基于参数微扰法精确计算铍离子Be^(2+)和硼离子B^(3+)的基态能量

Highly Accurate Ground State Energy Calculation of Ions Be^(2+) and B^(3+) Based on the Parameter Perturbation Method

建立含有屏蔽参数σ的铍离子Be^(2+)(z=4)和硼离子B^(3+)(z=5)的哈密顿方程.以有效核电荷数为z*=z-σ的类氢原子基态1s和激发态ns(n=2,3,…)组合的双电子波函数,作为铍离子Be^(2+)和硼离子B^(3+)的基态近似波函数.应用参数微扰法确定铍离子Be^(2+)的屏蔽参数σ=0.56350197和硼离子B^(3+)的屏蔽参数σ=0.525070444,应用参数微扰法计算铍离子Be^(2+)三级近似基态能量和硼离子B^(3+)四级近似基态能量的理论值与实验值的误差为ΔE≈10^(-4)~10^(-5)a.u..

The Hamilton equation of the ions Be^(2+)(z = 4)and B^(3+)(z = 5)including shielding effect parameterσwere established.A combination of the ground state 1s and the excited state ns(n =2,3,…)wave functions of two hydrogen-like atoms as the two electrons' wave function with effective nuclear charge number of z*=z-σwas chosen as the ground state approximate wave functions of the ions Be^(2+)and B^(3+).The shielding parametersσare determined asσ=0.56350197 for Be^(2+)andσ=0.525070444 for B^(3+)respectively by parameter perturbation method.The calculation results show that the error of the ground state energy of the ions Be^(2+)in third order approximation or B^(3+)in fourth order approximation with the perturbation method isΔE ≈10^(-4)~10^(-5)a.u.in comparison with the experimental values.