Quantum Monte Carlo techniques aim at providing a description of complex quantum systems such as nuclei and nucleonic matter from first principles, i.e., realistic nuclear interactions and currents. ...The methods are similar to those used for many-electron systems in quantum chemistry and condensed matter physics, but are extended to include spin-isospin, tensor, spin-orbit, and three-body interactions. This review shows how to build the atomic nucleus from the ground up. Examples include the structure of light nuclei, electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter. Quantum Monte Carlo methods have proved 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. The nuclear interactions and currents are reviewed along with a description of 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. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. 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 are also described. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
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We carry out an ab initio calculation of the neutrino flux-folded inclusive cross sections measured on ^{12}C by the MiniBooNE and T2K Collaborations in the charged-current quasielastic regime. The ...calculation is based on realistic two- and three-nucleon interactions, and on a realistic nuclear electroweak current with one- and two-nucleon terms that are constructed consistently with these interactions and reproduce low-energy electroweak transitions. Numerically exact quantum Monte Carlo methods are utilized to compute the nuclear weak response functions, by fully retaining many-body correlations in the initial and final states and interference effects between one- and two-body current contributions. We employ a nucleon axial form factor of the dipole form with Λ_{A}=1.0 or 1.15 GeV, the latter more in line with a very recent lattice QCD determination. The calculated cross sections are found to be in good agreement with the neutrino data of MiniBooNE and T2K, and antineutrino MiniBooNE data, yielding a consistent picture of nuclei and their electroweak properties across a wide regime of energy and momenta.
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In recent years local chiral interactions have been derived and implemented in quantum Monte Carlo methods in order to test to what extent the chiral effective field theory framework impacts our ...knowledge of few- and many-body systems. In this Letter, we present Green's function Monte Carlo calculations of light nuclei based on the family of local two-body interactions presented by our group in a previous paper in conjunction with chiral three-body interactions fitted to bound- and scattering-state observables in the three-nucleon sector. These interactions include Δ intermediate states in their two-pion-exchange components. We obtain predictions for the energy levels and level ordering of nuclei in the mass range A=4-12, accurate to ≤2% of the binding energy, in very satisfactory agreement with experimental data.
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Cross sections for inclusive neutrino scattering off deuteron induced by neutral and charge-changing weak currents are calculated from threshold up to 150 MeV energies in a chiral effective field ...theory including high orders in the power counting. The contributions beyond leading order (LO) in the weak current are found to be small, and increase the cross sections obtained with the LO transition operators by a couple of percent over the whole energy range (0--150) MeV. Furthermore, the cutoff dependence is negligible, and the predicted cross sections are within ~2% of, albeit consistently larger than, corresponding predictions obtained in conventional meson-exchange frameworks.
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The astrophysical S factor for proton-proton weak capture is calculated in chiral effective field theory over the center-of-mass relative-energy range 0-100 keV. The chiral two-nucleon potential ...derived up to next-to-next-to-next-to leading order is augmented by the full electromagnetic interaction including, beyond Coulomb, two-photon and vacuum-polarization corrections. The low-energy constants entering the weak current operators are fixed so as to reproduce the A=3 binding energies and magnetic moments and the Gamow-Teller matrix element in tritium β decay. Contributions from S and P partial waves in the incoming two-proton channel are retained. The S factor at zero energy is found to be S(0)=(4.030±0.006)×10(-23) MeV fm(2), with a P-wave contribution of 0.020×10(-23) MeV fm(2). The theoretical uncertainty is due to the fitting procedure of the low-energy constants and to the cutoff dependence.
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Experimental form factors of the hydrogen and helium isotopes, extracted from an up-to-date global analysis of cross sections and polarization observables measured in elastic electron scattering from ...these systems, are compared to predictions obtained in three different theoretical approaches: the first is based on realistic interactions and currents, including relativistic corrections (labeled as the conventional approach); the second relies on a chiral effective field theory description of the strong and electromagnetic interactions in nuclei (labeled χEFT); the third utilizes a fully relativistic treatment of nuclear dynamics as implemented in the covariant spectator theory (labeled CST). For momentum transfers below fm−1 there is satisfactory agreement between experimental data and theoretical results in all three approaches. However, at fm−1, particularly in the case of the deuteron, a relativistic treatment of the dynamics, as is done in the CST, is necessary. The experimental data on the deuteron A structure function extend to fm−1, and the close agreement between these data and the CST results suggests that, even in this extreme kinematical regime, the study of few-body form factors provides no evidence for new effects coming from quark and gluon degrees of freedom at short distances.
Two-nucleon momentum distributions are calculated for the ground states of nuclei with mass number A< or =8, using variational Monte Carlo wave functions derived from a realistic Hamiltonian with ...two- and three-nucleon potentials. The momentum distribution of np pairs is found to be much larger than that of pp pairs for values of the relative momentum in the range (300-600) MeV/c and vanishing total momentum. This order of magnitude difference is seen in all nuclei considered and has a universal character originating from the tensor components present in any realistic nucleon-nucleon potential. The correlations induced by the tensor force strongly influence the structure of np pairs, which are predominantly in deuteronlike states, while they are ineffective for pp pairs, which are mostly in 1S0 states. These features should be easily observable in two-nucleon knockout processes, such as A(e,e'np) and A(e,e'pp).
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