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

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