氦原子和类氦离子基态能量的变分计算及相对论修正

采用一个包含坐标伸缩系数的简单有效的变分波函数,同时考虑到核的运动,利用Mathematic a语言开发了一个用变分法计算三体问题的程序,对氦原子和类氦离子(H^-,He,Li ⁺,Be⁺⁺,B³⁺,C⁴⁺,N⁵⁺,O ⁶⁺)的非相对论基态能量和解析波 函数进行了变分计算.在此基础上,对非相对论哈密顿量进行相对论和辐射修正,并考虑到有 限核电荷半径的影响,得到了氦原子和类氦离子高精度的基态能量值. 关键词： 氦原子 类氦离子 变分法 基态能量 相对论修正

Variational calculations and relativistic corrections to the nonrelativistic ground energies of the helium atom and the helium-like ions

Mathematica language is used to make a program that can solve the three_body pro blem with variational method. Considering the nuclear motion, the nonrelativisti c ground energies and the analytic wave functions of the helium atom and the hel ium_like ions (H⁺, He, Li⁺, Be⁺⁺, B³⁺, C⁴⁺, N⁵⁺, O⁶⁺) are presented by using a simp le effective variational wave funct ion with a flexible parameter k. Based on these results, the influence of a finite nucleus charge radius, the relativistic and radiative corrections on the nonrelativistic Hamiltonian are discussed. The high precision values of the heli um atom and the helium_like ions ground energies are evaluated.