Examining the role of transfer coupling in sub-barrier fusion of ${}^{46,50}\mathrm{Ti}+{}^{124}\mathrm{Sn}$

Background: The presence of neutron transfer channels with positive $Q$ values can enhance sub-barrier fusion cross sections. Recent measurements of the fusion excitation functions for ${}^{58}\mathrm{Ni}+{}^{132,124}\mathrm{Sn}$ found that the fusion enhancement due to the influence of neutron transfer is smaller than that in ${}^{40}\mathrm{Ca}+{}^{132,124}\mathrm{Sn}$ although the $Q$ values for multineutron transfer are comparable.

Purpose: To investigate the differences observed between the fusion of Sn + Ni and Sn + Ca.

Methods: Fusion excitation functions for ${}^{46,50}\mathrm{Ti}+{}^{124}\mathrm{Sn}$ have been measured at energies near the Coulomb barrier.

Results: A comparison of the barrier distributions for ${}^{46}\mathrm{Ti}+{}^{124}\mathrm{Sn}$ and ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ shows that the ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ system has a barrier strength resulting from the coupling to the very collective octupole state in ${}^{40}\mathrm{Ca}$ at an energy significantly lower than the uncoupled barrier.

Conclusions: The large sub-barrier fusion enhancement in ${}^{40}\mathrm{Ca}$ induced reactions is attributed to both couplings to neutron transfer and inelastic excitation, with the octupole vibration of ${}^{40}\mathrm{Ca}$ playing a major role.

Figure 1

Ground-state $Q$ values as a function of the number of neutrons picked up by ${}^{46}\mathrm{Ti}, {}^{40}\mathrm{Ca}$, and ${}^{58}\mathrm{Ni}$ from ${}^{124}\mathrm{Sn}$. Only the channels with positive $Q$ values are shown.

Figure 2

Fusion excitation functions for (a) ${}^{46}\mathrm{Ti}+{}^{124}\mathrm{Sn}$ and (b) ${}^{50}\mathrm{Ti}+{}^{124}\mathrm{Sn}$. The measurements were performed in inverse kinematics at HRIBF and in normal kinematics at ANU. Also shown are the ER cross sections predicted by the statistical model code evapor, the results of one-dimensional barrier penetration model (uncoupled) calculations, and the results of coupled-channel calculations including up to two-phonon excitations of the projectile and target. The barrier height predicted by the frozen Hartree-Fock (HF) method is shown by the solid arrow, whereas the barrier height predicted by the time-dependent HF method (TDHF) is shown by the dotted arrow.

Figure 3

Fusion excitation functions calculated by ccfull subtracted from those measured for + ${}^{46}\mathrm{Ti}+{}^{124}\mathrm{Sn}$ and ${}^{50}\mathrm{Ti}+{}^{124}\mathrm{Sn}.$

Figure 4

Reduced barrier heights predicted by the frozen Hartree-Fock method, Broglia-Winther systematics, the Bass model, and the Sao Paulo model as a function of $Z_P{Z}_T{e}^2/R$ for ${}^{40,48}\mathrm{Ca}+{}^{124,132}\mathrm{Sn}, {}^{46,50}\mathrm{Ti}+{}^{124,132}\mathrm{Sn}$, and ${}^{58,64}\mathrm{Ni}+{}^{124,132}\mathrm{Sn}$.

Figure 5

Comparisons of reduced fusion excitation functions for (a) ${}^{40,48}\mathrm{Ca}+{}^{96}\mathrm{Zr}$, (b) ${}^{40,48}\mathrm{Ca}+{}^{124}\mathrm{Sn}$, (c) ${}^{40,48}\mathrm{Ca}+{}^{132}\mathrm{Sn}$, (d) ${}^{46,50}\mathrm{Ti}+{}^{124}\mathrm{Sn}$, (e) ${}^{58,64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$, and (f) ${}^{58,64}\mathrm{Ni}+{}^{132}\mathrm{Sn}$. The data points shown by the crosses in (e) are for ${}^{64}\mathrm{Ni}+{}^{118}\mathrm{Sn}$. The reduced energy is obtained by dividing the center-of-mass energy by the barrier height predicted by the frozen HF method.

Figure 6

Comparison of the reduced fusion excitation functions for ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ [7], ${}^{48}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ [5], ${}^{50}\mathrm{Ti}+{}^{124}\mathrm{Sn}$, and ${}^{46}\mathrm{Ti}+{}^{124}\mathrm{Sn}$.

Figure 7

Comparison of barrier distributions for ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ [7] and ${}^{46}\mathrm{Ti}+{}^{124}\mathrm{Sn}$ obtained from the measured fusion excitation functions.

Figure 8

Reduced barrier distributions for (a) ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$, (b) ${}^{46}\mathrm{Ti}+{}^{124}\mathrm{Sn}$, and (c) ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$, calculated by the coupled-channel code ccfull. The results of coupled-channel calculations including inelastic excitations of the projectile are shown by the broken curves and inelastic excitations of both the projectile and target are shown by the solid curves. The experimental data are shown by the open circles.