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In this project, we have investigated the 5-nucleon model system in thepicture of the specific alpha-state structure, by extending the Yakubovskyscheme with the inclusion of the spin and isospin degrees of freedom. TheYakubovsky formalism for the 5-nucleon system in the effective alpha-neutronattractive model leads to a set of two coupled equations, based on two relevantalpha-nucleon sub-cluster components. To this regard, by switching off thefifth nucleon interactions, the 5-nucleon Yakubovsky equations can be reducedto a typical 4-nucleon problem. To calculate the 5- and 4-nucleon bound stateequations, the coupled equations are projected in the momentum space in termsof the Jacobi momenta. In the calculations two different spin-dependent and onespinindependent nucleon-nucleon potential types are dedicated, such asAfnan-Tang S3, Malfliet-Tjon I/III and Volkov potentials,respectively. The someobtained binding energy differences between the 4-nucleon system in thealpha-state and the 5-nucleon system in the case of alpha-nucleon structuredemonstrating the effective interaction between the alpha and an attractiveneutron. The obtained results for the effective interaction are consistenteither for spin-independent and spin-dependent interactions. Also,the bindingenergy results are in excellent compatibility with the achieved results byother techniques.

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