Capture cross sections for the near symmetric ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ reaction

Capture-fission cross sections were measured for the near symmetric reaction between the massive nuclei ${}^{124}\mathrm{Sn}$ and ${}^{96}\mathrm{Zr}$ for center of mass energies from 195 to 265 MeV. Coincident fission fragments were detected and separated from elastic and deep inelastic scattering products by angle/energy/mass conditions. The measured capture cross sections agree quite well with calculations using the dinuclear system (DNS) model. The DNS model also predicts the fusion cross section for this reaction with a fusion barrier height of 208.0 MeV. The deduced extra push energy, corresponding to this barrier height, differs from that deduced from evaporation residue measurements.

Figure 1

Extra push as determined from the mean fusion barrier height $E_B$ and the barrier height calculated with the Bass potential, $V_B$, versus the effective entrance channel fissility $x_{\mathrm{eff}}$ [$x_{\mathrm{eff}}$ is defined as $x_{\mathrm{eff}}=(Z^2/A){}_{\mathrm{eff}}/(Z^2/A){}_{\mathrm{crit}}$, where $(Z^2/A){}_{\mathrm{eff}}=4Z_1{Z}_2/(A_1^{1/3}{A}_2^{1/3}(A_1^{1/3}+A_2^{1/3})$ and $(Z^2/A){}_{\mathrm{crit}}=50.883(1-1.7826I^2)$ with $I=(N-Z)/A$]. The experimental points are taken from Refs. [1, 2], with ${}^{124}\mathrm{Sn}+{}^{96,94,92,90}\mathrm{Zr}$ systems selected. The theoretical prediction by Bjornholm and Swiatecki [12] is shown by a line.

Figure 2

The schematic drawing of the experimental setup. Four strip detectors (DSSDs) were used in the first setup, above and below the reaction plane, and in the second setup an annular detector (AD) was used.

Figure 3

(a) Simulated coincident events for the reaction of 600 MeV ${}^{124}\mathrm{Sn}$ with ${}^{96}\mathrm{Zr}$ assuming the fragment detectors are at ${30}^{°}\pm {10}^{°}$. The events arising from inelastic scattering with $Q=-40$ MeV are shown as contours while the symmetric fission events from the same simulation are shown in a scatter plot for ease of comparison with the experimental data in Panel (b). (b) The same plot as in Panel (a) except the points represent the measured data with gates applied to isolate the symmetric fission events.

Figure 4

Excitation function for the ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ capture-fission reaction. The one-dimensional barrier penetration model prediction is represented by a thick dot-dashed line, the predicted capture and fusion cross sections using DNS model [30] are represented by solid and dashed lines, and the results of a coupled channels calculation are shown as a dotted line. The DNS model prediction for the evaporation residue cross section is shown as a thin dot-dashed line while the experimental data are from Ref. [2].

Figure 5

Reduced excitation function for the ${}_{50}^{124}$Sn + ${}_{40}^{96}$Zr and ${}_{18}^{40}$Ar + ${}_{72}^{180}$Hf reactions which both lead to ${}^{220}\mathrm{Th}$ as a function of $E_{c.m.}$/$V_B$. The ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ data were taken from Ref. [9].