Background: Heavy-ion fusion reactions at energies below the Coulomb barrier are strongly influenced by the coupling of different internal degrees of freedom of the interacting nuclei with the relative motion degrees of freedom. These couplings leads to a distribution of fusion barriers which results in significant enhancement in the sub-barrier fusion cross sections.

Purpose: To study the effect of collective excitations and neutron transfer channels in the fusion of ${}^{28}\mathrm{Si}$ with ${}^{142,150}\mathrm{Nd}$ at energies around the Coulomb barrier.

Method: The fusion excitation function for the ${}^{28}\mathrm{Si}+{}^{142,150}\mathrm{Nd}$ reactions were measured at energies $\approx 15\%$ below to $\approx 15\%$ above the Coulomb barrier, using the Heavy Ion Reaction Analyzer. Measured fusion excitation function is analyzed using the coupled-channels formalism. Fusion barrier distributions are extracted from the measured cross sections following the double differential method as well as the Gaussian analytic method.

Results: The vibrational coupling of the target nucleus and rotational coupling of projectile nucleus along with $2n$-transfer channel reasonably reproduced the fusion excitation function for the ${}^{28}\mathrm{Si}+{}^{142}\mathrm{Nd}$ reaction. Transfer coupling strength of 0.23 is used in the calculation. Rotational coupling of ${}^{28}\mathrm{Si}$ and ${}^{150}\mathrm{Nd}$ along with the $2n$-transfer channel could not reproduce the fusion excitation for the ${}^{28}\mathrm{Si}+{}^{150}\mathrm{Nd}$ reaction. The barrier distribution is expressed as a superposition of three Gaussian components for both reactions with minimum ${\chi }^2$ values.

Conclusion: Barrier distribution using Gaussian analytic method is quite useful in understanding the coupling schemes at below barrier energies. The coupling scheme that reproduced the fusion excitation function reasonably could not reproduce the distribution of fusion barrier in case of ${}^{28}\mathrm{Si}+{}^{142}\mathrm{Nd}$ reaction. The rotational excitations of ${}^{28}\mathrm{Si}$ and ${}^{150}\mathrm{Nd}$ along with $2n$-transfer channel also could not reproduce the barrier distribution for the ${}^{28}\mathrm{Si}+{}^{150}\mathrm{Nd}$ reaction, indicating the possible role of other transfer channels.

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• Low & intermediate energy heavy-ion reactions
• Nuclear fusion
• Nuclear reactions