We report quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A ≤ 7 using a realistic Hamiltonian containing the Argonne v 18 two-nucleon and Urbana IX three-nucleon potentials. A detailed description of the Green's function Monte Carlo algorithm for systems with state-dependent potentials is given and a number of tests of its convergence and accuracy are performed. We find that the Hamiltonian being used results in ground states of both 6 Li and 7 Li that are stable against breakup into subclusters, but somewhat underbound compared to experiment. We also have results for 6 He, 7 He, and their isobaric analogs. The known excitation spectra of all these nuclei are reproduced reasonably well and we predict a number of excited states in 6 He and 7 He. We also present spin-polarized onebody and several different two-body density distributions. These are the first microscopic calculations that directly produce nuclear shell structure from realistic interactions that fit NN scattering data.

Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

We report quantum Monte Carlo calculations of superfluid Fermi gases with short-range two-body attractive interactions with infinite scattering length. The energy of such gases is estimated to be (0.44 ± 0.01) times that of the noninteracting gas, and their pairing gap is approximately twice the energy per particle. PACS: 03.75.Fi, 05.30.Fk, 21.65.+F In dilute Fermi gases the pair interactions have a range much smaller than the interparticle spacing. However, when the two-particle scattering length is large, these short range interactions can modify the gas properties significantly. A well known example is low density neutron matter which may occur in the inner crust of neutron stars [1]. The two-neutron interaction has a range of ∼ 2 fm, but the scattering length is large, −18 fm, so that even at densities as small as one percent of the nuclear density the parameter ak F has magnitude much larger than one. Bertsch proposed in 1998 that solution of the idealized problem of a dilute Fermi gas in the limit ak F → −∞ could give useful insights into the properties of low density neutron gas.Cold dilute gases of 6 Li atoms have been produced in atom traps. The interaction between these atoms can be tuned using a known Feshbach resonance; and the estimated value of ak F in the recent experiment [2] is ∼ −7.4. As the interaction strength is increased beyond that for a = −∞, we get bosonic two-fermion bound states. In this sense a dilute Fermi gas with large a is in between weak coupling BCS superfluid and dilute Bose gases with Bose-Einstein condensation [3]. Attempts to produce Bose gases in the limit, a/r 0 → ∞ using Feshbach resonances [4,5], are in progress, and their energy has been recently estimated using variational methods [6].In the a → −∞ limit k 2 F /m is the only energy scale, and the ground state energy of the interacting dilute Fermi gas is proportional to the noninteracting Fermi gas energy:Baker [7] and Heiselberg [8] have attempted to obtain the value of the constant ξ from expansions of the Fermi gas energy in powers of ak F . Heiselberg obtained ξ = 0.326, while Baker's values are ξ = 0.326 and 0.568. Fermi gases with attractive pair interaction become superfluid at low temperature. The BCS expressions in terms of the scattering length were given by Leggett [9], and they were used to study the properties of superfluid dilute Fermi gases, as a function of ak F , by Engelbrecht, Randeria and Sá de Melo [10]. For ak F = −∞ they obtain an upperbound, ξ = 0.59, using the BCS wave function. These gases are also estimated to have large gaps comparable to the ground state energy per particle.Here we report studies of Fermi gases with quantum Monte Carlo methods using the model potential:The zero energy solution of the two-body Schrödinger equation with this potential is tanh(µr)/r and corresponds to a = −∞. The effective range is 2/µ, and in order to ensure that the gas is dilute we use µr 0 > 10, where r 0 is the unit radius; ρr 3 0 = 3/4π. All the results presented here are for µr 0 = 12; however some ...

We present realistic models of pion-exchange three-nucleon interactions obtained by fitting the energies of all the 17 bound or narrow states of 3 ≤ A ≤ 8 nucleons, calculated with less than 2% error using the Green's function Monte Carlo method. The models contain two-pion-exchange terms due to πN scattering in S-and P-waves, three-pion-exchange terms due to ring diagrams with one ∆ in the intermediate states, and a phenomenological repulsive term to take into account relativistic effects, the suppression of the two-pion-exchange two-nucleon interaction by the third nucleon, and other effects. The models have five parameters, consisting of the strength of the four interactions and the short-range cutoff. The 17 fitted energies are insufficient to determine all of them uniquely. We consider five models, each having three adjustable parameters and assumed values for the other two. They reproduce the observed energies with an rms error < 1% when used together with the Argonne v 18 two-nucleon interaction. In one of the models the πN S-wave scattering interaction is set to zero; in all others it is assumed to have the strength suggested by chiral effective field theory. One of the models also assumes that the πN P-wave scattering interaction has the strength suggested by effective field theories, and the cutoff is adjusted to fit the data. In all other models the cutoff is taken to be the same as in the v 18 interaction. The effect of relativistic boost correction to the two-nucleon interaction on the strength of the repulsive three-nucleon interaction is estimated. Many calculated properties of A ≤ 8 nuclei, including radii, magnetic dipole and electric quadrupole moments, isobaric analog energy differences, etc., are tabulated. Results obtained with only Argonne v ′ 8 and v 18 interactions are also reported. In addition, we present results for 7-and 8-body neutron drops in external potential wells.

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