Microscopic study of noncentral effects in heavy-ion fusion reactions with spherical nuclei

Fusion reactions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O},{}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$, and ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$ have been investigated by using the three-dimensional (3D) time-dependent Hartree-Fock approach with and without density constraint. The interaction potentials and effective mass parameters are studied. It is found that both the nucleus-nucleus interaction potentials and the effective mass parameters of these systems depend on the impact parameter. Such noncentral effects on fusion cross sections are also investigated. It is shown that the noncentral effect can reduce the fusion cross sections significantly when the incident energy is just above the barrier, while it becomes weaker with the increasing incident energy and can be totally neglected when the energy is up to twice as much as the barrier height in these spherical colliding systems.

Figure 1

Time evolution of the quadrupole moments of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ (a) for head-on collisions at five different incident energies and (b) for different impact parameters from 0 to 5 fm with $\Delta b=1$ fm at $E_{\mathrm{c}.\mathrm{m}.}=70$ MeV.

Figure 2

Time evolution of the moment of inertia of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ calculated in three different ways at $E_{\mathrm{c}.\mathrm{m}.}=12$ MeV and $b=3$ fm.

Figure 3

(a) The N-N potentials for head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ at various incident energies. (b) The effective N-N potentials and the collective kinetic energies of the relative motion as well as the excitation and the rotational energies at various impact parameters at $E_{\mathrm{c}.\mathrm{m}.}=12$ MeV. Panels (c) and (d) contain the same curves as (b) for $E_{\mathrm{c}.\mathrm{m}.}=20$ MeV; for clarity the curves are separated into two subfigures. The insets in (b) and (d) are zooms of $V\left(R\right)$ around the barrier centroids.

Figure 4

The same as Fig. 3, but for ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$. (b) At $E_{\mathrm{c}.\mathrm{m}.}=56$ MeV and (c) at $E_{\mathrm{c}.\mathrm{m}.}=100$ MeV.

Figure 5

The same as Fig. 3, but for ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$. (b) At $E_{\mathrm{c}.\mathrm{m}.}=110$ MeV and (c) at $E_{\mathrm{c}.\mathrm{m}.}=180$ MeV.

Figure 6

N-N potential and the collective kinetic energy of the relative motion as well as the excitation and the rotational energies of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ at $E_{\mathrm{c}.\mathrm{m}.}=12$ MeV and $b=3$ fm.

Figure 7

Effective mass parameters (a) for head-on collisions of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ at various incident energies and (b) for various impact parameters at $E_{\mathrm{c}.\mathrm{m}.}=12$ MeV, and (c) the same as (b) but at $E_{\mathrm{c}.\mathrm{m}.}=20$ MeV.

Figure 8

The same as Fig. 7, but for ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$. (b) At $E_{\mathrm{c}.\mathrm{m}.}=56$ MeV and (c) at $E_{\mathrm{c}.\mathrm{m}.}=100$ MeV.

Figure 9

The same as Fig. 7, but for ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$. (b) At $E_{\mathrm{c}.\mathrm{m}.}=110$ MeV and (c) at $E_{\mathrm{c}.\mathrm{m}.}=180$ MeV.

Figure 10

The penetration probability as a function of the impact parameter of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ at various incident energies with and without considering the noncentral effect of $V\left(R\right)$ and $M\left(R\right)$ (see text).

Figure 11

Fusion excitation functions of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ obtained from TDHF sharp cutoff (solid squares), the DC-TDHF (lines) with potentials in Fig. 4, Eq. (12), with (spheres) and without (crosses) the noncentral effect. The experimental data extracted from Refs. [42, 43] are shown for comparison.