Noncompound nucleus decay contribution in the ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ reaction using various formulations of nuclear proximity potential

The earlier study of excitation functions of ${}^{105}\mathrm{Ag}^{*}$, formed in the ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ reaction, based on the dynamical cluster-decay model (DCM), using the pocket formula for nuclear proximity potential is extended to the use of other nuclear interaction potentials derived from the Skyrme energy density functional (SEDF) based on the semiclassical extended Thomas Fermi (ETF) approach and to the use of the extended-Wong model of Gupta and collaborators. The Skyrme forces used are the old SIII and SIV and the new SSk, GSkI, and KDE0(v1) given for both normal and isospin-rich nuclei, with densities added in the frozen-density approximation. Taking advantage of the fact that different Skyrme forces provide different barrier characteristics, we look for the “barrier modification” effects in terms of choosing an appropriate force and hence for the existence or nonexistence of noncompound nucleus (nCN) effects in this reaction. Interestingly, independent of the choice of Skyrme or proximity force, the extended-Wong model fits the experimental data nicely, without any barrier modification and hence no nCN component in the measured fusion cross section, which consists of light-particle evaporation residue (ER) and intermediate-mass fragments (IMFs) up to mass 13, i.e., ${\sigma }_{\mathrm{fusion}}^{\mathrm{Expt}.}={\sigma }_{\mathrm{ER}}+{\sigma }_{\mathrm{IMFs}}$. However, the predicted fusion cross section due to the extended-Wong model is much larger, possibly because of the so-far missing fusion-fission (ff) component in the data. On the other hand, in agreement with the earlier work using the pocket proximity potential, the DCM fits only some data (mainly IMFs) for only some Skyrme forces, and hence it presents the chosen reaction as a case of a large nCN component, whose empirically estimated content is fitted for use of the DCM with a fragment preformation factor taken equal to one, i.e., using $\mathrm{DCM}\left(P_0=1\right)$, by introducing “barrier modification” through changing the neck-length parameter $\Delta R$ for a best fit to the empirical nCN data in each (ER and IMF) decay channel. Also, the ff component of the DCM is predicted to lie around the symmetric mass $A/2\pm 16$. All calculations are made for deformed and oriented coplanar nuclei.

Figure 1

Interaction potentials for the ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ reaction at a fixed $E_{\mathrm{c}.\mathrm{m}.}$ and fixed ${\theta }_i$ values, calculated for the $\ell =0$ case of six different nuclear potentials in the frozen-density approximation.

Figure 2

${\theta }_i$-integrated (for $\Phi =0^{\circ }$ case) cross section summed up to angular momentum $\ell$, plotted as a function of $\ell$ itself for ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ at a fixed $E_{\mathrm{c}.\mathrm{m}.}$, using different Skyrme forces and the Blocki et al. potential in the extended-Wong model.

Figure 3

Mass fragmentation potential $V\left(A_2\right)$, minimized in charge coordinate ${\eta }_Z$, for the decay of ${}^{105}{\mathrm{Ag}}^{*}$ formed in the ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}$ = 41.097 MeV and at ${\ell }_{\min }$ and ${\ell }_{\max }$ values, using the KDE0(v1) force.

Figure 4

Preformation probability $P_0$ as a function of angular momentum $\ell$ for ER decay channels of ${}^{105}{\mathrm{Ag}}^{*}$ formed in the ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}$= 41.097 MeV, for the KDE0(v1) force.

Figure 5

Same as for Fig. 4, but for penetration probability $P$, calculated for $\ell$ up to ${\ell }_{\max }=61\hslash ,$ fixed for $P_0\sim {10}^{-10}.$ Here, $P\le {10}^{-5}$ for ${\ell }_{\min }=17\hslash$.

Figure 6

Calculated (a) fusion evaporation residue cross section ${\sigma }_{\mathrm{ER}}$ and (b) IMF cross section ${\sigma }_{\mathrm{IMFs}}$, for the decay of ${}^{105}{\mathrm{Ag}}^{*}$, using different Skyrme force potentials, compared with experimental data at $E_{\mathrm{c}.\mathrm{m}.}$= 41.097 MeV.

Figure 7

DCM-calculated ER cross section as a function of $\Delta R$, using the KDE0(v1) force.