Non-coplanar compact configurations of nuclei and non-compound-nucleus contribution in the fusion cross section of theC12+Nb93reaction

Abstract

Background: In our earlier study of the $^{12}\mathrm{C}+^{93}\mathrm{Nb}\ensuremath{\rightarrow}^{105}\mathrm{Ag}^{*}$ reaction at three near- and below-barrier energies (${E}_{\mathrm{c}.\mathrm{m}.}=41.097$, 47.828, and 54.205 MeV), using the dynamical cluster-decay model (DCM) with various nuclear interaction potentials (the Blocki et al. pocket formula and others derived from the Skyrme energy density formalism) for compact, coplanar $({\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0})$ nuclei, we found a large non-compound-nucleus (nCN) contribution in the measured fusion cross section of this reaction.Purpose: In the present work, we look for the effect of using non-coplanar, compact configurations $({\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0})$, in the Blocki et al. pocket formula of the nuclear proximity potential, on the non-compound-nucleus (nCN) contribution, using the DCM.Methods: Allowing the $\mathrm{\ensuremath{\Phi}}$ degree of freedom in the DCM formalism, we calculate the compound-nucleus (CN) and nCN cross sections. The only parameter of the DCM is the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$, which also fits the empirically determined nCN cross section nearly exactly, under the assumption of considering it like a quasifission process where the fragment preformation factor ${P}_{0}=1$.Results: With the $\mathrm{\ensuremath{\Phi}}$ degree of freedom included, at the higher two energies the nCN cross section gets enhanced, and hence the pure CN cross section is decreased, since the calculated (total) fusion cross section is fitted to experimental data. The parameter $\mathrm{\ensuremath{\Delta}}R$ for the nCN contribution is smaller, and hence the reaction time larger, than for the CN decay process. Also, the contributing angular momentum ${\ensuremath{\ell}}_{\mathrm{max}}$ value increases in going from ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$ to ${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0}$ for both the CN and nCN processes. The intermediate mass fragments (IMFs), measured up to mass 13 in this reaction, are shown extended up to mass 16, and the fusion-fission $(ff)$ region is identified as $A/2\ifmmode\pm\else\textpm\fi{}16$, the same as for the ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$ case.Conclusions: As a result of enhanced nCN cross section due to ${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0}$, the CN fusion probability ${P}_{\mathrm{CN}}$ for $^{105}\mathrm{Ag}^{*}$ changes its behavior from an increasing to a decreasing function of center-of-mass energy ${E}_{\mathrm{c}.\mathrm{m}.}$, and hence belongs to the group of weakly fissioning nuclei, instead of the strongly fissioning superheavy nuclei for ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$. On the other hand, with measured IMFs taken to represent the $ff$ component, non-coplanarity simply increases the magnitude of CN survival probability ${P}_{\mathrm{surv}}$, although its functional dependence on ${E}_{\mathrm{c}.\mathrm{m}.}$ remains the same as for weakly fissioning nuclei. In other words, on adding the $\mathrm{\ensuremath{\Phi}}$ degree of freedom, the inconsistent result of ${P}_{\mathrm{CN}}$ behaving like strongly fissioning superheavy nuclei and ${P}_{\mathrm{surv}}$ like the weakly fissioning nuclei for ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$ changes to both ${P}_{\mathrm{CN}}$ and ${P}_{\mathrm{surv}}$ behaving consistently like those of weakly fissioning nuclei. Thus, our calculations advocate for ${\mathrm{\ensuremath{\Phi}}}_{c}$ as an important degree of freedom, like deformations of nuclei themselves.