The [formula omitted] finite [formula omitted] matter three-body cluster energy in the periodic boxes

Abstract

The lowest order constrained variational (LOCV) method is used for the finite nucleonic matter in the periodic boxes (PBLOCV). Using the cluster expansion of the energy, the PBLOCV symmetric nuclear (pure neutron) matter energies for the different number of nucleons are found at the three-body cluster level. In these computations, the Bethe homework, as well as the central part of the AV′8 ((AV′8)c) potentials, are employed. Considering the three-body cluster energy, the (PB)LOCV energies become consistent with those of (PB) Fermi hypernetted chain ((PB)FHNC). By increasing the number of nucleons, the PBLOCV symmetric nuclear (pure neutron) matter three-body cluster energy becomes almost constant (changes at most 15%). It is demonstrated that including the Bethe homework interaction, the ratio of the three-body cluster energy to that of two-body (R) is less than 0.17. The corresponding PBLOCVSNMR for the (AV′8)c potential is about 1 (1.9), at low (high) densities. As a result, the approximation of the PBLOCV formalism is valid for the pure neutron matter with the Bethe homework potential. Employing the (AV′8)c interaction in the PBLOCVSNM calculations, the LOCV normalization constraint probably needs to be extended to the three-body cluster term to improve the PBLOCV approximation.