Fusion enhancement within a collective clusterization approach applied to the isotopic chain of neutron-rich light-mass compound nuclei

Abstract

The dynamics of neutron-rich light-mass compound nuclei $^{24,25,26,27}\mathrm{Mg}^{*}$ formed in $^{12,13,14,15}\mathrm{C}+^{12}\mathrm{C}$ fusion reactions, respectively, is explored at different ${E}_{\mathrm{c}.\mathrm{m}.}$ values within the dynamical cluster decay model (DCM). DCM is based on the quantum mechanical fragmentation theory, which treats the binary fragmentation of emitting compound nucleus as light particles (LPs), intermediate mass fragments (IMFs), as well as symmetric mass fragments (SMFs), on equal footing, which is not the case with other fission and statistical models. All calculations are made for spherical considerations and angular momenta taken up to the $\ensuremath{\ell}$-critical value for the respective reactions. A fusion enhancement is observed as we go from compound nuclei (CN) having an even number of neutrons ($^{24,26}\mathrm{Mg}^{*}$) to CN with the odd number of neutrons ($^{25,27}\mathrm{Mg}^{*}$). Interestingly, we find that the only parameter of the DCM, the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ related to the barrier lowering, is in linear relation with ${\ensuremath{\sigma}}_{\mathrm{Fusion}}$ at chosen incident laboratory energy. The fusion enhancement is found to be larger for odd neutron number nuclei, which indicates the influence of unpaired neutrons on fusion cross sections. Within the formalism of DCM, the phenomenon of fusion enhancement finds its base in the process of collective clusterization, which is quite evident from the larger values of summed-up preformation probability for the reactions having odd mass projectiles or forming odd mass CN. The DCM calculated fusion cross sections are in good agreement with the available experimental data for the given reactions.