Dynamic microscopic study of pre-equilibrium giant resonance excitation and fusion in the reactions ${}^{132}$Sn $+$ ${}^{48}$Ca and ${}^{124}$Sn $+$ ${}^{40}$Ca

We study pre-equilibrium giant dipole resonance (GDR) excitation and fusion in the neutron-rich system ${}^{132}$Sn $+$ ${}^{48}$Ca at energies near the Coulomb barrier, and we compare photon yields and total fusion cross sections to those of the stable system ${}^{124}$Sn $+$ ${}^{40}$Ca. The dynamic microscopic calculations are carried out on a three-dimensional lattice using both the time-dependent Hartree-Fock (TDHF) method and the density-constrained TDHF method. We demonstrate that the peak of the GDR excitation spectrum occurs at a substantially lower energy than expected for an equilibrated system, thus reflecting the very large prolate elongation of the dinuclear complex during the early stages of fusion. Our theoretical fusion cross sections for both systems agree reasonably well with recent data measured at the Holifield Radioactive Ion Beam Facility.

Figure 1

Time evolution of isoscalar multipole moments for a head-on collision of Sn on Ca at $E_{\mathrm{c}}.\mathrm{m}.=130$ MeV. Two isotopic combinations are considered as indicated.

Figure 2

Time evolution of isovector quadrupole moment (top), dipole amplitude $D\left(t\right)$ (middle), and the neutron leakage outside the analyzing volume (bottom) for the head-on collision of Sn on Ca at $E_{\mathrm{c}}.\mathrm{m}.=130$ MeV. Two isotopic combinations are considered as indicated.

Figure 3

Power spectrum of pre-equilibrium dipole radiation following a central collision at $E_{\mathrm{c}}.\mathrm{m}.=130$ MeV of ${}^{132}$Sn $+$ ${}^{48}$Ca (left panel) and ${}^{124}$Sn $+$ ${}^{40}$Ca (right panel). Results are shown for spectral analysis over the whole simulation time (lower panels, red) and over three shorter intervals as indicated (upper panels). The radiation power spectrum of the (deformed) ground state of the compound system is shown by the dashed curve (lower panels).

Figure 4

TDHF calculation of the total fusion cross section at energies above the barrier. At fixed $E_{\mathrm{c}}.\mathrm{m}.$ energy, the neutron-rich system ${}^{132}$Sn $+$ ${}^{48}$Ca shows a higher cross section than the stable system ${}^{124}$Sn $+$ ${}^{40}$Ca.

Figure 5

DC-TDHF calculation of the heavy-ion potential $V\left(R\right)$ for the neutron-rich system ${}^{132}$Sn+${}^{48}$Ca. The energy-dependent potential is shown at five $E_{\mathrm{c}}.\mathrm{m}.$ energies. The point Coulomb potential is given for comparison.

Figure 6

Microscopic mass parameter $M\left(R\right)$ (in units of the reduced mass $\mu$), calculated at several $E_{\mathrm{c}}.\mathrm{m}.$ energies.

Figure 7

Solid lines: original heavy-ion potentials $V\left(R\right)$ corresponding to the mass parameter $M\left(R\right)$. Dashed lines: transformed potentials $U\left(\overline{R}\right)$ corresponding to the reduced mass $\mu$.

Figure 8

Total fusion cross section for the neutron-rich system ${}^{132}$Sn+${}^{48}$Ca. Compared are DC-TDHF calculations using the energy-dependent heavy-ion potential in Fig. 7 with unrestricted TDHF calculations (see Fig. 4) at energies above the barrier.

Figure 9

Comparison between scaled experimental fusion cross sections [3] and theoretical results obtained with the DC-TDHF method and with unrestricted TDHF.