Competition between direct and sequential two-neutron transfers in the ${}^{18}\mathrm{O}+{}^{28}\mathrm{Si}$ collision at 84 MeV

In this work we study the simultaneous and sequential two-neutron transfer mechanisms to the ${}^{28}\mathrm{Si}$ nucleus induced by $(t,p)$ and $({}^{18}\mathrm{O},{}^{16}\mathrm{O})$ reactions. New experimental cross sections for the ${}^{28}\mathrm{Si}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{30}\mathrm{Si}$ reaction at 84 MeV are also presented. Direct reaction calculations are carried out within the exact finite range coupled reaction channel, for the simultaneous transfer of the two-neutron cluster, and the second-order distorted wave Born approximation, for the sequential transfer. Two different models are considered to describe the two-neutron cluster. The spectroscopic information was obtained from a shell-model calculation with a psdmod interaction for the target overlaps where the $1p_{3/2}, 1p_{1/2}, 1d_{3/2}, 1d_{5/2}$, and $2s_{1/2}$ orbitals are included as valence subspace. We show that simultaneous and sequential two-neutron transfers are competing mechanisms for the population of the ground state in ${}^{30}\mathrm{Si}$. A systematic analysis of the two-neutron transfer induced by the $({}^{18}\mathrm{O},{}^{16}\mathrm{O})$ reaction indicates that the static deformation of target nuclei impacts the two-neutron transfer mechanism.

Figure 1

Excitation energy spectrum of ${}^{30}\mathrm{Si}$ populated by the ${}^{28}\mathrm{Si}({}^{18}\mathrm{O},{}^{16}\mathrm{O})$ reaction at $E_{lab}=84MeV$. Low-lying states in ${}^{30}\mathrm{Si}$ are labeled with numbers (see Table 1) and the one-neutron threshold energy ($S_n$) is indicated with a dashed line.

Figure 2

Coupling schemes of the projectile and target overlaps used in the (a) direct and (b) sequential two-neutron transfer reaction calculations.

Figure 3

Comparison of the angular distribution of ${}^{28}\mathrm{Si}(t,p){}^{30}\mathrm{Si}$ reaction at 18 MeV [3] for the transition to (a) the ground state, (b) the first-excited state at 2.235 MeV), (c) the second-excited state at 3.498 MeV, and (d) the sum of the 3.769 MeV and the 3.788 MeV states in ${}^{30}\mathrm{Si}$ nuclei. The green dotted, red solid, and blue dashed curves correspond to the extreme cluster, independent coordinates, and sequential model, respectively.

Figure 4

Comparison between experimental and theoretical angular distributions for elastic and inelastic scattering for (${}^{18}\mathrm{O}+{}^{28}\mathrm{Si}$) at 56 MeV [17]. The SSP curve stands for optical potential with the shape of São Paulo potential with 1.0 and 0.6 factors in the real and imaginary terms.

Figure 5

Angular distributions for the transfer of two neutrons to (a) the ground state, (b) the first-excited state 2.235 MeV, (c) the second-excited state 3.498 MeV, and (d) the fourth-excited state 3.788 MeV for the ${}^{28}\mathrm{Si}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{30}\mathrm{Si}$ reaction at 56 MeV [17]. The green dotted, red solid, and blue dashed curves represent the extreme cluster, the independent coordinates, and the sequential models, respectively.

Figure 6

Comparison of the experimental angular distribution with the extreme cluster, independent coordinates and sequential models calculations for the ${}^{28}\mathrm{Si}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{30}\mathrm{Si}$ reaction at 84 MeV.

Figure 7

Comparison of the experimental angular distribution with the microscopic cluster model calculations for the ${}^{28}\mathrm{Si}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{30}\mathrm{Si}$ reaction at 84 MeV.