LAUSR

Abstract The lowest order constrained variational ( L O C V ) method is used for the finite n u c l e o n i c matter in the periodic boxes ( P B L O C V ). Using the cluster expansion of the energy, the P B L O C V 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 A V ′ 8 ( ( A V ′ 8 ) c ) potentials, are employed. Considering the three-body cluster energy, the ( P B ) L O C V energies become consistent with those of ( P B ) Fermi h y p e r n e t t e d chain ( ( P B ) F H N C ). By increasing the number of nucleons, the P B L O C V 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 P B L O C V S N M R for the ( A V ′ 8 ) c potential is about 1 (1.9), at low (high) densities. As a result, the approximation of the P B L O C V formalism is valid for the pure neutron matter with the Bethe homework potential. Employing the ( A V ′ 8 ) c interaction in the P B L O C V S N M calculations, the L O C V normalization constraint probably needs to be extended to the three-body cluster term to improve the P B L O C V approximation.