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We study the implications of isospin symmetry in nuclear systems on two-body distributions and derive relations between different densities or momentum distributions of a given nucleus or of different nuclei in the same isospin multiplet. A connection between neutrinoless double beta decay transition of mirror nuclei and two-body densities is also obtained. The relations are numerically verified by means of quantum Monte Carlo calculations. We discuss the relevance of these results to the analysis of nuclear short-range correlations and also show that isospin symmetry allows us to extract information about the spectator nucleons when a short-range correlated pair is formed.

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one and two-dimensional interacting quantum gases with Gaussian interactions, as well as to $^4$He confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods., 8 pages, 6 figures

We discuss the construction of a nuclear Energy Density Functional (EDF) from ab initio calculations, and we advocate the need of a methodical approach that is free from ad hoc assumptions. The equations of state (EoS) of symmetric nuclear and pure neutron matter are computed using the chiral NNLO$_{\rm sat}$ and the phenomenological AV4$^\prime$+UIX$_{c}$ Hamiltonians as inputs in the Self-consistent Green's Function (SCGF) and Auxiliary Field Diffusion Monte Carlo (AFDMC) methods, respectively. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio-based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The NNLO$_{\rm sat}$-based EDF produces encouraging results, whereas the AV4$^\prime$+UIX$_{c}$-based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our work paves the way for a practical and systematic way to merge ab initio nuclear theory and DFT, while at the same time it sheds light on some of the critical aspects of this procedure., Comment: 14 pages, 6 figures

The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schr\"odinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of $A\ensuremath{\le}4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

We propose a novel semiclassical approach to intranuclear cascades, which takes as input quantum Monte Carlo nuclear configurations and uses a semiclassical, impact-parameter-based algorithm to model the propagation of protons and neutrons in the nuclear medium. We successfully compare our simulations to available proton-carbon scattering data and nuclear-transparency measurements. By analyzing the dependence of the simulated observables upon the ingredients entering our intranuclear cascade algorithm, we provide a quantitative understanding of their impact. Particular emphasis is devoted to the role played by nuclear correlations, the Pauli exclusion principle, and interaction probability distributions.

A new numerical study calculates the interaction cross section between neutrinos and the carbon nucleus and finds a good match with extant data, a key step toward characterizing neutrino flavor oscillations.

An ab initio Green's function Monte Carlo (GFMC) method is introduced for calculating total rates of muon weak capture in light nuclei with mass number $A\ensuremath{\le}12$. As a first application of the method, we perform a calculation of the rate in $^{3}\mathrm{H}$ and $^{4}\mathrm{He}$ in a dynamical framework based on realistic two- and three-nucleon interactions and realistic nuclear charge-changing weak currents. The currents include one- and two-body terms induced by $\ensuremath{\pi}$- and $\ensuremath{\rho}$-meson exchange, and $N$-to-$\mathrm{\ensuremath{\Delta}}$ excitation, and are constrained to reproduce the empirical value of the Gamow-Teller matrix element in tritium. We investigate the sensitivity of theoretical predictions to current parametrizations of the nucleon axial and induced pseudoscalar form factors as well as to two-body contributions in the weak currents. The large uncertainties in the measured $^{4}\mathrm{He}$ rates obtained from bubble-chamber experiments (carried out over 50 years ago) prevent us from drawing any definite conclusions. No data exist for $^{3}\mathrm{H}$, but results are compared to those of a recent Faddeev calculation as a validation of the present GFMC method.

The first laser spectroscopic determination of the change in the nuclear charge radius for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-accuracy measurement of the isotope shift in the $2{s}^{2}2p\text{ }\text{ }{^{2}P}_{1/2}\ensuremath{\rightarrow}2{s}^{2}3s\text{ }\text{ }{^{2}S}_{1/2}$ ground state transition in boron atoms. Accuracy is increased by orders of magnitude for the stable isotopes $^{10,11}\mathrm{B}$ and the results are used to extract their difference in the mean-square charge radius $⟨{r}_{c}^{2}{⟩}^{11}\ensuremath{-}⟨{r}_{c}^{2}{⟩}^{10}=\ensuremath{-}0.49(12)\text{ }\text{ }{\mathrm{fm}}^{2}$. The result is qualitatively explained by a possible cluster structure of the boron nuclei and quantitatively used to benchmark new ab initio nuclear structure calculations using the no-core shell model and Green's function Monte Carlo approaches. These results are the foundation for a laser spectroscopic determination of the charge radius of the proton-halo candidate $^{8}\mathrm{B}$.

The electromagnetic responses obtained from Green's function Monte Carlo (GFMC) calculations are based on realistic treatments of nuclear interactions and currents. The main limitations of this method comes from its nonrelativistic nature and its computational cost, the latter hampering the direct evaluation of the inclusive cross sections as measured by experiments. We extend the applicability of GFMC in the quasielastic region to intermediate momentum transfers by performing the calculations in a reference frame that minimizes nucleon momenta. Additional relativistic effects in the kinematics are accounted for employing the two-fragment model. In addition, we developed a novel algorithm, based on the concept of first-kind scaling, to compute the inclusive electromagnetic cross section of $^4$He through an accurate and reliable interpolation of the response functions. A very good agreement is obtained between theoretical and experimental cross sections for a variety of kinematical setups. This offers a promising prospect for the data analysis of neutrino-oscillation experiments that requires an accurate description of nuclear dynamics in which relativistic effects are fully accounted for., 10 pages, 7 figures

Scaling features of the nuclear electromagnetic response functions unveil aspects of nuclear dynamics that are crucial for interpretating neutrino- and electron-scattering data. In the large momentum-transfer regime, the nucleon-density response function defines a universal scaling function, which is independent of the nature of the probe. In this work, we analyze the nucleon-density response function of $^{12}$C, neglecting collective excitations. We employ particle and hole spectral functions obtained within two distinct many-body methods, both widely used to describe electroweak reactions in nuclei. We show that the two approaches provide compatible nucleon-density scaling functions that for large momentum transfers satisfy first-kind scaling. Both methods yield scaling functions characterized by an asymmetric shape, although less pronounced than that of experimental scaling functions. This asymmetry, only mildly affected by final state interactions, is mostly due to nucleon-nucleon correlations, encoded in the continuum component of the hole SF., 15 pages, 11 figures

Quasielastic neutrino scattering is an important aspect of the experimental program to study fundamental neutrino properties including neutrino masses, mixing angles, mass hierarchy, and charge-conjugation parity (CP)- violating phase. Proper interpretation of the experiments requires reliable theoretical calculations of neutrino-nucleus scattering. In this paper we present calculations of response functions and cross sections by neutral-current scattering of neutrinos off $^{12}\mathrm{C}$. These calculations are based on realistic treatments of nuclear interactions and currents, the latter including the axial, vector, and vector-axial interference terms crucial for determining the difference between neutrino and antineutrino scattering and the CP-violating phase. We find that the strength and energy dependence of two-nucleon processes induced by correlation effects and interaction currents are crucial in providing the most accurate description of neutrino-nucleus scattering in the quasielastic regime.

We have studied the scaling properties of the electromagnetic response functions of $^4$He and $^{12}$C nuclei computed by the Green's Function Monte Carlo approach, retaining only the one-body current contribution. Longitudinal and transverse scaling functions have been obtained in the relativistic and non relativistic cases and compared to experiment for various kinematics. The characteristic asymmetric shape of the scaling function exhibited by data emerges in the calculations in spite of the non relativistic nature of the model. The results are consistent with scaling of zeroth, first and second kinds. Our analysis reveals a direct correspondence between the scaling and the nucleon-density response functions., 11 pages, 15 figures

The electromagnetic responses of carbon obtained from the Green's function Monte Carlo and spectral function approaches using the same dynamical input are compared in the kinematical region corresponding to momentum transfer in the range 300--570 MeV. The results of our analysis, aimed at pinning down the limits of applicability of the approximations involved in the two schemes, indicate that the factorization ansatz underlying the spectral function formalism provides remarkably accurate results down to momentum transfer as low as 300 MeV. On the other hand, it appears that at 570 MeV relativistic corrections to the electromagnetic current not included in the Monte Carlo calculations may play a significant role in the transverse channel.

The longitudinal and transverse electromagnetic response functions of ^{12}C are computed in a "first-principles" Green's function Monte Carlo calculation, based on realistic two- and three-nucleon interactions and associated one- and two-body currents. We find excellent agreement between theory and experiment and, in particular, no evidence for the quenching of the measured versus calculated longitudinal response. This is further corroborated by a reanalysis of the Coulomb sum rule, in which the contributions from the low-lying J^{π}=2^{+}, 0_{2}^{+} (Hoyle), and 4^{+} states in ^{12}C are accounted for explicitly in evaluating the total inelastic strength.

The formalism based on factorization and nuclear spectral functions has been generalized to treat transition matrix elements involving two-nucleon currents, whose contribution to the nuclear electromagnetic response in the transverse channel is known to be significant. We report the results of calculations of the inclusive electron-carbon cross section, showing that the inclusion of processes involving two-nucleon currents appreciably improves the agreement between theory and data in the dip region, between the quasielastic and Δ-production peaks. The relation to approaches based on the independent particle of the nucleus and the implications for the analysis of flux-integrated neutrino-nucleus cross sections are discussed.

The excitation of two particle-two hole final states in neutrino-nucleus scattering has been advocated by many authors as the source of the excess cross section observed by the MiniBooNE Collaboration in the quasi elastic sector. We analyse the mechanisms leading to the appearance of these final states, and illustrate their significance through the results of accurate calculations of the nuclear electromagnetic response in the transverse channel. A novel approach, allowing for a consistent treatment of the amplitudes involving one- and two-nucleon currents in the kinematical region in which the non relativistic approximation breaks down, is outlined., Comment: Physical Review C, in press. arXiv admin note: text overlap with arXiv:1312.1210

The authors calculate $a\phantom{\rule{0}{0ex}}b$-$i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ quasi-elastic electromagnetic and neutral-weak response functions for $A=4$ and $A=12$ nuclei by using realistic nuclear two- and three-body forces and one- and two-body electroweak currents, in combination with quantum Monte Carlo methods and maximum-entropy techniques. In the electromagnetic case, their novel approach allows a direct comparison with experimental data. The results challenge the conventional picture that quasi-elastic inclusive scattering is dominated by single-nucleon knockout.

The formalism based on correlated basis functions and the cluster expansion technique has been recently employed to derive an effective interaction from a realistic nuclear hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground state energy, the effective mass and the momentum distribution, shows that the effective interaction approach is remarkably accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications., Comment: 10 pages, 13 figures

An ab initio calculation of the sum rules of the neutral weak response functions in 12C is reported, based on a realistic Hamiltonian, including two- and three-nucleon potentials, and on realistic currents, consisting of one- and two-body terms. We find that the sum rules of the response functions associated with the longitudinal and transverse components of the (spacelike) neutral current are largest and that a significant portion (≃30%) of the calculated strength is due to two-body terms. This fact may have implications for the MiniBooNE and other neutrino quasielastic scattering data on nuclei.

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter and symmetric nuclear matter obtained using these models of three-nucleon forces. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. The ambiguity concerning the treatment of the contact term of the chiral inspired potentials is discussed., Comment: 14 pages, 8 figures