Uncoupling correlated calculations in atomic physics: Very high accuracy and ease

An uncoupled correlated variational method (i.e., explicitly using the interelectronic coordinates) for calculations involving several electrons is introduced. All the overlap and Hamiltonian matrix elements, including those involving the electron-electron interaction, are simple products of one-dimensional integrations. Although simple to implement, the method yields the best available energy for the ground state of the He zeroth-order Hamiltonian ${H}_{0}{=H}_{1}{+H}_{2}{+1/r}_{12}.$ Preliminary nonoptimized and nonextrapolated calculations yield $E=\ensuremath{-}2.9037243770341195938(50)\mathrm{a}.\mathrm{u}.$