Solution of the pair equation using a finite discrete spectrum

A method for the solution of the pair equation, by summation over a complete and finite basis set, is presented. The basis set is obtained by diagonalization of a discretized Hermitian one-particle Hamiltonian. The number of operations required to solve the radial pair equation is proportional to $N^3$ where N is the number of radial lattice points used. An application to the ground state of helium, evaluating the total energy to an accuracy of a few parts in ${10}^8$, is presented. The method is equally well applicable to the study of pair correlation in many-electron atoms.