新环形库仑势的束缚连续跃迁矩阵元

The bound-continuous transition matrix element for a new ring-shaped coulomb potential

利用新环形库仑势的归一化的束缚态径向波函数和按“k/2π标度”归一化的散射态径向波函数,本文给出了新环形库仑势的任意幂次的束缚连续跃迁矩阵元的通项表达式.为了简化高幂次的束缚连续跃迁矩阵元的计算,我们还推导出了不同幂次的束缚连续跃迁矩阵元之间所满足的递推关系,并提出了计算径向波函数微商的矩阵元的计算办法.本文结果可广泛的用于原子与分子的散射问题特别是环形分子的散射问题之中.

The analytical formulas of bound-continuous transition matrix elements for a new ring-shaped Coulomb potential are obtained by the normalized radial wavefunctions of the bound states and on the ＂k/2π scale＂ the normalized radial wavefunctions of scattering states. In order to simplify the calculation of the bound-continuous transition matrix elements in the case of the high power-orders, the recurrence relations of different power order transition matrix elements are derived. The calculation methods of the matrix elements for radial wavefunctions differentiation are also given. The results may be. useful in a great diversity of scattering problems for atoms or molecules, especially ring-shaped organic molecules.