Skyrme forces and decay of the ${}_{104}{}^{266}\mathrm{Rf}^{*}$ nucleus synthesized via different incoming channels

The excitation functions for the production of ${}^{262}\mathrm{Rf}$, ${}^{261}\mathrm{Rf}$, and ${}^{260}\mathrm{Rf}$ isotopes via $4n$-, $5n$-, and $6n$-decay channels from the ${}^{266}\mathrm{Rf}^{*}$ compound nucleus are studied within the dynamical cluster-decay model (DCM), including deformations ${\beta }_{2i}$ and so-called hot-optimum orientations ${\theta }_i$ which support symmetric fission, in agreement with experiments. The data are available for ${}^{18}\mathrm{O}+{}^{248}\mathrm{Cm}$ and ${}^{22}\mathrm{Ne}+{}^{244}\mathrm{Pu}$ reactions, respectively, at the energy ranges of $E_{\mathrm{lab}}=88.2$ to 101.3 and 109.0 to 124.8 MeV. For the nuclear interaction potentials, we use the Skyrme energy density functional (SEDF) based on semiclassical extended Thomas Fermi (ETF) approach, which means an extension of the earlier study of excitation functions of ${}^{266}\mathrm{Rf}^{*}$ formed in ${}^{18}\mathrm{O}+{}^{248}\mathrm{Cm}$ reaction, based on the DCM using the pocket formula for nuclear proximity potential, showing interaction dependence. The Skyrme forces used here are the old SIII and SIV and new GSkI and KDE0(v1) given for both normal and isospin-rich nuclei, with densities added in frozen density approximation. Interestingly, the DCM gives an excellent fit to the measured data on fusion evaporation residue (ER) for both the incoming channels (${}^{18}\mathrm{O}+{}^{248}\mathrm{Cm}$ and ${}^{22}\mathrm{Ne}+{}^{244}\mathrm{Pu}$) at the energy range $E_{\mathrm{lab}}=88.2$ to 124.8 MeV, independent of the entrance channel and Skyrme force used. The possible fusion-fission (ff) and quasifission (qf) mass regions of fragments on DCM are also predicted. The DCM with Skyrme forces is further used to look for all the possible target-projectile (t-p) combinations forming the cold compound nucleus (CN) ${}^{266}\mathrm{Rf}^{*}$ at the CN excitation energy of $E_{\mathrm{lab}}$ for hot compact configurations. The fusion evaporation residue cross sections, for the proposed new reactions in synthesizing the CN ${}^{266}\mathrm{Rf}^{*}$, are also estimated for the future experiments, and role of mass asymmetry of nuclei is indicated.

Figure 1

Schematic configuration of two equal or unequal axially symmetric deformed, oriented nuclei, lying in the same plane (azimuthal angle $\mathrm{\Phi }=0^{\circ }$) for various ${\theta }_1$ and ${\theta }_2$ values in the range $0^{\circ }$ to ${180}^{\circ }$. The ${\theta }_i$ are measured anticlockwise from the colliding axis and angle ${\alpha }_i$ clockwise from the symmetry axis.

Figure 2

Scattering potentials $V(R,\ell )$ for ${}^{266}\mathrm{Rf}^{*}\to {}^{262}\mathrm{Rf}+4n$ at a fixed temperature $T=1.32$ MeV (equivalently, $E_{\mathrm{lab}}=94.8$ MeV), illustrated for SIII Skyrme force at different angular momentum $\ell$ values varying from ${\ell }_{min}=23\hslash$ to ${\ell }_{max}=120\hslash$ ($\ell <{\ell }_{min}$ values do not contribute; see text).

Figure 3

Mass fragmentation potential $V\left(A_i\right),i=1$, 2 at $\ell ={\ell }_{max}$ for the formation of CN ${}^{266}\mathrm{Rf}^{*}$ at $T=1.32$ MeV corresponding to $E_{\mathrm{lab}}=94.8$ MeV, $E^{*}=44.8$ MeV, calculated at fixed $R=R_t+\mathrm{\Delta }R$ with $\mathrm{\Delta }R=2.0$ fm, and with ${\beta }_{2i}$ deformations and optimum hot orientations included for all possible (t-p) combinations, using Skyrme forces (a) SIII, (b) SIV, (c) GSkI, and (d) KDE0(v1).

Figure 4

Same as for Fig. 3, but for optimum cold orientations.

Figure 5

Preformation yields for hot configurations referring to the fragmentation potentials in Fig. 3.

Figure 6

Preformation yields for cold configurations referring to the fragmentation potentials in Fig. 4.

Figure 7

Scattering potentials $V\left(R\right)$ for cold fusion reaction valleys with hot-compact configurations of Fig. 3 at a fixed temperature $T=1.32$ MeV ($E^{*}=44.8$ MeV) and ${\ell }_{max}=120\hslash$, illustrated for SIII Skyrme force.

Figure 8

Same as for Fig. 3, but for $\mathrm{\Delta }{R}_{4n,5n,6n}=1.91$, 2.6, and 3.0 fm for SIII force; $\mathrm{\Delta }R=2.1832$, 2.9414, and 2.492 fm for SIV force; $\mathrm{\Delta }R=1.8446$, 2.909, and 3.0 fm for GSkI force; $\mathrm{\Delta }R=2.9031$, 2.7838, and 2.718 fm for KDE0(v1) force; and 1.0 fm for light fragment masses $A_2=1-3$ and 7–133 (and the complementary heavy fragments), for the best fit to data in Fig. 10 at $E_{\mathrm{lab}}=94.8$ MeV for $4n$, $5n$, and $6n$ emission from ${}^{266}\mathrm{Rf}^{*}$ formed via ${}^{18}\mathrm{O}+{}^{248}\mathrm{Cm}$ reaction.

Figure 9

Channel cross section ${\sigma }_{xn}$, for $4n$, $5n,$ and $6n$ decay of ${}^{266}\mathrm{Rf}^{*}$, plotted as a function of angular momentum $\ell$. The cutoff ${\sigma }_{xn}<{10}^{-18}$ pb, limit ${\ell }_{min}=23$ and ${\ell }_{max}=120\hslash$. The small wiggles in curves are due to the instability in the calculations.

Figure 10

DCM calculated hot fusion excitation function of evaporation channels in (a) ${}^{266}\mathrm{Rf}^{*}\to {}^{262}\mathrm{Rf}+4n$, (b) ${}^{266}\mathrm{Rf}^{*}\to {}^{261}\mathrm{Rf}+5n$, and (c) ${}^{266}\mathrm{Rf}^{*}\to {}^{260}\mathrm{Rf}+6n$, compared with experimental data [2, 8] for ${}^{18}\mathrm{O}+{}^{248}\mathrm{Cm}$ (solid spheres) and ${}^{22}\mathrm{Ne}+{}^{244}\mathrm{Pu}$ (open squares) entrance channels. The calculations, made for different Skyrme forces, are at the best fitted $\mathrm{\Delta }R$ values for the observed ${\mathrm{E}}_{\mathrm{lab}}$ energies, and lines or curves are to guide the eyes.

Figure 11

The best-fitted neck-length parameter $\mathrm{\Delta }R$ as a function of $E_{\mathrm{lab}}$ energy for neutron evaporation residues from ${}^{266}\mathrm{Rf}^{*}$ formed in reaction channes ${}^{18}\mathrm{O}+{}^{248}\mathrm{Cm}$ (solid symbols) and ${}^{22}\mathrm{Ne}+{}^{244}\mathrm{Pu}$ (open symbols), using (a) SIII, (b) SIV, (c) GSkI, and (d) KDE0(v1) Skyrme forces.

Figure 12

$\ell$-summed preformation probability $P_0$, penetration probability $P,$ and channel cross section ${\sigma }_{A_i},i=1$, 2, plotted as a function of fragment mass number $A_i$.