Nucleus-nucleus potential with shell-correction contribution and deep sub-barrier fusion of heavy nuclei

It is suggested that the full nucleus-nucleus potential consists of the macroscopic and shell-correction parts. The deep sub-barrier fusion hindrance takes place in a nucleus-nucleus system with a strong negative shell-correction contribution to the full heavy-ion potential, while a strong positive shell-correction contribution to the full potential leads to weak enhancement of the deep sub-barrier fusion cross section.

Figure 1

Fusion cross sections evaluated by using both the macroscopic and shell-correction parts of the nucleus-nucleus potential (solid line) compared with the experimental data (dots) for the reaction ${}^{16}$O + ${}^{208}$Pb [28]. The fusion cross sections obtained with the help of the macroscopic part on the nucleus-nucleus potential is shown by the dashed line.

Figure 2

Full and macroscopic potentials for system ${}^{16}$O + ${}^{208}$Pb evaluated in my approach. The sudden-density (sudden) [18], Krappe-Nix-Sirk (KNS) [14], Bass (Bass80) [1], Bass (Bass74) [12], proximity (Prox77) [13], proximity (Prox2000) [17], and Winther [16] potentials are presented too. Upper panel show the potentials in a wide range, while the bottom panel show the potentials around barriers. The vertical dashed line on the bottom panel shows the touching distance $R_t$.

Figure 3

Fusion cross sections for reactions ${}^{48}$Ca + ${}^{48}$Ca. The experimental data are taken from Ref. [29] and the notation is the same as in Fig. 1.

Figure 4

Fusion cross sections for the reaction ${}^{58}$Ni + ${}^{54}$Fe. The experimental data are from Ref. [30]. The fusion cross sections obtained by using the macroscopic and shell-correction parts of the nucleus-nucleus potential are shown by the solid line; the fusion cross sections evaluated without the shell-correction contribution to the potential, by the dashed line; and the fusion cross sections calculated with the opposite shell-correction contribution, by the dash-dotted line.