  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.
