Field Diffusion Monte Carlo Method Research Articles

Maximally local two-nucleon interactions at N3LO in Δ -less chiral effective field theory

We present new maximally local two-nucleon interactions derived in Δ-less chiral effective field theory up to next-to-next-to-next-to-leading order (N3LO), which include all contact and pion-exchange contributions to the nuclear Hamiltonian up to this order. Our interactions are fit to nucleon-nucleon phase shifts using a Bayesian statistical approach, and explore a wide cutoff range from 0.6–0.9 fm (≈660–440MeV). These interactions can be straightforwardly employed in quantum Monte Carlo methods, such as the auxiliary field diffusion Monte Carlo method. Together with local three-nucleon forces, calculations with these new interactions will provide improved benchmarks for the structure of atomic nuclei and serve as crucial input to analyses of astrophysical phenomena of neutron stars, such as binary neutron-star mergers. Published by the American Physical Society 2024

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion MonteCarlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Ground-state properties of 4He and 16O extrapolated from lattice QCD with pionless EFT

We extend the prediction range of Pionless Effective Field Theory with an analysis of the ground state of 16O in leading order. To renormalize the theory, we use as input both experimental data and lattice QCD predictions of nuclear observables, which probe the sensitivity of nuclei to increased quark masses. The nuclear many-body Schrödinger equation is solved with the Auxiliary Field Diffusion Monte Carlo method. For the first time in a nuclear quantum Monte Carlo calculation, a linear optimization procedure, which allows us to devise an accurate trial wave function with a large number of variational parameters, is adopted. The method yields a binding energy of 4He which is in good agreement with experiment at physical pion mass and with lattice calculations at larger pion masses. At leading order we do not find any evidence of a 16O state which is stable against breakup into four 4He, although higher-order terms could bind 16O.

Benchmark Results for Few-Body Hypernuclei

The Non-Symmetrized Hyperspherical Harmonics method (NSHH) is introduced in the hypernuclear sector and benchmarked with three different ab-initio methods, namely the Auxiliary Field Diffusion Monte Carlo method, the Faddeev-Yakubovsky approach and the Gaussian Expansion Method. Binding energies and hyperon separation energies of three- to five-body hypernuclei are calculated by employing the two-body $\Lambda$N component of the phenomenological Bodmer-Usmani potential, and a hyperon-nucleon interaction simulating the scattering phase shifts given by NSC97f. The range of applicability of the NSHH method is briefly discussed.

Effects of the two-body and three-body hyperon-nucleon interactions inΛhypernuclei

Background: The calculation of the hyperon binding energy in hypernuclei is crucial to understanding the interaction between hyperons and nucleons. Purpose: We assess the relative importance of two- and three-body hyperon-nucleon force by studying the effect of the hyperon-nucleon-nucleon interaction in closed shell \Lambda-hypernuclei from A=5 to 91. Methods: The \Lambda-binding energy has been calculated using the auxiliary field diffusion Monte Carlo method for the first time, to study light and heavy hypernuclei within the same model. Results: Our results show that including a three-body component in the hyperon-nucleon interaction leads to a saturation of the \Lambda-binding energy remarkably close to the experimental data. In contrast, the two-body force alone gives an unphysical limit for the binding energy. Conclusions: The repulsive contribution of the three-body hyperon-nucleon-nucleon force is essential to reproduce, even qualitatively, the binding energy of the hypernuclei in the mass range considered.

Equation of state of low-density neutron matter, and the1S0pairing gap

We report results of the equation of state of neutron matter in the low-density regime, where the Fermi wave vector ranges from $0.4\ensuremath{\leqslant}{k}_{F}\ensuremath{\leqslant}1.0 \phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$. Neutron matter in this regime is superfluid because of the strong and attractive interaction in the ${}^{1}{S}_{0}$ channel. The properties of this superfluid matter are calculated starting from a realistic Hamiltonian that contains modern two- and three-body interactions. The ground state energy and the ${}^{1}{S}_{0}$ superfluid energy gap are calculated using the auxiliary field diffusion Monte Carlo method. We study the structure of the ground state by looking at pair distribution functions as well as the Cooper-pair wave function used in the calculations.

Auxiliary Field Diffusion Monte Carlo Calculation of Nuclei withA≤40with Tensor Interactions

We calculate the ground-state energy of (4)He, (8)He, (16)O, and (40)Ca using the auxiliary field diffusion Monte Carlo method in the fixed-phase approximation and the Argonne v(6)' interaction which includes a tensor force. Comparison of our light nuclei results to those of Green's function Monte Carlo calculations shows the accuracy of our method for both open and closed-shell nuclei. We also apply it to (16)O and (40)Ca to show that quantum Monte Carlo methods are now applicable to larger nuclei.

S01Superfluid Phase Transition in Neutron Matter with Realistic Nuclear Potentials and Modern Many-Body Theories

The 1S0 pairing in neutron matter is studied using realistic two- and three-nucleon interactions. The auxiliary field diffusion Monte Carlo method and correlated basis function theory are employed to get quantitative and reliable estimates of the gap. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about 2.5 MeV at kF approximately 0.8 fm(-1) in BCS and 2.2-2.4 MeV at kF approximately 0.6 fm(-1)in correlated matter. In general, the computed medium polarization effects are much smaller than those previously estimated within all theories. Truncations of Argonne to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same data set. The three-nucleon interaction provides an additional increase of the gap of about 0.35 MeV.

Auxiliary field diffusion Monte Carlo calculation of ground state properties of neutron drops

The auxiliary field diffusion Monte Carlo method has been applied to simulate droplets of 7 and 8 neutrons. Results for realistic nucleon–nucleon interactions, which include tensor, spin–orbit and three-body forces, plus a standard one-body confining potential, have been compared with analogous calculations obtained with Green's function Monte Carlo methods. We have studied the dependence of the binding energy, the one-body density and the spin–orbit splittings of 7n on the depth of the confining potential. The results obtained show an overall agreement between the two quantum Monte Carlo methods, although there persist differences in the evaluation of spin–orbit forces, as previously indicated by bulk neutron matter calculations. Energy density functional models, largely used in astrophysical applications, seem to provide results significantly different from those of quantum simulations. Given its scaling behavior in the number of nucleons, the auxiliary field diffusion Monte Carlo method seems to be one of the best candidate to perform ab initio calculations on neutron rich nuclei.

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

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 $(A\alt 100)$. 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 $v_6$ 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 energy per particle of zero-temperature neutron matter is investigated, with particular emphasis on the role of the $\vec L\cdot\vec S$ interaction. An analysis of the importance of explicit spin--orbit correlations in the description of the system is carried out by the auxiliary field diffusion Monte Carlo method. The improved nodal structure of the guiding function, constructed by explicitly considering these correlations, lowers the energy. The proposed spin--backflow orbitals can conveniently be used also in Green's Function Monte Carlo calculations of light nuclei.

Spin Susceptibility of Neutron Matter at Zero Temperature

The auxiliary field diffusion Monte Carlo method is applied to compute the spin susceptibility and the compressibility of neutron matter at zero temperature. Results are given for realistic interactions which include both a two-body potential of the Argonne type and the Urbana IX three-body potential. Simulations have been carried out for about 60 neutrons. We find an overall reduction of the spin susceptibility by about a factor of 3 with respect to the Pauli susceptibility for a wide range of densities. Results for the compressibility of neutron matter are also presented and compared with other available estimates obtained for semirealistic nucleon-nucleon interactions by using other techniques.