Cold Neutrons Trapped in External Fields

The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine the binding energies and densities of many neutrons interacting via realistic microscopic interactions and confined in external fields. We perform calculations for different external fields and across several shells to place important constraints on inhomogeneous neutron matter, and hence the large isospin limit of the nuclear energy density functionals that are used to predict properties of heavy nuclei and neutron star crusts. We find important differences between microscopic calculations and current density functionals; in particular, the isovector gradient terms are significantly more repulsive than in traditional models, and the spin-orbit and pairing forces are comparatively weaker.

Figure 1

Energies divided by $\hslash \omega N^{4/3}$ for neutrons in HO fields with $\hslash \omega =10\mathrm{MeV}$ (top) and 5 MeV (bottom). Filled symbols indicate ab initio calculations; the dashed lines are Thomas-Fermi results (see text); the lower curves are from the Skyrme SLY4 interaction and the upper curves show the modified SLY4 interaction described in the text.

Figure 2

Energies per particle for neutrons in the Woods-Saxon field; symbols as in Fig. 1.

Figure 3

Calculated radii of neutrons confined in HO (upper) and WS (lower) fields compared to original and adjusted Skyrme models (see text).

Figure 4

Calculated densities of neutrons in HO potentials compared to Skyrme models (see text).