Quantum Monte Carlo methods for nuclear physics

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.

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

“…While this V low−k framework is an extremely appealing setup based on Wilsonian renormalization, to date this universal interaction has not been determined from data directly and one has to proceed via a fitted and bare N N interaction since off-shellness is required [17]. However, inferring a N N interaction from data, is not the full story, and three-nucleon, and possibly higher multi-nucleon, interactions are needed to describe residual contributions to nuclear binding energies [18]. As is well known, their strength and form are also affected by the chosen off-shell behavior of the N N interaction and a universal V low−k three-nucleon interaction remains to be found.…”

The EOS of Neutron Matter and the Effect of Λ Hyperons to Neutron Star Structure

“…Although simpler to use in QMC calculations, the AV8' provides almost the same accuracy as AV18 in fitting NN scattering data. The three-body force is not as well constrained as the NN interaction, but its inclusion in realistic nuclear Hamiltonians is important to correctly describe the binding energy of light nuclei [8]. The Urbana IX (UIX) three-body force has been originally proposed in combination with the Argonne AV18 and AV8' [12].…”

The Hyperon Puzzle in Neutron Stars

“…A very promising ab initio many-body approach to determine the hyperonic matter EoS is the quantum Monte Carlo method (see [51] for a review). Recently a first attempt to solve the hyperon puzzle, within this approach, has been performed in [48], where the EoS of an infinite system of neutrons and Λ particles (nΛ-matter) has been considered as an approximation of the more realis-tic situation of β-stable hyperonic matter.…”