Dynamical cluster-decay model for hot and rotating light-mass nuclear systems, applied to low-energy $^{32}$S + $^{24}$Mg $\to ^{56}$Ni reaction
The dynamical cluster-decay model (DCM) is developed further for the decay of hot and rotating compound nuclei (CN) formed in light heavy-ion reactions. The model is worked out in terms of only one parameter, namely the neck-length parameter, which is related to the total kinetic energy TKE(T) or effective Q-value $Q_{eff}(T)$ at temperature T of the hot CN, defined in terms of the both the light-particles (LP), with $A \leq$ 4, Z $\leq$ 2, as well as the complex intermediate mass fragments (IMF), with $4 < A < 20, Z > 2$, is considered as the dynamical collective mass motion of preformed clusters through the barrier. Within the same dynamical model treatment, the LPs are shown to have different characteristics as compared to the IMFs. The systematic variation of the LP emission cross section $σ_{LP}$, and IMF emission cross section $σ_{IMF}$, calculated on the present DCM match exactly the statistical fission model predictions. It is for the first time that a non-statistical dynamical description is developed for the emission of light-particles from the hot and rotating CN. The model is applied to the decay of $^{56}$Ni formed in the $^{32}$S + $^{24}$Mg reaction at two incident energies E$_{c.m.}$ = 51.6 and 60.5 MeV. Both the IMFs and average $\bar{TKE}$ spectra are found to compare reasonably nicely with the experimental data, favoring asymmetric mass distributions. The LPs emission cross section is shown to depend strongly on the type of emitted particles and their multiplicities.