Accurate and simple wavefunctions for the helium isoelectronic sequence with correct cusp conditions

Abstract

Simple and accurate wavefunctions for the He atom and He-like isoelectronic
\nions are presented. These functions—the product of hydrogenic one-electron
\nsolutions and a fully correlated part—satisfy all the coalescence cusp conditions
\nat the Coulomb singularities. Functions with different numbers of parameters
\nand different degrees of accuracy are discussed. Simple analytic expressions
\nfor the wavefunction and the energy, valid for a wide range of nuclear charges,
\nare presented. The wavefunctions are tested, in the case of helium, through
\nthe calculations of various cross sections which probe different regions of the
\nconfiguration space, mostly those close to the two-particle coalescence points.