Dynamical effects in fusion with exotic nuclei

Background: Reactions with stable beams have demonstrated strong interplay between nuclear structure and fusion. Exotic beam facilities open new perspectives to understand the impact of neutron skin, large isospin, and weak binding energies on fusion. Microscopic theories of fusion are required to guide future experiments.

Purpose: To investigate new effects of exotic structures and dynamics in near-barrier fusion with exotic nuclei.

Method: Microscopic approaches based on the Hartree-Fock (HF) mean-field theory are used for studying fusion barriers in ${}^{40-54}\text{Ca}+{}^{116}\text{Sn}$ reactions for even isotopes. Bare potential barriers are obtained assuming frozen HF ground-state densities. Dynamical effects on the barrier are accounted for in time-dependent Hartree-Fock (TDHF) calculations of the collisions. Vibrational couplings are studied in the coupled-channel framework and near-barrier nucleon transfer is investigated with TDHF calculations.

Results: The development of a neutron skin in exotic calcium isotopes strongly lowers the bare potential barrier. However, this static effect is not apparent when dynamical effects are included. On the contrary, a fusion hindrance is observed in TDHF calculations with the most neutron-rich calcium isotopes which cannot be explained by vibrational couplings. Transfer reactions are also important in these systems due to charge equilibration processes.

Conclusions: Despite its impact on the bare potential, the neutron skin is not seen as playing an important role in the fusion dynamics. However, the charge transfer with exotic projectiles could lead to an increase of the Coulomb repulsion between the fragments, suppressing fusion. The effects of transfer and dissipative mechanisms on fusion with exotic nuclei deserve further studies.

Figure 1

Example of the bare nucleus-nucleus potential from the frozen HF method (dashed and dot-dashed lines) and the Akyüz-Winther phenomenological potential [54] (solid line) for ${}^{40}\text{Ca}+{}^{116}\text{Sn}$. The dashed lines show the maximum AW barrier energy at $V=119.7$ MeV and $r=11.3$ fm.

Figure 2

Frozen HF barriers of calcium isotopes on ${}^{116}\text{Sn}$. Two different parametrizations are used. Also included are the macroscopic Akyüz-Winther potential barriers.

Figure 3

HF proton (dashed lines) and neutron (solid lines) root mean square radii in calcium isotopes for two parametrizations of the Skyrme functional. The experimental charge radii (crosses) are from Refs. [59, 60].

Figure 4

Distance between fragment centers of masses in ${}^{40}\text{Ca}+{}^{116}\text{Sn}$ central collisions as a function of time. Fusion is achieved at $E_{\mathrm{c}.\mathrm{m}.}=117.4$ MeV (solid line) while separation of the nuclei occurs at $E_{\mathrm{c}.\mathrm{m}.}=117.3$ MeV (dashed line).

Figure 5

Bare potential barrier energies from the frozen HF method and TDHF fusion thresholds for ${}^A\text{Ca}+{}^{116}\text{Sn}$ are plotted with respect to the calcium mass number for the SLy4d (solid lines) and UNEDF1 (dashed lines) parametrizations.

Figure 6

(a) Time evolution of the octupole moment induced by an octupole boost on ${}^{40}\text{Ca}$ in the linear regime. (b) Associated strength function computed from Eq. (5).

Figure 7

Frozen HF (cirlces) barriers in ${}^A\text{Ca}+{}^{116}\text{Sn}$ are compared with TDHF fusion thresholds (squares) and coupled-channels average barriers with couplings to the $3_1^{-}$ state in calcium isotopes (diamonds).

Figure 8

Proton number probability distributions in the outgoing TLF in ${}^{40}\text{Ca}+{}^{116}\text{Sn}$ (a) and ${}^{54}\text{Ca}+{}^{116}\text{Sn}$ (b) central collisions at an energy of 99.9% of the TDHF fusion threshold.

Figure 9

The average proton (left axis) and neutron number (right axis) of the TLF. The dashed line and open triangles show the anticipated ${\overline{Z}}_{\text{TLF}}$ value assuming the system is fully equilibriated with the TLF having $N_{\text{TLF}}={\overline{N}}_{\text{TLF}}$. The original target $Z$ and $N$ (horizontal dotted line) are also shown.