Test of shell-model interactions for nuclear structure calculations.
The binding energy and excitation spectra of 6Li are calculated in a no-core shell-model space giving encouraging results. The results of this calculation are then treated as a theoretical experiment, against which different effective-interaction approximations are compared. In this way insight into the perturbation expansion for the effective interaction is obtained.
Comparison of the effective interaction to various orders in different mass regions
The convergence of the perturbation expansion for the effective interaction to be used in shell-model calculations is investigated as a function of the mass number A, from A = 4 to A = 208. As the mass number increases, there are more intermediate states to sum over in each higher-order diagram which contributes to the effective interaction. Together with the fact that the energy denominators in each diagram are smaller for larger mass numbers, these two effects could largely enhance higher-order contributions to the effective interaction, thereby deteriorating the order-by-order convergence of the effective interaction. This effect is counterbalanced by the short range of the nucleon - nucleon interaction, which implies that its matrix elements are weaker for valence single-particle states in `large' nuclei with large mass number as compared to those in light nuclei. These effects are examined by comparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from A = 4 to A = 208. The implications for nuclear structure calculations are discussed.
HIGHER-ORDER TERMS AND THE APPARENT NON-CONVERGENCE OF THE PERTURBATION EXPANSION FOR THE EFFECTIVE INTERACTION IN FINITE NUCLEI.
Abstract We have calculated all significant terms through third order in the reaction matrix G which contribute to the perturbation series for the J = 0, T = 1 effective interaction between two valence nucleons in the mass-18 nuclei and also a few selected fourth-order terms. We have shown that the perturbation series does not converge order-by-order to third order in G and that certain large third-order terms tend to cancel the second-order contribution. An intuitive physical picture of the process giving rise to this effect and to analogous effects in related calculations of the effective charge is given. This picture suggests a rearrangement of the perturbation series into physically significant groups of diagrams, so that each group converges order-by-order in G . However, one must then find some way to sum all these groups of diagrams. We conclude that simple perturbation theory is not a reliable method for calculating the effective two-nucleon interaction in mass-18 nuclei, when currently standard calculational techniques are used, and that the success of first- plus second-order perturbation theory in fitting experimental spectra for these nuclei is unexplained.