Static Response of Neutron Matter

We generalize the problem of strongly interacting neutron matter by adding a periodic external modulation. This allows us to study from first principles a neutron system that is extended and inhomogeneous, with connections to the physics of both neutron-star crusts and neutron-rich nuclei. We carry out fully nonperturbative microscopic quantum Monte Carlo calculations of the energy of neutron matter at different densities, as well as different strengths and periodicities of the external potential. In order to remove systematic errors, we examine finite-size effects and the impact of the wave function ansatz. We also make contact with energy-density functional theories of nuclei and disentangle isovector gradient contributions from bulk properties. Finally, we calculate the static density-density linear response function of neutron matter and compare it with the response of other physical systems.

Figure 1

Neutron-matter energy per particle as a function of density using NN interactions and AFDMC calculations. Squares correspond to the case without a one-body potential; diamonds to a one-body potential of fixed strength $2v_q=0.5E_F$, periodicity $q=4\pi /L$, and plane-wave single-particle orbitals (PW); circles to a one-body potential of fixed strength $2v_q=0.5E_F$, periodicity $q=4\pi /L$, and optimized single-particle orbitals (opt.).

Figure 2

Neutron-matter energy per particle as a function of one-body potential strength at a density of $n=0.10{\mathrm{fm}}^{-3}$, using $\mathrm{NN}+\mathrm{NNN}$ interactions and a one-body potential periodicity $q=4\pi /L$. Circles correspond to AFDMC results, while the solid line follows from the SLy4 energy-density functional. The dashed line shows SLy4 results with a modified isovector gradient term. Inset: AFDMC and SLy4 results in the absence of a one-body potential.

Figure 3

Static-response function of neutron matter at a density of $n=0.10{\mathrm{fm}}^{-3}$. Points follow from AFDMC results using $\mathrm{NN}+\mathrm{NNN}$ interactions, as well as several one-body strengths and periodicities. The line is the Lindhard function describing the response of a noninteracting Fermi gas. Inset: Finite-size dependence of a noninteracting Fermi gas in the presence of a one-body potential of fixed strength $2v_q=0.5E_F$ and periodicity $q=4\pi /L$.