Comparative study of the LOCV and the FHNC approaches for the nucleonic matter problem

The nucleonic matter problem is investigated by comparing the lowest order constrained variational (LOCV) method with the Fermi hypernetted chain (FHNC) theory, emphasizing the role of the LOCV correlation functions. In this way, the central correlation functions are used in the LOCV formalism, for the Bethe homework problem. It is shown that the LOCV computations reasonably agree with those of FHNC. Moreover, the FHNC calculations are performed with the LOCV correlation functions. It is found that, assuming the LOCV or the parametrized correlation functions, the FHNC computations do not change significantly. So, one may conclude that the mentioned consistencies refer to the choice of the LOCV correlation functions. Because, the contribution of the many-body cluster terms can be ignored, if the LOCV correlation functions satisfy the normalization constraint. Then, using the AV 18 interaction, the operator-dependent (OD) correlation functions are employed in the LOCV calculations. Note that the LOCV OD correlation functions are obtained by averaging over the states. It turns out that the overall behaviour of the LOCV OD correlation functions are similar to those of FHNC. Although, due to the many-body effects which are considered in the FHNC calculations, the LOCV results fairly differ from those of FHNC. Finally, it is worth mentioning that, unlike the recent FHNC calculations, the spin-orbit-dependent correlation functions are included in the LOCV approach.