CORRELATED 2-ELECTRON WAVE-FUNCTIONS OF ANY SYMMETRY

Using a procedure originally due to Hylleraas, a convenient expansion in coupled spherical harmonics which terminates in a very small number of terms is applied to the treatment of fully correlated two-electron wave functions of any symmetry (total angular momentum, parity, and s pin). Coupled equations satisfied by these wave functions are derived which are well adapted to computation and which we discretize on a num erical lattice utilizing the basis-spline collocation method. Use of t his method which relies on very flexible basis functions is intended t o facilitate subsequently the consideration of time-dependent rearrang ements such as autoionization, photoionization, and electron-impact ex citation and ionization. Here, we describe the underlying theoretical and computational methods concerning our treatment of the two-electron problem, the lattice discretization, and partial eigensolution by dam ped relaxation. Results of explicit calculations are given regarding t he ground state and two low-lying singly excited states of helium.