The LOCV averaged two-nucleon interactions versus the density-dependent M3Y potential for the heavy-ion collisions

Folding model analysis of $ ^{12}C- ^{12}C $ and $ ^{16}O- ^{16}O $ elastic scattering using the density-dependent LOCV averaged effective interaction

“…In the present work, the LOCV density dependent averaged effective two-body interaction (AEI ) is generated though the LOCV method with the bare nucleon-nucleon phenomenological Reid 68 potential, and inserted as an input to the folding model calculations. In our previous work [20], we obtained the direct and the exchange parts of the density dependent nucleon-nucleon AEI as follows (see the appendix for the definition of a and V):…”

“…Here, we chose VD(EX) (r) and F D(EX) (ρ) to give the best fit to the LOCV VD(EX) There are many different functions which can fit F D(EX) (ρ) well enough. A detailed role of description of density-dependent factor (F ) can be found in our previous work, the reference [20], where we stated that the LOCV AEI includes a radial part and a densitydependent part and we show that, the radial part form of the LOCV AEI is fixed in any density (exactly like the M3Y type interactions) and the EOS of SN M without taking into account the density-dependent factor did not fulfill the saturation condition and the system was collapsed (see the figure 7 of the reference [20]). But one should notice that our densitydependent factor is not an external factor and it comes from the LOCV calculations.…”

“…In the reference [21], we compared the direct and exchange parts of the LOCV AEI with the corresponding results of the M3Y interactions. (see the figures ( 1) and ( 4) of the reference [20])…”

“…In our recent paper [20] , we derived the averaged effective two-body interactions (AEI ) through the lowest order constrained variational (LOCV ) calculations for the SN M with the Reid 68 [23], the -Reid 68 [24] (which takes into the account the effect of three-body force (T BF )) and the Aυ 18 [25] interactions as the input phenomenological nucleon-nucleon potentials, and reformulated them in the radial and density-dependent parts as well as its direct and exchange components . Note that the radial parts are fixed and density dependent functions only depend on density which becomes a constant at fix density, i.e.…”

“…The RT comes out in case of calculating the single particle energy and the corresponding potential. But in the present work, we intend to apply the lowest order constrained variational averaged effective interaction LOCV AEI, which was generated by using the input Reid 68 potential in our previous work [20], as the effective NN interaction, into the folding model to test the validity of our interaction in describing the HI elastic scattering. In this paper, we limit ourselves to the elastic scattering of spherical projectile and spherical target nuclei, so we consider the 12 A brief discussion about the LOCV method is given in the appendix A.…”