Folded Diagram S-D Shell Nuclear Structure Calculations with the Paris Nucleon-Nucleon Potential.
We have carried out a series of microscopic nuclear structure calculations in which, starting from the free nucleon-nucleon interaction, we find the energy levels of sd shell nuclei. In preparation, we briefly review several effective interaction theories which are formulated in terms of the(, ) folded diagrams (FD) and the Q-box. The folded diagrams are included by either solving for the energy dependent effective interaction self-consistently (SC) or by including the folded diagrams explicitly. In the latter case, the folded diagrams are grouped either according to the number of folds (F(,n)) or as prescribed by the Lee-Suzuki iteration formula (LS). Special attention is given to the proper treatment of 1-body connected diagrams in the calculation of the 2-body effective interaction. We then briefly describe the recently proposed Paris nucleon-nucleon potential and carry out a series of comparisons between it and the Reid potential. While the phase shifts are, of course, quite similar, the Paris potential, which is strongly energy (p('2)) dependent, differs from the Reid potential in other respects. Notable among these are the differences in the strength of the tensor force and in the nuclear matter defect wave function. We also calculate the (energy dependent) G-matrix appropriate for the sd shell for the Paris potential. The effective interaction diagrammatic expansion is then expressed in terms of the G-matrix interaction. To evaluate the Q-box diagrams in an angular momentum coupled(' ) representation, we develop a new set of diagram rules to treat the angular momentum factors. We introduce the notion of ladder diagrams and give techniques for evaluating diagrams by recoupling and expressing them as the product of ladders. The diagram formulae can thus be obtained almost by inspection and are also shown to be much more efficient for computation. The implications of these for future calculations are examined. We consider 4 approximations for the basic Q-box. These are (C1)(' ). the inclusion of diagrams up to 2('nd) order in G, (C2) 2('nd) order plus hole-hole phonons, (C3) 2('nd) order plus (bare TDA) particle-hole phonons, and (C4) 2('nd) order plus both hole-hole and particle-hole phonons. The folded diagrams are included using the SC, F(,n), and LS methods, and the calculations are done in parallel for the Paris and Reid potentials. We calculate the effective interaction matrix elements and the spectra of ('18)O, ('18)F, ('19)O, ('19)F, and ('20)Ne. The contribution of the folded diagrams was found to be quite large, typically about 30%. Also, due to the greater energy dependence of higher order diagrams, the effect of folded diagrams is much greater in higher orders. That is, the contribution from higher order diagrams is greatly reduced by the folded diagrams. The convergence of the FD series(, ) deteriorates with the inclusion of higher order Q-box processes in the F(,n) method, but remains excellent in the LS method. As for which nucleon-nucleon potential is "best", the ground state binding energies obtained from the Paris potential are significantly closer to the experimental values than are the ones from the Reid potential. However, the excitation spectra from both potentials are very similar. All in all, the C4 Q-box, including both(' ) hole-hole and particle-hole phonons, using the Paris potential, gives the best results.
- Pub Date:
- Physics: Nuclear