Compact Wavefunctions for He-like Systems

Wavefunctions which are compact, but still quite accurate, are extremely valuable as tools for gaining understanding of quantum systems. Here we study the ground electronic states of the three-body systems comprising the He isoelectronic series, using spatial wavefunctions that depend exponentially on all the interparticle distances, i.~e. of the form $(1+{\sf P}_{12})\exp(-\alpha r_1 -\beta r_2 -\gamma r_{12})$, where $r_1$ and $r_2$ are the electron nuclear distances, $r_{12}$ is the electron-electron separation, and ${\sf P}_{12}$ permutes the electron coordinates. When the nonlinear parameters are carefully optimized (a nontrivial task), this type of basis is found to be extraordinarily efficient; using as few as four basis functions, it is found that nonrelativistic energies are reproduced to within 38 microhartrees of the exact values, an error far less than for compact wavefunctions previously proposed by others. Other properties, including those totally dependent upon the electron correlation, are also well represented.