Swelling of nuclei embedded in neutron-gas and consequences for fusion

Fusion of very neutron rich nuclei may be important to determine the composition and heating of the crust of accreting neutron stars. We present an exploratory study of the effect of the neutron-gas environment on the structure of nuclei and the consequences for pycnonuclear fusion cross sections in the neutron drip region. We studied the formation and properties of oxygen and calcium isotopes embedded in varying neutron-gas densities. We observe that the formed isotope is the drip-line nucleus for the given effective interaction. Increasing the neutron-gas density leads to the swelling of the nuclear density. We have used these densities to study the effect of this swelling on the fusion cross sections using the São Paulo potential. At high neutron-gas densities the cross section is substantially increased but at lower densities the modification is minimal.

Figure 1

Mean-field potentials for neutrons and protons (solid lines) for the system with $Z=8$ and 520 neutrons. The dashed lines indicate the energies of the bound single-particle states with degeneracies shown in brackets.

Figure 2

(a) Total density profiles for bound states; (b) density profiles for bound neutrons (solid lines) and protons (dashed lines), for the system with $Z=8$ and $n=20,520$, and 1020 neutrons.

Figure 3

Ion-ion potentials $V_{SP}\left(R\right)=V_F\left(R\right)+V_C\left(R\right)$ for ${}^{28}\mathrm{O}$ isotope as a function of the external neutron-gas density. Also shown is the point-Coulomb interaction. Densities are in units of $\mathrm{gm}/{\mathrm{cm}}^3$.

Figure 4

Astrophysical $S$ factor versus center of mass energy for fusion of ${}^{28}\mathrm{O}$ isotope as a function of external neutron-gas density. Cross-sections are calculated using the São Paulo barriers and the IWBC method.

Figure 5

The cross-sectional density ($y=0$ plane) profile of the ${}^{28}\mathrm{O}+500n$ system. The neutron density is low enough to have shell structures leading to the formation of neutron arms.

Figure 6

Mean-field potentials for neutrons and protons (solid lines) for the system with $Z=20$ and 540 neutrons. The dashed lines show the mean-field potential of ${}^{60}\mathrm{Ca}$ in free space.

Figure 7

(a) Total density profiles for bound states; (b) density profiles for bound neutrons (solid lines) and protons (dashed lines), for the system with $Z=20$ and $n=40,540$, and 1040 neutrons.

Figure 8

Ion-ion potentials $V_{SP}\left(R\right)=V_F\left(R\right)+V_C\left(R\right)$ between two ${}^{60}\mathrm{Ca}$ isotopes as a function of the external neutron-gas density. Also shown is the point-Coulomb interaction. Densities are in units of $\mathrm{gm}/{\mathrm{cm}}^3$.

Figure 9

Fusion cross section as a function of center-of-mass energy for the fusion of two ${}^{60}\mathrm{Ca}$ isotopes calculated for changing external neutron-gas density. Cross sections are calculated using the São Paulo barriers and the IWBC method.