Correlated atomic pair functions by the e(-rho)-method. I. Ground state 1(1)S and lowest excited states n(1)S (n > 1) and n(3)S of helium

Some low n(1)S and n(3)S states of the helium atom are computed with the ai d of the e-e method which formulates the electronic wave function of the 2 electrons as psi = e(-e) F, where rho = Z(r(1) + r(2)) - 1/2 r(12) and here Z = 2. Both the differential and the integral equation for F contain a pse udopotential (V) over tilde instead of the true potential V that contrary t o V is finite. For the ground state, F = 1 yields nearly the Hartree-Fock S CF accuracy, whereas a multinomial expansion in r(1), r(2), r(12) yields a relative error of about 10(-7). All integrals can be computed analytically and are derived from one single "parent" integral.