Effect of repulsive and attractive three-body forces on nucleus-nucleus elastic scattering

Abstract

The effect of the three-body force (TBF) is studied in nucleus-nucleus elastic scattering on the basis of Brueckner theory for nucleon-nucleon $(\mathit{NN})$ effective interaction (complex $G$ matrix) in the nuclear matter. A new $G$ matrix called CEG07 proposed recently by the present authors includes the TBF effect and reproduces a realistic saturation curve in the nuclear matter, and it is shown to well reproduce proton-nucleus elastic scattering. The microscopic optical potential for the nucleus-nucleus system is obtained by folding the $G$ matrix with nucleon density distributions in colliding nuclei. We first analyze in detail the $^{16}\mathrm{O}+^{16}\mathrm{O}$ elastic scattering at $E/A=70$ MeV. The observed cross sections are nicely reproduced up to the most backward scattering angles only when the TBF effect is included. The use of the frozen-density approximation (FDA) is essentially important to properly estimate the effect of the TBF in nucleus-nucleus scattering. Other prescriptions for defining the local density have also been tested, but only the FDA prescription gives a proper description of the experimental cross sections as well as the effect of the TBF. The effects of the three-body attraction and the $\ensuremath{\omega}$-rearrangement term are also analyzed. The CEG07 interaction is compared with CDM3Y6, which is a reliable and successful effective density-dependent $\mathit{NN}$ interaction used in the double-folding model. The CEG07 $G$ matrix is also tested in the elastic scattering of $^{16}\mathrm{O}$ by the $^{12}\mathrm{C}$, $^{28}\mathrm{Si}$, and $^{40}\mathrm{Ca}$ targets at $E/A=93.9$ MeV, and in the elastic scattering of $^{12}\mathrm{C}$ by the $^{12}\mathrm{C}$ target at $E/A=135$ MeV with great success. The decisive effect of the TBF is clearly seen also in those systems. Finally, we have tested CEG07a, CEG07b, and CEG07c for the $^{16}\mathrm{O}+^{16}\mathrm{O}$ system at various energies.