Effectiveα+αandα+NPotentials from Resonating-Group Calculations

Abstract

The method of the resonating-group structure is used to study the a-\-a and a+N systems. With a nucleon-nucleon potential of a near-Serber exchange mixture, it is found that good agreement with the empirical phase-shift data can be obtained. Using the resultant radial scattering functions, effective potentials between the clusters are derived, which yield the same phase shifts as does the resonating-group calculation. These potentials are quite similar to the phenomenological potentials obtained by Ali and Bodmer, and Darriulat et al. in the a-\-a case and by Swan and Pearce in the a+N case. They consist of a hard core with a radius which is weakly energy-dependent but strongly /-dependent and an attractive long-range part which has only a weak dependence on the relative orbital angular momentum and the energy in both evenand odd-/ states. In addition, it is found that the long-range part has an odd-even feature which has previously been noted by Gammel and Thaler in their phenomenological study of the a+p scattering data, but has not been commonly considered in the usual local-potential approach to a scattering problem. Based on the experience here, an effective potential is also proposed for those cases where a straightforward application of the resonating-group method is impractical.

Alpha–alpha potential up to 47.3 MeV bombarding energy

“…The magnitude of the depth of the potential in both cases is about the same but shifted from each other. It is of interest to note that the EDF potential is similar to the one calculated by Thompson et al [34] using RGM, in particular, in the depth and tail region. Above the 30 MeV bombarding energy, if one allows the freedom to vary the parameters at every energy, much improved fits to the data can be obtained even around 38 MeV.…”

“…The lines of investigations such as the generator coordinate method (GCM) [32], the resonating group method (RGM) [19,25,34,35], the orthogonality condition model (OCM) [36] and the folding potential method [26] involve the determination of this potential from nucleon-nucleon interaction. However, none of these investigations prescribes a unique potential that could be used over a broad range of energy.…”

A Relaxation Method for Nonlocal and Non-Hermitian Operators

“…In the collocation method, for equation obtained via the resonating group method instance, one always faces the problem of the number and (RGM) which contains a Hermitian, nonlocal, energy-distribution of the grid points. An increase of the number dependent interaction [1,2]. Other characteristic examples of collocation points to obtain results of higher accuracy in this respect are the effective Hamiltonians for the Fad-usually requires not only huge memory but also special deev [3] and the integro-differential equation approach techniques for handling large matrices.…”

STUDY OF N + $alpha$ SYSTEM WITH THE RESONATING-GROUP METHOD.

“…Thus it is interesting to compare the results obtained with this potential with those of our previous calculation where a simpler nucleon-nucleon potential was used. 6) For this· purpose, we omit the spin-orbit term in eq. (5) Together with our previous finding that excellent results can also be obtained in the el + 0, case5), this leads us to believe that, at least in the low-and medium-energy region, the use of a near-Serber potential which yields a good fit to the low-energy nuclecn-nucleon scattering data is quite sufficient in a resonatinggroup calculation on light nuclear systems.…”