Concurrent Vector Algorithms for Spline Solutions of the Helium Pair Equation

Abstract

An algorithm for the solution of the pair equation for helium is described, suitable for concurrent vector pro cessors. Emphasis is placed on minimizing memory re quirements so that the technique may be extended to systems with more electrons. The pair function is ex panded in a series of partial waves whose radial factor is represented by a tensor product of B-splines. Perfor mance is analyzed for the ground and first excited 1 S state, and for the lowest 3 S and 1,3 P states. An odd-even, column Nesbet algorithm is derived for solving the gen eralized eigenvalue problem and is shown to converge in all cases.