Absence of a maximum in theSfactor at deep sub-barrier energies in the fusion reaction40Ca + 40Ca

Abstract

The fusion reaction ${}^{40}$Ca + ${}^{40}$Ca was very recently reinvestigated by the Legnaro group and cross sections down to $\ensuremath{\mu}$b were measured. In the present work this reaction is analyzed within the coupled-channel formalism including ${2}^{+}$, ${3}^{\ensuremath{-}}$, and ${5}^{\ensuremath{-}}$ phonon states. The heavy-ion entrance channel potential is calculated within the double-folding prescription and comprises a direct local term and a local equivalent of the nonlocal knock-on exchange component. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion. Coupling potentials are calculated from the $G$-matrix Michigan three-range Yukawa-type semirealistic nucleon-nucleon interaction (M3Y) as well as one modern parametrization of the density-dependent Gogny effective interaction. Realistic deformation parameters are used. The best fit to the data is not pointing to a possible maximum in the astrophysical $S$-factor as in a previous study on sub-barrier fusion involving ${}^{48}$Ca projectiles.