Singular-value decomposition of the nucleon-nucleon reactance matrix

We use the singular-value decomposition (SVD) method to obtain a separable approximation of a prescribed rank M to the reactance matrix K. The main virtue of the method is that, as measured by the Frobenius norm, the approximation is the best possible. We test this method for the triplet S-D nucleon-nucleon scattering state by calculating a rank-4 approximation to the K-matrix for the Reid and Paris potentials. We compare two applications of the method: one in which the K-matrix is treated as a matrix defined on a momentum mesh, and the other in which K is treated as an integral operator. We find that the Frobenius norm of the former is one order of magnitude smaller than the latter. Further, we find that the error in the on-shell quantities such as the phase shifts and mixing parameters is decidedly smaller than the error obtained with a Weinberg-state expansion of corresponding rank.