Folded diagrams and 1s-Od effective interactions derived from Reid and Paris nucleon-nucleon potentials

Abstract

The sd-shell effective-interaction matrix elements are derived from the Paris and Reid potentials using a microscopic folded-diagram effective-interaction theory. A comparison of these matrix elements is carried out by calculating spectra and energy centroids for nuclei of mass 18 to 24. The folded diagrams were included by both solving for the energy-dependent effective interaction self-consistently and by including the folded diagrams explicitly. In the latter case the folded diagrams were grouped either according to the number of folds or as prescribed by the Lee and Suzuki iteration technique; the Lee-Suzuki method was found to converge better and yield the more reliable results. Special attention was given to the proper treatment of one-body connected diagrams in the calculation of the two-body effective interaction. We first calculate the (energy-dependent) G-matrix appropriate for the sd-shell for both potentials using a momentum-space matrix-inversion method which treats the Pauli exclusion operator essentially exactly. This G-matrix interaction is then used to calculate the irreducible and non- folded diagrams contained in the Q ̂ - box . The effective-interaction matrix elements are obtained by evaluating a Q ̂ - box folded diagram series. We considered four approximations for the basic Q ̂ - box . These were (C1) the inclusion of diagrams up to 2nd order in G, (C2) 2nd order plus hole-hole phonons, (C3) 2nd order plus (bare TDA) particle-hole phonons, and (C4) 2nd order plus both hole-hole and particle-hole phonons. The contribution of the folded diagrams was found to be quite large, typically about 30%, and to weaken the interaction. Also, due to the greater energy dependence of higher-order diagrams, the effect of folded diagrams was much greater in higher orders. That is, the contribution from higher-order diagrams for most cases was greatly reduced by the folded diagrams. The convergence of the folded-diagram series deteriorates with the inclusion of higher-order Q ̂ - box processes in the method which groups diagrams by the number of folds, but remains excellent in the Lee-Suzuki method. Whereas the inclusion of the particle-hole phonon was essential to obtain agreement with experiment in earlier work, when the folded diagrams are included the effect of the particle-hole phonon is to reduce the amount of binding. All four approximations to both potentials produce interactions which badly underbind nuclei. The excitation spectra given by these interactions are, however, all rather similar to each other. The Paris interaction produces more binding than does the Reid, but differences between results obtained with the two interactions were often less than differences obtained in the four approximations. Essentially no difference was found between the effective non-central interactions from the Reid and Paris potentials after including the folded diagrams, although these two potentials themselves are quite different, especially in the strength of the tensor force. Comparisons between.calculated spectra and experiment were done for 18O, 18F, 19F, 20O, 20Ne, 22Ne, 22Na and 24Mg.