Study of nuclear medium effects on the effective interaction based on the one boson exchange model

In this work, starting from a realistic nucleon-nucleon interaction based on the one-boson exchange model for the nuclear force, we attempted a microscopic derivation of the effective interaction which may be appropriate for nuclear structure as well as for nucleon-nucleus scattering problems. Short-range correlations and medium polarization as well as relativistic effects on both particle-hole and $\Delta$-hole interactions have been investigated. For the nucleon-nucleon case short-range correlations are basically restricted to S-states and affect mainly the central components of the effective interaction. In contrast, the $\Delta$-nucleon interaction is essentially unaffected by short-range correlations due to the Pauli principle restrictions and the momentum mismatch between the central components of the correlation operator and the tensor component of the bare transition potential. Based on these analyses it is shown that short-range correlation effects can be summarized in a very simple correlation operator. The medium polarization affects dominantly the scalar-isoscalar component of in the nucleon-nucleon sector and tends to cure the caused by the strongly attractive interaction due to Short-range correlations. In the $\Delta$-nucleon sector the medium polarization enhances the $\Delta$-nucleon coupling strength (g$^{'}_{o})_{\Delta N}$ much more than the corresponding nucleon-nucleon coupling g$^{'}_{o}$, the reason being again the Pauli principle. Relativistic effective give a considerable repulsive contribution in the scalar-isoscalar component of the effective interaction; lowever, in the present calculation these effects alone are not yet able to cure the instability of nuclear matter. The $\Delta$-nucleon coupling strength (g$^{'}_{o})_{\Delta N}$ is enhanced by $\sim$ 17 % with respect to the conventional G-matrix result (no inclusion of relativistic effects) and together core polarization effects enhance (g$^{'}_{o})_{\Delta N}$ by $\sim$ 35 %. Relativistic effects also show a number of interesting features which may improve the agreement with experimental data