Solution of the Specific Model of Five-Body Problem to Investigate the Effective Alpha-Nucleon Interaction in a Partial-wave Analysis

In this paper, we have solved a simple specific model of the five-body problem in the framework of the Yakubovsky equations, restricted to the configurations of the alpha-nucleon types only, to investigate the effective interaction between an inert alpha-particle and a neutron. In general case, the Yakubovsky scheme for the solution of the five-body system leads to a set of four coupled equations related to four independent configurations, which can be restricted to two coupled ones, to describe the effective alpha-nucleon structure model, namely an inert four-body alpha-core and a nucleon. Hence, in such a model, the other configurations will not be taken into account. To calculate the binding energies of the five-body system in the model of alpha- nucleon structure, the two coupled equations are represented in the momentum space on the basis of the Jacobi momenta. After an explicit evaluation of the two coupled integral equations in a partial-wave analysis, the obtained equations are the starting point for a numerical calculation as an eigenvalue equation form, using typical iteration method. In the first step to the calculations, i.e. applying some spin-independent potential models, some obtained binding energy differences between the four-body as an alpha-particle and the five-body as an alpha-nucleon systems suggest that a simple effective interaction between an inert alpha-particle and a nucleon is attractive and of about 13 MeV. In addition, the represented binding energy results with respect to the regarded spin-independent potentials are in fair agreement with the obtained results from other methods.