Improvement to wave functions and energy values of the ground state of helium

Nonrelativistic wave functions and energy values for the ground state of helium are calculated accurately by using the conventional Rayleigh-Ritz technique. However, the trial wave functions used are more general than those used by Hylleraas and others. They contain interelectronic separation coordinates in the exponential function beside the variational parameters. Groups of three- and four-parameter wave functions are obtained with comparatively smaller energies. Also, improved wave functions and energies have been obtained by solving determinants of orders 7, 13, 22, 34, 50, 70, 95, and 125, using a simple model. The last determinant yields an energy value of -2.903 724 371 a.u., as compared with -2.903 724 370 a.u. obtained by Pekeris by solving a determinant of order 715. The first determinant (ten parameters) yields an energy value of -2.903 425 858 a.u., as compared with the recent value of -2.9022 a.u. computed by Tweed with the use of a 41-parameter wave function.