顿量，他们的列入是直接在本方法。作为一个例子，我们解决了三个和四个粒子通过短程中心相互作用和库仑势相互作用的情况。
英文摘要：
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form, well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it, and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential.
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