超球谐展开的收敛行为He原子的^3S态

On Convergence Patterns of the Hyperspherical Harmonic Expansion for the Excited ~3S Helium Atom

利用相关函数一超球谐-广义Laguerre函数方法（CFHHGLF），研究He原子3S态波函数向超球谐函数展开的收敛行为．截止于l＝0，1，2的超球谐函数给出的本征能分别与组态相互作用（CI）的s-、sp-、spd-极限能一致．仅用44个超球谐函数，便得到了与精确的HylleraasCI变分能量小数点后第5位的23S、33S和43S态本征能吻合．

The convergence patterns of the hyperspherical harmonic expansion for theexcited 3S states of the helium atom have been studied with the correlation function-hyperspherlcal harmonic-generalized Laguerre function method(CFHHGLF). The convergenteigenenergies at l=0, 1, 2 agree well with the s-limits, sp-limits and spd-limits of the configurationinteraction (CI) method. With only 44 hyperspherical harmonics, the eigenenergies of the 2 3S,33S and 4 3S states are the same as those from the exact Hylleraas variational method.