Quantum Monte Carlo methods for nuclear physics (1412.3081v2)

Abstract: 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.

• The paper demonstrates that QMC methods yield high-precision predictions of nuclear structure and interactions using realistic nucleon-nucleon and three-nucleon forces.
• It employs VMC and GFMC techniques to capture both long-range clustering and short-range correlations, including tensor forces and spin-isospin interactions.
• The study validates QMC methods by reproducing experimental data and informing equations of state critical to understanding neutron star properties.

Quantum Monte Carlo Methods for Nuclear Physics: An Overview

The paper "Quantum Monte Carlo methods for nuclear physics," authored by J. Carlson, S. Gandolfi, and colleagues, provides a comprehensive review of Quantum Monte Carlo (QMC) techniques as applied to the paper of nuclear systems. These methods have demonstrated significant effectiveness in exploring the structure and interactions of light nuclei and dense nuclear matter, offering predictions grounded in realistic nuclear interactions and currents.

QMC methods, particularly Variational Monte Carlo (VMC) and Green's Function Monte Carlo (GFMC), have been pivotal in achieving high-precision calculations of light nuclear systems. These techniques enable the treatment of many-body quantum systems, facilitating the exploration of nuclear phenomena such as spectra, form factors, and electroweak responses. The paper illustrates that QMC methodologies capture both long-range cluster aspects and short-range correlations, including tensor forces and spin-isospin interactions that are crucial for an accurate depiction of nuclear environments.

The authors detail the adaptability of QMC methods for dense matter studies, such as neutron matter, which is pivotal in understanding neutron stars' properties. The incorporation of realistic Hamiltonians, including nucleon-nucleon (NN), and three-nucleon (3N) interactions, such as the Argonne $v_{18}$ and Illinois models, are discussed. Such interactions are shown to successfully reproduce experimental data, thereby validating the application of QMC techniques to derive insights into nuclear matter's equation of state (EOS). The resulting predictions contribute significantly to neutron stars' radius and mass calculations, aligning with recent astrophysical observations.

The paper addresses the role of nuclear interactions at various momentum scales, highlighting the challenges posed by the strong coupling of spin and spatial degrees of freedom in nuclear environments. The authors emphasize the need for diverse phenomena to be treated coherently within a unified framework. Analyzing nuclear electroweak response functions and low-energy scattering, these methods reveal the critical nature of two-body currents and many-body forces in interpreting electron and neutrino scattering experiments. Notably, they highlight the importance of meson-exchange currents, non-impulse approximations, and spin-orbit effects, which contribute significantly to observables like magnetic moments and form factors.

Progress in the field has been attributed to the advancements in computational methodologies and high-performance computing capabilities. The future of QMC applications in nuclear physics is promising, with potential expansions to heavier nuclei and refined studies of superfluidity and clustering properties in both finite nuclei and infinite nuclear matter. The implications for artificial and astrophysical nuclear processes are profound, providing a framework for understanding phenomena such as beta decay, neutrinoless double-beta decay, and the intricate architectures of neutron stars.

The research underscored by Carlson et al. marks a pivotal advancement in computational nuclear physics, setting the stage for future explorations that integrate next-generation computational resources and further refined interaction models. This trajectory is expected to yield new insights into both fundamental nuclear physics and its cosmological and astrophysical applications. The continuing development of QMC techniques thus represents a cornerstone for both theoretical advancements and the interpretation of empirical data across various nuclear domains.