Barrier distributions and signatures of transfer channels in the ${}^{40}\mathrm{Ca}+{}^{\mathrm{58,64}}\mathrm{Ni}$ fusion reactions at energies around and below the Coulomb barrier

Background: The nuclear structure of colliding nuclei is known to influence the fusion process. Couplings of the relative motion to nuclear shape deformations and vibrations lead to an enhancement of the sub-barrier fusion cross section in comparison with the predictions of one-dimensional barrier penetration models. This enhancement is explained by coupled-channels calculations including these couplings. The sub-barrier fusion cross section is also affected by nucleon transfer channels between the colliding nuclei.

Purpose: The aim of the present experiment is to investigate the influence of the projectile and target nuclear structures on the fusion cross sections in the ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ and ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$ systems.

Methods: The experimental and theoretical fusion excitation functions as well as the barrier distributions were compared for these two systems. Coupled-channels calculations were performed using the ccfull code.

Results: Good agreement was found between the measured and calculated fusion cross sections for the ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ system. The situation is different for the ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$ system where the coupled-channels calculations with no nucleon transfer clearly underestimate the fusion cross sections below the Coulomb barrier. The fusion excitation function was, however, well reproduced at low and high energies by including the coupling to the neutron pair-transfer channel in the calculations.

Conclusions: The nuclear structure of the colliding nuclei influences the fusion cross sections below the Coulomb barrier for both ${}^{40}\mathrm{Ca}+{}^{\mathrm{58,64}}\mathrm{Ni}$ systems. Moreover, we highlighted the effect of the neutron pair-transfer channel on the fusion cross sections in ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$.

Figure 1

Experimental fusion excitation functions for ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ [15] (filled circles), ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ [12] (solid triangles), and ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ [17] (open circles) in reduced coordinates. $R_b$ and $V_b$ denote the Coulomb barrier radius and height, respectively [21].

Figure 2

Fusion excitation functions for ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ [24] (filled circles), ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ [22] (solid triangles), and ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ [28] (open circles) in reduced coordinates. $R_b$ and $V_b$ denote the Coulomb barrier radius and height, respectively [21].

Figure 3

Two-dimensional spectrum of time of flight (${\mathrm{TOF}}_1$) vs residual energy ($E_R$) measured in the present experiment. The group of evaporation residues (ERs) is clearly seen and the colored points (see scale on the right) correspond to fusion events satisfying the coincidence conditions mentioned in the text.

Figure 4

Experimental angular distributions at $E_{\mathrm{lab}}=121$ MeV for ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ (filled circles, scale on the left $y$ axis) and ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$ (open circles, scale on the right $y$ axis). Gaussian fits are shown with lines.

Figure 5

Experimental fusion excitation functions for ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ (filled circles) and ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$ (open circles) in reduced coordinates. For comparison, the ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ data from Ref. [29] are also reported (solid triangles). CC calculations are shown with lines (see text for details).

Figure 6

Experimental fusion excitation function for ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ (filled circles). For comparison, the ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ data from Ref. [29] are also reported (solid triangles). In this case, a linear scale is used for ${\sigma }_f$.

Figure 7

Upper panel: Experimental barrier distribution for ${}^{40}\mathrm{Ca}+{}^{58}\mathrm{Ni}$ (filled circles) in reduced coordinates. Lower panel: Experimental barrier distribution for ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$ (open circles) in reduced coordinates. For the two systems, CC calculations are shown with lines (see text for details).

Figure 8

Upper panel: Reduced experimental (open circles) fusion excitation function for ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$. Lower panel: Reduced experimental (open circles) barrier distribution for ${}^{40}\mathrm{Ca}+{}^{64}\mathrm{Ni}$. CC calculations, including the neutron pair-transfer coupling, are shown with lines (see text for details)