Precise nonvariational calculations on the helium atom

The Schroedinger equation is solved directly for the ground state and excited 2 1S state of the helium atom by using a rapidly convergent hyperspherical method which involves no adjustable parameters. The double and triple coalescence points are taken into account analytically. The center-of-mass motion is treated nonperturbatively, and the cases of infinite and finite nuclear masses are considered. The inclusion of 169 hyperspherical functions yields the precision of a few parts in 109 and 108 for the expectation value of the Hamiltonian operator and for all other expectation values, respectively, for the ground state, with only slightly less accuracy for the excited state