Singular-value decomposition of the nucleon-nucleon reactance matrix

Summary  We use the singular-value decomposition (SVD) method to obtain a separable approximation of a prescribed rankM to the reactance matrixK. 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 tripletS-D nucleon-nucleon scattering state by calculating a rank-4 approximation to theK-matrix for the Reid and Paris potentials. We compare two applications of the method: one in which theK-matrix is treated as a matrix defined on a momentum mesh, and the other in whichK 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.