The first step in the study of heavy nuclei and neutron stars is to investigate the asymmetric nuclear matter. The problem of asymmetric nucleonic system has been previously studied by variational approaches e.g. the lowest order constrained variational (LOCV), the Fermi HyperNetted Chain (FHNC) and the Monte Carlo (MC). In 2013, the problem of asymmetric nuclear matter in periodic boxes was studied by the FHNC approach, so the effects of the asymmetry and the finite size were estimated. Considering the importance of the asymmetric nuclear matter and the effects of the finite size, in this study, similar to the FHNC calculations in the periodic boxes (PBFHNC), finite systems in PBLOCV, with different number of nucleons, for various ratios of proton to neutron, are studied in the LOCV’s framework, the two-body cluster approximation is used in the PBLOCV formalism to obtain energy per particle subjected to the normalization constraint for a finite number of nucleons, the results are compared with the calculations of infinite systems and the results of the PBLOCV approach for neutron and symmetric matter. Fortunately, mentioned results illustrate the effects of asymmetry, on the other hand, unlike the thermodynamic limit, in the finite systems, the normalization constraint is not completely satisfied, which is due to the effects of the finite size. However, by increasing the volume of the boxes, the normalization constraint in the periodic box improves. As a result, The PBLOCV energy per particle approaches the corresponding LOCV’s counterpart for larger boxes. In addition, analyzing the anisotropic behavior of the PB two-body distribution function, the dependence of the correlation function on the number of mesh points and the effect of the number of neighbors on the smallness parameter is investigated in this thesis. It should be noted that the accuracy of the PBLOCV’s results for asymmetric systems, as well as the symmetric and neutron systems, is completely dependent on the number of nucleons in the box. Also, the mentioned results can be used in the Monte Carlo approach to report the energy of asymmetric nucleonic system.
