Nuclear mean field and double-folding model of the nucleus-nucleus optical potential

Abstract

Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density-and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic 12 C+ 12 C and 16 O+ 12 C scattering at the refractive energies, where the Airy structure of the nuclear rainbow has been well established. The RT was found to affect significantly the real nucleus-nucleus optical potential at small internuclear distances, giving the potential strength close to that implied by the realistic optical model description of the Airy oscillation.

Consistent mean-field description of theC12 + C12optical potential at low energies and the astrophysical

“…The mean-field based CDM3Y3 density dependent interaction [44], well tested in HF studies of nuclear matter [47] and the nucleon mean-field potential [51], has been used in an extended DFM approach [48] to calculate the real OP for elastic 12 C+ 12 C scattering at low energies. To validate the use of the DFM at low energies, a realistic adiabatic approximation (8) for the 12 C+ 12 C overlap density has been suggested to replace the FDA normally used in DFM calculation at energies above 10 MeV/nucleon.…”

“…This adiabatic density approximation (ADA) is then used in the new version of the DFM [48] that properly includes also the nucleon rearrangement term, to predict the nuclear mean-field potential built up in the 12 C+ 12 C collision at low energies. The reliability of the folded 12 C+ 12 C potential predicted by the present DFM calculation is carefully tested in the OM analysis of the elastic 12 C+ 12 C scattering over a wide range of energies below 10…”

“…factor accounts for the in-medium energy dependence of the CDM3Y3 interaction (5), and is determined self-consistently [48] using the local relative momentum (4).…”

Phenomenological Nuclear Potential Shapes for Optical Model Analyses of 16O+12C Elastic Scattering

“…The refractive effects observed in certain HI interactions, where the scattering is sensitive to the central (nuclear) potential inside the strong absorption radii, have been used as a practical tool for understanding the nature of the OM potential. In particular, these effects have been discussed for 16 [6,7,10,15,18,[28][29][30][31][32] systems in the literature. Eventually, the reported complex nuclear potentials of those scattering reactions have been described as the composition of deep and attractive potentials for the real part plus weaker and absorbing potentials for the imaginary part.…”

Study of the nuclear medium by 12C + 12C elastic scattering analysis at low energy region

“…In fact, the folding model, which is obtained by averaging an appropriate nucleon-nucleon (NN) interaction over the matter distributions [8,[17][18][19][20], is an appropriate approach for this purpose. Many analyses focus on the study of the effective interaction and nuclear distribution, which are known as the important inputs of the folding model [8,[17][18][19][20]. Besides, the nuclear medium, which is defined as the nuclear environment around the interaction between two nucleons, is an important physical ingredient of the mean field needed to investigate with the aspect for understanding details the real regime of the 12 C + 12 C reaction process.…”