奇异短程势的J矩阵方法
Singular Short Range Potentials in the J-Matrix Approach
摘要：
我们使用J矩阵方法的工具来评估的S矩阵，然后推导出的束缚和共振态的能量奇异屏蔽库仑势，解析和分段可微。J-矩阵的方法允许我们吸收的1/r奇异性的潜在的参考哈密顿量，然后分析处理。计算是使用一个无限平方可积的基础上，支持三对角矩阵表示的参考哈密顿。其余部分的潜在的，这是约束和定期无处不在，是一个有效的数值方案，在一个合适的基础上使用高斯求积近似。为了展示我们的方法的力量，我们已经考虑了最微妙的区域接近的束缚-非束缚过渡，并比较我们的结果有利地与现有的数值数据。
英文摘要：
We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1/r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.
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