集体多极展开与量子三体问题中的微扰理论
Collective multipole expansions and the perturbation theory in the quantum three-body problem
摘要：
考虑了三粒子势能的微扰理论。导出了三个自由粒子的连续波函数的一阶修正。它表明，使用的集体多极展开的自由三体格林函数的Wigner $D$ -函数的集合可以减少微扰矩阵元素的维数从12到6。导出了自由格林函数集体多极展开系数的显式表达式。发现$S$波的多极系数只依赖于三个变量，而不是像高阶多极那样依赖于六个变量。发展的理论的三体分子分裂过程的可能应用进行了讨论。
英文摘要：
The perturbation theory with respect to the potential energy of three particles is considered. The first-order correction to the continuum wave function of three free particles is derived. It is shown that the use of the collective multipole expansion of the free three-body Green function over the set of Wigner $D$-functions can reduce the dimensionality of perturbative matrix elements from twelve to six. The explicit expressions for the coefficients of the collective multipole expansion of the free Green function are derived. It is found that the $S$-wave multipole coefficient depends only upon three variables instead of six as higher multipoles do. The possible applications of the developed theory to the three-body molecular break-up processes are discussed.
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