The atomic three‐body problem. An accurate lower bond calculation using wave functions with logarithmic terms

Accurate lower and upper bounds for the nonrelativistic ground state energies E 0 of the real systems 4 He, H − , D − , and T − were calculated by the method of variance minimization using wave functions which include logarithmic terms. In addition, an analogous treatment with an infinite mass approximation for H − , He, and the isoelectronic series up to Z = 10 was carried out. Especially for H − and He the results (a.u.) are given by\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - 0.52775101712297_4 < E_0 (H^ -) < - 0.52775101654373_9 } \\ { - 2.90372437703413_4 < E_0 (He) < - 2.90372437703411_9 .} \\ \end{array} $$\end{document} These values have an absolute error smaller than 1.28 · 10 −4 cm −1 for H −1 and 3.10 · 10 −9 cm −1 for He. Moreover it is shown that a variation of nuclear mass m n for the H − species does not produce a second discrete eigenvalue.