Microscopic study of fusion reactions with a weakly bound nucleus: Effects of deformed halo

We present a microscopic study on the fusion reactions ${}^{14,15}\mathrm{C}+{}^{232}\mathrm{Th}$ by emphasizing the effect of deformed halo structure on reaction dynamics within the framework of time-dependent density functional theory. The internuclear potentials are obtained by using the density-constraint frozen Hartree-Fock approach and then are adopted to calculate the fusion cross sections of ${}^{14,15}\mathrm{C}+{}^{232}\mathrm{Th}$, taking all the orientations of deformed reactants into account. Our microscopic calculations not only reproduce the enhancement of fusion cross sections at sub-barrier energies without any adjustable parameters, but also reveal the underlying mechanism of this enhancement, which is driven by the deformed halo structure of ${}^{15}\mathrm{C}$. More interestingly, by performing particle number projection based on the wave functions from time-dependent Hartree-Fock simulation, we find that the one-neutron transfer probabilities are more sensitive to the orientations of ${}^{15}\mathrm{C}$ than ${}^{232}\mathrm{Th}$, indicating the notable effects of halo structure on the reaction dynamics.

Figure 1

Relative position of deformed projectile and target. ${\theta }_{\mathrm{P}}$ (${\theta }_{\mathrm{T}}$) labels the angle between the symmetry axis of the deformed projectile (target) and the collision axis (denoted by the black line).

Figure 2

Two-dimensional density distribution for the ground states of ${}^{14}\mathrm{C}$ and ${}^{15}\mathrm{C}$ in the static HF calculations with the density functional SLy5. The $z$ axis is the symmetry axis.

Figure 3

Internuclear potentials for ${}^{14,15}\mathrm{C}+{}^{232}\mathrm{Th}$ by using the DC-FHF method with SLy5 density functional. For ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ the selected potentials are labeled as the orientations of ${}^{15}\mathrm{C}$ and ${}^{232}\mathrm{Th}$: ${\theta }_{\mathrm{P}}$ and ${\theta }_{\mathrm{T}}$. $6^{\circ }$ and $80.4^{\circ }$ are the first and last nodes for seven-point Gaussian quadrature. For ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}, {}^{14}\mathrm{C}$ has a spherical ground state and the selected potentials are labeled as the orientation of ${}^{232}\mathrm{Th}$: ${\theta }_{\mathrm{T}}$.

Figure 4

The comparison between calculated fusion cross sections and experimental ones for ${}^{14,15}\mathrm{C}+{}^{232}\mathrm{Th}$. Experimental data of ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ and ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ are taken from Ref. [23] and labeled by red solid circles and black solid diamonds, respectively. Calculated fusion cross sections for ${}^{14}\mathrm{C}+{}^{232}\mathrm{Th}$ and ${}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ are shown by red and black lines. The blue solid and dashed lines represent the fusion cross sections with tip and side orientations of ${}^{15}\mathrm{C}$, respectively.

Figure 5

Calculated one-neutron transfer probability of the fusion $\text{reaction}{}^{15}\mathrm{C}+{}^{232}\mathrm{Th}$ by using TDHF with the particle number projection technique. The incident energies for all orientations are taken to be 54 MeV.