Neutron matter at zero temperature with an auxiliary field diffusion Monte Carlo method

Abstract

The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many nucleon systems (A < ∼ 100). We use a path constraint to control the fermion sign problem. We have made simulations for realistic interactions, which include tensor and spin-orbit two-body potentials as well as three-nucleon forces. The Argonne v ′ 8 and v ′ 6 two nucleon potentials plus the Urbana or Illinois three-nucleon potentials have been used in our calculations. We compare with fermion hypernetted chain results. We report results of a Periodic Box-FHNC calculation, which is also used to estimate the finite size corrections to our quantum Monte Carlo simulations. Our AFDMC results for v6 models of pure neutron matter are in reasonably good agreement with equivalent Correlated Basis Function (CBF) calculations, providing energies per particle which are slightly lower than the CBF ones. However, the inclusion of the spin-orbit force leads to quite different results particularly at relatively high densities. The resulting equation of state from AFDMC calculations is harder than the one from previous Fermi hypernetted chain studies commonly used to determine the neutron star structure.

Spin-orbit induced backflow in neutron matter with auxiliary field diffusion Monte Carlo method

“…The results of the FHNC/SOC calculations of Ref. [1] with the AU 8 ′ Hamiltonian and a trial function of the type F 6 (not containing spin-orbit correlations), give values for ∆E LS quite close to the AFDMC ones, which may confirm this hypothesis.…”

“…It is well known that they provide very close results for the energy per particle [4]. In addition, this discrepancy is confirmed by other FHNC/SOC calculations [1], performed by using the approximations of Ref. [11] and the AU 8 ′ Hamiltonian.…”

“…The AFDMC calculations of Ref. [1], performed with the simplified, but still realistic, version of the Argonne twobody potential, v 8 ′ [4], plus the Urbana IX three-body interaction (AU 8 ′ Hamiltonian) get energy differences ∆E LS between the AU 8 ′ Hamiltonians with and without the spin-orbit potential which are small and positive. At ρ = ρ 0 , ∆E LS = 0.2 MeV and at ρ = 2ρ 0 , ∆E LS = 1.12 MeV.…”

Density-dependent nucleon-nucleon interaction from three-nucleon forces

“…(11). The strength U 0 , adjusted to reproduce the empirical nuclear matter saturation density, is U 0 = 0.0048 MeV with v 18 .…”

Variational Method for Nuclear Matter with an Explicit Energy Functional

“…The closeness of our results to those obtained by AFDMC and FHNC may imply that the repulsive part of the UIX predominates over the 2π-exchange part in normal neutron matter. In this figure, in addition, we compare E 2 /N without TBF calculated by the EEF and AFDMC [7]: They are also close to each other. Further detail on this is given in Ref.…”