奇异Hylleraas三电子积分
Singular Hylleraas three-electron integrals
摘要：
在少数电子系统中的主导量子电动力学效应的计算涉及$1/r_i^3$和$1/r_{ij}^3$形式的电子间距离的奇异矩阵元素。积分时，非相对论性波函数表示与Hylleraas基础表示的结果进行了研究。各种权力的电子坐标和主积分的递推关系推导出适合于高精度数值计算的形式。
英文摘要：
Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic wave function is represented with a Hylleraas basis representation are studied. Recursion relations for various powers of the electron coordinates and the master integrals are derived in a form suited for high precision numerical evaluations.
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