Use of the R matrix method for bound-state calculations. I. General theory

In the close-coupling (CC) method of electron-atom collision theory, wavefunctions Psi E for a system containing (N+1) electrons are expanded in terms of products of N-electron 'target' functions multiplied by fully optimised orbital functions for a 'colliding' electron. The method can also be used to calculate energies E n and functions Psi n for bound states of the (N+1)-electron system: this is often referred to as the 'frozen cores' (FCS) approximation. In the R-matrix method the CC problem is solved for an inner region, r<or=a, subject to a fixed boundary condition at r=a to give functions psi k belonging to energies E=e k . Functions Psi E for any E can be expected in terms of the Psi k and matched to functions for the outer region, r>or=a. The paper includes a discussion of the FCS approximation and a summary of R-matrix theory. Techniques are described for calculating orthonormal sets of outer-region solutions correct to first order in the long-range multipole potentials. Matching of inner-region to outer-region solutions gives an eigenvalue problem for the determination of the energies E n which is solved using scanning techniques which do not require estimates of the E n to be provided.