超球坐标下相关函数对锂原子基态本征能收敛行为的影响

Effect of Different Correlation Functions on Convergence Pattern in the CFHHGLF Calculations of the Lithium Atom

在超球坐标下，由３个对称相关函数ｅｘｐ［－α（ｒ１＋ｒ２＋ｒ３）］（α分别为，２．７６和核电荷数ｚ），利用相关函数－超球谐－广义Ｌａｇｕｅｒｒｅ函数方法（ＣＦＨＨＧＬＦ）直接求解Ｌｉ原子的Ｓｃｈｒｄｉｎｇｅｒ方程，计算基态本征能。从数值来看，α＝ｚ结果最好，其次是α＝２．７６，变参数α较差；而从径向的收敛速度来看，变参数α收敛最快，α＝２．７６收敛较慢，α＝ｚ时本征能只有当对称基超过１００时才呈现收敛趋势。结果表明，在超球谐展开方案下只有α＝ｚ的相关函数才能得到高精度的本征能量。

Three simple spatially symmetric correlation functions exp[-α(r1+r2+r3)](variable parameter a by E+3/2α2=0,constant α,2.76 and the nuclear charge z,respectively)are used to carry out the correlation-function hyperspherical-harmonic and generalized-Laguerre-function(CFHHGLF)calculations of the ground state lithium atom.With 215 symmetric bases of the two-dimensional irreducible representation for the permutation group S3,constructed from nine-dimensional hyperspherical harmonics,the CFHHGLF calculations provide the best eigenenergy of-7.473 122 a.u.as α=z,followed by α=2.76,-7.450 788 a.u.,and the variable parameter α,-7.413 668 a.u.,while from the convergence rate in the hyperradial direction,the variable parameter α generates the fastest convergence eigenenergy,and as α=.76 the eigenenergy slowly converges,as α=z the eigenenergy converges only when over 100 symmetry bases are taken into account.In view of the accuracy as well as the stability of the eigenenergy,symmetric exponent correlation function with α=z should be considered to obtain high precise eigenenergy in hyperspherical harmonic method.