Correlated two-electron wave functions of any symmetry

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Abstract
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 spin). Coupled equations satisfied by these wave functions are derived which are well adapted to computation and which we discretize on a numerical lattice utilizing the basis-spline collocation method. Use of this method which relies on very flexible basis functions is intended to facilitate subsequently the consideration of time-dependent rearrangments such as autoionization, photoionization, and electron-impact excitation 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 damped relaxation. Results of explicit calculations are given regarding the ground state and two low-lying singly excited states of helium.