Variational correction to Wigner R-matrix theory of scattering

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Abstract
Three stages in the development of R-matrix scattering theory are discussed. The standard calculation using N basis functions is variationally stable in the N-dimensional basis space, yet results often converge slowly with increasing N. As an improvement the Hamiltonian is separated into two parts, a soluble H0 and a potential V. The Buttle correction (1967) is used to account for H0 exactly. This is equivalent to solving the approximate Hamiltonian H0+VN where VN is an N*N matrix approximation to V. The exact solution to the approximate Hamiltonian may be considered as a trial wavefunction for the full Hamiltonian H. The problem of obtaining scattering information from this trial wavefunction which is variationally stable against arbitrary variations, as opposed to variations in a finite trial space is discussed.

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