Role of the neck degree of freedom in cold fusion reactions

Mass parameters for collective variables of dinuclear systems formed in cold fusion reactions are microscopically calculated with the linear response theory making use of the width of single-particle states and the fluctuation-dissipation theorem. The single-particle spectrum and potential energy surface of the adiabatic two-center shell model are used. The microscopical mass parameter in the neck is found to be much larger than one obtained with the hydrodynamical model. Therefore, the dinuclear system lives a rather long time, comparable to the characteristic time of fusion and, correspondingly, the fusion can be considered at fixed neck parameter. With an adiabatic melting of the dinuclear system along the internuclear distance into a compound system one cannot explain the experimental trends in cold fusion reactions.

Figure 1

The calculated mass parameter $M_{\lambda \lambda }$ in units ${10}^{3}m{\text{fm}}^2$ as a function of $\lambda$ and $\varepsilon$ in the ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction.

Figure 2

The calculated mass parameter $M_{\varepsilon \varepsilon }$ in units ${10}^{3}m{\text{fm}}^2$ as a function of $\lambda$ and $\varepsilon$ in the ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction.

Figure 3

Contours of the potential energy surface, in units of MeV, calculated in the $(\lambda ,\varepsilon )$ plane for the ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction. The potential energy is with respect to the liquid-drop energy of the spherical compound nucleus. The dynamical trajectories are calculated at $\lambda \left(0\right)=1.53,\varepsilon \left(0\right)=0.75$ (solid line) and $\lambda \left(0\right)=1.59,\varepsilon \left(0\right)=0.85$ (dashed line) with microscopic mass coefficients. The dynamical trajectory calculated at $\lambda \left(0\right)=1.53,\varepsilon \left(0\right)=0.75$ with the Werner-Wheeler masses is presented by a dotted line. The initial kinetic energy is zero for all trajectories shown.

Figure 4

Contours of the potential energy surface, in units of MeV, calculated in the $(\lambda ,\varepsilon )$ plane for the ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ reaction. The potential energy is with respect to the liquid-drop energy of the spherical compound nucleus. The dynamical trajectories are calculated at $\lambda \left(0\right)=1.53,\varepsilon \left(0\right)=0.75$ (solid line) and $\lambda \left(0\right)=1.53,\varepsilon \left(0\right)=0.8$ (dashed line) with microscopic mass coefficients and zero initial kinetic energy. The dynamical trajectory calculated at $\lambda \left(0\right)=1.53,\varepsilon \left(0\right)=0.75$ with microscopic mass coefficients and 1 MeV initial kinetic energy is presented by dotted line.

Figure 5

Time-dependence of the neck parameter $\varepsilon$ in the ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction calculated with microscopic (solid line) and Werner-Wheeler (dotted line) mass parameters. The initial conditions are $\lambda \left(0\right)=1.53,\varepsilon \left(0\right)=0.75$, and zero kinetic energy.

Figure 6

Contours of the potential energy surface, in units of MeV, calculated in the $(\lambda ,\varepsilon )$ plane for the ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ reaction. The potential energy is with respect to the liquid-drop energy of the spherical compound nucleus. The dynamical trajectories are calculated at $\lambda \left(0\right)=1.51,\varepsilon \left(0\right)=0.75$ with microscopic mass coefficients (solid line) and with the Werner-Wheeler masses (dotted line). The initial kinetic energy is zero for all trajectories shown.

Figure 7

Contours of the potential energy surface, in units of MeV, calculated in the $(\lambda ,\varepsilon )$ plane for the ${}^{78}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction. The potential energy is with respect to the liquid-drop energy of the spherical compound nucleus.

Figure 8

Potentials as functions of elongation $\lambda$ at indicated values of $\varepsilon$ in the systems ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ (solid lines), ${}^{50}\mathrm{Ti}+{}^{208}\mathrm{Pb}$ (dashed lines), ${}^{54}\mathrm{Cr}+{}^{208}\mathrm{Pb}$ (dotted lines), ${}^{58}\mathrm{Fe}+{}^{208}\mathrm{Pb}$ (thick solid lines), ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ (dash-dotted lines), and ${}^{70}\mathrm{Zn}+{}^{208}\mathrm{Pb}$ (dash-dot-dotted lines). The potential energy is with respect to the liquid-drop energy of the corresponding spherical compound nucleus.

Figure 9

The same as in Fig. 8, but for the systems ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ (solid lines), ${}^{72}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ (dashed lines), and ${}^{78}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ (dotted lines).