发表机构
Huanggang Normal University; Hubei Normal University; Zhengzhou Normal University（黄冈师范学院; 湖北师范大学; 郑州师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出非相对论展开方法，用于推导轻原子和分子体系的高阶有效能量修正算符，并数值验证了氢原子、氢分子离子、氦原子和氢分子基态在$m\alpha^8$阶的Dirac-Coulomb能量及Breit势修正，方法可靠且可扩展。
AI 中文摘要
非相对论展开方法被应用于轻原子和分子体系的Dirac-Coulomb能量及一阶相对论Breit势修正，以推导少体系统的高阶有效能量修正算符。研究发现，在$m\alpha^8$阶的有效算符包含不完全可分离的发散项。这些发散必须与由低阶能量修正算符的二阶和三阶微扰产生的发散联合消除，而这种消除可以通过非相对论数值展开方法自动完成。利用高斯基组，我们数值计算了氢原子、氢分子离子、氦原子和氢分子的基态在$m\alpha^8$阶以内的Dirac-Coulomb能量和相对论Breit势修正的贡献。这些结果证实了本方法的可靠性，并使其能够扩展到更复杂的系统。
英文摘要
The nonrelativistic expansion method is applied to the Dirac-Coulomb energy and first order relativistic Breit potential corrections for light atomic and molecular systems to derive high-order effective energy correction operators for few-body systems. It is found that effective operators at the $mα^8$ order contain incompletely separable divergences. These divergences must be canceled jointly with divergences arising from second- and third-order perturbations of lower-order energy correction operators, and such cancellation can be accomplished automatically by the nonrelativistic numerical expansion approach. Using Gaussian basis sets, we numerically compute contributions to the Dirac-Coulomb energy and relativistic Breit potential corrections up to order $mα^8$ for the ground states of the hydrogen atom, hydrogen molecular ion, helium atom, and hydrogen molecule. These results confirm the reliability of the present method and enable its extension to more complex systems.
