Yakubovsky scheme to study the 4- and 5-nucleon systems in the case of alpha-state structure with spin-dependent nucleon-nucleon potentials

In this project, we have investigated the 5-nucleon model system in the picture of the specific alpha-state structure, by extending the Yakubovsky scheme with the inclusion of the spin and isospin degrees of freedom. The Yakubovsky formalism for the 5-nucleon system in the effective alpha-neutron attractive model leads to a set of two coupled equations, based on two relevant alpha-nucleon sub-cluster components. To this regard, by switching off the fifth nucleon interactions, the 5-nucleon Yakubovsky equations can be reduced to a typical 4-nucleon problem. To calculate the 5- and 4-nucleon bound state equations, the coupled equations are projected in the momentum space in terms of the Jacobi momenta. In the calculations two different spin-dependent and one spinindependent nucleon-nucleon potential types are dedicated, such as Afnan-Tang S3, Malfliet-Tjon I/III and Volkov potentials,respectively. The some obtained binding energy differences between the 4-nucleon system in the alpha-state and the 5-nucleon system in the case of alpha-nucleon structure demonstrating the effective interaction between the alpha and an attractive neutron. The obtained results for the effective interaction are consistent either for spin-independent and spin-dependent interactions. Also,the binding energy results are in excellent compatibility with the achieved results by other techniques.