Fusion of ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ and ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$ below the Coulomb barrier

Background: No data on the fusion excitation function of ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ in the energy region near the Coulomb barrier existed prior to the present work, while fusion of ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$ was investigated in detail some years ago, down to very low energies, and clear evidence of fusion hindrance was noticed at relatively high cross sections. ${}^{48}\mathrm{Ti}$ and ${}^{58}\mathrm{Fe}$ are soft and have a low-lying quadrupole excitation lying at $\approx 800–900$ keV only. Instead, ${}^{58}\mathrm{Ni}$ and ${}^{54}\mathrm{Fe}$ have a closed shell (protons and neutrons, respectively) and are rather rigid.

Purpose: We aim to investigate (1) the possible influence of the different structures of the involved nuclei on the fusion excitation functions far below the barrier and, in particular, (2) whether hindrance is observed in ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$, and to compare the results with current coupled-channels models.

Methods: ${}^{48}\mathrm{Ti}$ beams from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro were used. The experimental setup was based on an electrostatic beam separator, and fusion-evaporation residues (ERs) were detected at very forward angles. Angular distributions of ERs were measured.

Results: Fusion cross sections of ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ have been obtained in a range of nearly six orders of magnitude around the Coulomb barrier, down to $\sigma \simeq 2 \mu \mathrm{b}$. The sub-barrier cross sections of ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ are much larger than those of ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$. Significant differences are also observed in the logarithmic derivatives and astrophysical $S$ factors. No evidence of hindrance is observed, because coupled-channels calculations using a standard Woods-Saxon potential are able to reproduce the data in the whole measured energy range. Analogous calculations for ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$ predict clearly too large cross sections at low energies. The two fusion barrier distributions are wide and display a complex structure that is only qualitatively fit by calculations.

Conclusions: It is pointed out that all these different trends originate from the dissimilar low-energy nuclear structures of the involved nuclei. In particular, the strong quadrupole excitations in ${}^{48}\mathrm{Ti}$ and ${}^{58}\mathrm{Fe}$ produce the relative cross section enhancement and make the barrier distribution $\approx 2$ MeV wider, thus probably pushing the threshold for hindrance below the measured limit.

Figure 1

Fusion excitation functions of ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ measured in this work, and of ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$ as reported in Ref. [6]. The abscissa is the energy relative to the AW Coulomb barrier.

Figure 2

(a) Logarithmic derivatives of the excitation functions for ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ and ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$, obtained as incremental ratios between nearby points. (b) Astrophysical S factors for the two systems. They are normalized using the Sommerfeld parameter ${\eta }_0$ calculated in the vicinity of the Coulomb barrier.

Figure 3

Barrier distributions BD obtained, for both systems, as the second derivative of the energy-weighted cross sections, using the three-points formula [13] with a step $\mathrm{\Delta }E\simeq 1.0$ MeV. The lines are the results of the CC calculations discussed in the text.

Figure 4

Excitation functions of ${}^{48}\mathrm{Ti}+{}^{58}\mathrm{Fe}$ (a) and of ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$ (b), compared to the CC calculations discussed in the text.