Role of the coupling between neck and radial degrees of freedom in evolution from dinucleus to mononucleus

Abstract

The coupled Langevin equations in two-dimensional collective space are used to study the dynamics of nuclear neck growth. Special attention is paid to the effects of coupling between neck and radial degrees of freedom on the evolution from dinucleus to mononuleus. The dynamic model is applied for the study of neck evolution of the mass asymmetric system $^{50}\mathrm{Ti}$ $+$ $^{249}\mathrm{Cf}$. In order to estimate the effects of the coupling, we use the equations in the coupled and uncoupled cases. Our results show that the coupling between neck and radial motions reduces the neck growth velocity and delays the transition from dinuclear to mononuclear regimes. In addition, by solving these dynamic equations we get the probability distributions of radial degree of freedom at the injection point ${s}_{\mathrm{in}}$ in the asymmetric fission valley. In this way, ${s}_{\mathrm{in}}$ is no longer an adjustable parameter in the fusion-by-diffusion model. The distributions obtained are located at positions very close to $s=0$. Moreover, the coupling significantly reduces the fluctuation in the ${s}_{\mathrm{in}}$ space. Our results show that the quasifissionlike events are unlikely to take place during the transition period for the mass asymmetric systems. Based on the ${s}_{\mathrm{in}}$ distribution obtained, the evaporation residue (ER) cross sections for $3n$ and $4n$ evaporation channels in the $^{50}\mathrm{Ti}$ $+$ $^{249}\mathrm{Cf}$ reaction leading to formation of ${}^{296}120$ and ${}^{295}120$ isotopes are calculated. The maximum ER cross sections in $3n$ and $4n$ channels with the ${s}_{\mathrm{in}}$ distributions are equal to $0.1$ and $0.065$ pb, respectively, which are more than two times larger than those obtained by the fusion-by-diffusion model with the ${s}_{\mathrm{in}}=0$ assumption.