Influences of isospin-asymmetry and skin thickness on fusion of oxygen isotopes at stellar energies

Fusion reactions with stable and radioactive isotopes of light nuclei are indicated to control the crustal composition, nucleosynthesis, and heating mechanism during nuclear burning in neutron stars. The role of isospin asymmetry and proton-/neutron-skin thickness in the fusion excitation function and its related astrophysical $S$ factor is investigated for the reactions involving ${}^{12,14-20,22,24,25,28}\mathrm{O}$ isotopes at sub-barrier energies of astrophysical interest. The calculations are performed in an extended quantum diffusion framework. Among many examined potentials, the only potentials based on the Skyrme-BSk19 and M3Y-Reid nucleon-nucleon interactions successfully reproduce the experimental ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$, ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$, ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$, and ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ fusion data, over the whole considered energy range. The height, radius, and curvature of the Coulomb barrier for the interactions involving proton-rich ${}^{12,15}\mathrm{O}$ isotopes are found to impede the near- and above-barrier fusion cross section and the corresponding $S$ factor relative to the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ reaction. However, the relatively small reduced mass and proton-skin thickness act to enhance fusion at deeply sub-barrier energies. For the interactions involving neutron-rich $\mathrm{O}(N>8)$ isotopes, the fusion enhancement due to the produced Coulomb barrier is supported by relatively large $Q$ values and neutron-skin thicknesses, against the increase of reduced masses. The neutron transfer is indicated to hinder the fusion in some ${}^{A_1}\mathrm{O}+{}^{A_2}\mathrm{O}$ $(A_2\ge A_1+4)$ reactions at sub-barrier energy.

Figure 1

The fusion excitation function (upper panel) and astrophysical $S$ factor factorized with ${\eta }_0=9.17$ (lower panel) for the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ fusion reaction calculated within the extended quantum diffusion approach using the SkSC14, KDEX, Skxs25, and BSk19 parametrizations of the Skyrme NN interaction and M3Y-Reid NN interaction. The experimental data (symbols) are from Refs. [64, 65, 66, 67].

Figure 2

The same as in Fig. 1, but for the (a) ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ [82, 83, 84], (b) ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$ [85], and (c) ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ [86] fusion reactions.

Figure 3

The fusion excitation function (upper panel) and astrophysical $S$ factor factorized with ${\eta }_0=9.17$ (lower panel) for the fusion reactions of ${}^{16}\mathrm{O}$ with ${}^{12,15,16,17,24,28}\mathrm{O}$ isotopes calculated with the Skyrme-BSk19 NN interaction and the M3Y-Reid interaction (for the ${}^{16}\mathrm{O}+{}^{12,28}\mathrm{O}$ reactions). The squares in (b) represent the calculated $S$ at the Coulomb barrier energy. The calculations of $S$ for the ${}^{16}\mathrm{O}+{}^{12,16,28}\mathrm{O}$ reactions using an analytical formula based on São Paulo potential [1] (${\eta }_0=7.95$) are presented in (b) for comparison. See the text for details.

Figure 4

The same as in Fig. 3, but for the fusion reactions of ${}^{12,15,16,20,25,28}\mathrm{O}$ isotopes with themselves.

Figure 5

(a) The total interaction potential for the ${}^{15}\mathrm{O}+{}^{15}\mathrm{O}$, ${}^{18}\mathrm{O}+{}^{18,22}\mathrm{O}$, ${}^{20}\mathrm{O}+{}^{20}\mathrm{O}$, and ${}^{16}\mathrm{O}+{}^{12,16,20,24}\mathrm{O}$ reactions based on the Skyrme-BSk19 NN interaction. (b) The same as in Fig. 3, but for the $S$ factor of the ${}^{18}\mathrm{O}+{}^{18}\mathrm{O}$, ${}^{20}\mathrm{O}+{}^{20}\mathrm{O}$, ${}^{16}\mathrm{O}+{}^{20}\mathrm{O}$, and ${}^{18}\mathrm{O}+{}^{22}\mathrm{O}$ fusion reactions to demonstrate the role of $2n$ transfer.

Figure 6

(a) Maximum value of the $S$ factor factorized with ${\eta }_0=9.17$, (b) its energy position, and (c) its relative position with respect to the Coulomb barrier hight obtained for the fusion reactions ${}^{16}\mathrm{O}+{}^{A=12,15,16,17,18,20,24,25,28}\mathrm{O}$ and ${}^A\mathrm{O}+{}^A\mathrm{O}$ with the Skyrme-BSk19 and M3Y-Reid potentials, as functions of the total isospin asymmetry of the projectile ($I_P$) and target ($I_T$) nuclei. The red crosses represents the obtained values upon considering the $2n$ transfer with positive $Q_{2n}$ for the ${}^{16}\mathrm{O}+{}^A\mathrm{O}$ reactions. The straight lines are the least-square fits to the calculations based on the Skyrme-BSk19 potential.

Figure 7

The energy position of the $S_{\max }$ relative to the Coulomb barrier height obtained for the fusion reactions ${}^{16}\mathrm{O}+{}^{A=12,15,16,17,18,20,24,25,28}\mathrm{O}$, ${}^{15}\mathrm{O}+{}^{19}\mathrm{O}$, ${}^{18}\mathrm{O}+{}^{14.22}\mathrm{O}$, ${}^{20}\mathrm{O}+{}^{15,24}\mathrm{O}$, and ${}^{A=12,14,15,16,17,18,20,22,24,25,28}\mathrm{O}+{}^A\mathrm{O}$ with the Skyrme-BSk19 potential as a function of the total neutron-skin thickness of the projectile (${\mathrm{\Delta }}_P$) and target (${\mathrm{\Delta }}_T$) nuclei. The negative $\mathrm{\Delta }$ represents proton-skin thickness. The straight line and the given expression represent the linear trend of the ${}^A\mathrm{O}+{}^A\mathrm{O}$ calculations.