基于参数微扰法精确计算铍离子Be2+和硼离子B3+的基态能量

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..

Highly Accurate Ground State Energy Calculation of Ions Be2+ and B3+ Based on the Parameter Perturbation Method

The Hamilton equation of the ions Be2 + (z =4) and B3 + (z =5) including shielding effect parameter σ were established.A combination of the ground state 1 s 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-σ was chosen as the ground state approximate wave functions of the ions Be2+ and g3+.The shielding parameters σ are determined as σ =0.56350197 for Be2+ and σ =0.525070444 for B3+ respectively by parameter perturbation method.The calculation results show that the error of the ground state energy of the ions Be2 + in third order approximation or B3 + in fourth order approximation with the perturbation method is △E ≈ 10 4 ～ 10-5 a.u.in comparison with the experimental values.