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Title: Quantum Monte Carlo formalism for dynamical pions and nucleons

Abstract

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schrodinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, a Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.

Authors:
; ; ;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE Office of Science - Office of Nuclear Physics
OSTI Identifier:
1595682
DOE Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article
Journal Name:
Physical Review. C, Nuclear Physics
Additional Journal Information:
Journal Volume: 98; Journal Issue: 3
Country of Publication:
United States
Language:
English

Citation Formats

Madeira, Lucas, Lovato, Alessandro, Pederiva, Francesco, and Schmidt, Kevin E. Quantum Monte Carlo formalism for dynamical pions and nucleons. United States: N. p., 2018. Web. doi:10.1103/PhysRevC.98.034005.
Madeira, Lucas, Lovato, Alessandro, Pederiva, Francesco, & Schmidt, Kevin E. Quantum Monte Carlo formalism for dynamical pions and nucleons. United States. doi:10.1103/PhysRevC.98.034005.
Madeira, Lucas, Lovato, Alessandro, Pederiva, Francesco, and Schmidt, Kevin E. Thu . "Quantum Monte Carlo formalism for dynamical pions and nucleons". United States. doi:10.1103/PhysRevC.98.034005.
@article{osti_1595682,
title = {Quantum Monte Carlo formalism for dynamical pions and nucleons},
author = {Madeira, Lucas and Lovato, Alessandro and Pederiva, Francesco and Schmidt, Kevin E.},
abstractNote = {In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schrodinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, a Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.},
doi = {10.1103/PhysRevC.98.034005},
journal = {Physical Review. C, Nuclear Physics},
number = 3,
volume = 98,
place = {United States},
year = {2018},
month = {9}
}

Works referenced in this record:

Modern theory of nuclear forces
journal, December 2009


Chiral effective field theory and nuclear forces
journal, June 2011


Ab initio no core shell model
journal, March 2013

  • Barrett, Bruce R.; Navrátil, Petr; Vary, James P.
  • Progress in Particle and Nuclear Physics, Vol. 69
  • DOI: 10.1016/j.ppnp.2012.10.003

Ab Initio Calculation of the Hoyle State
journal, May 2011


Coupled-cluster computations of atomic nuclei
journal, September 2014


The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
journal, March 2016


Self-consistent Green's functions formalism with three-body interactions
journal, November 2013


Quantum Monte Carlo methods for nuclear physics
journal, September 2015


Unified Approach for Molecular Dynamics and Density-Functional Theory
journal, November 1985


Lattice simulations for light nuclei: Chiral effective field theory at leading order
journal, January 2007


Lattice simulations for few- and many-body systems
journal, July 2009


Slow Electrons in a Polar Crystal
journal, February 1955


Nuclear forces from chiral lagrangians
journal, November 1990


Bethe–Salpeter approach for unitarized chiral perturbation theory
journal, November 2000


Nucleon-nucleon scattering from effective field theory
journal, November 1996


Renormalization of one-pion exchange and power counting
journal, November 2005


Renormalization of the NN interaction with a chiral two-pion-exchange potential: Central phases and the deuteron
journal, November 2006


On the Renormalization of the One–Pion Exchange Potential and the Consistency of Weinberg’s Power Counting
journal, October 2012


Triton binding energy and neutron-deuteron scattering up to next-to-leading order in chiral effective field theory
journal, August 2017


Chiral perturbation theory: Introduction and recent results in the one-nucleon sector
journal, January 2010


Green’s function Monte Carlo study of light nuclei
journal, November 1987


A quantum Monte Carlo method for nucleon systems
journal, January 1999


Local chiral effective field theory interactions and quantum Monte Carlo applications
journal, November 2014


Comparative study of three-nucleon potentials in nuclear matter
journal, February 2012


Analyzing the Fierz rearrangement freedom for local chiral two-nucleon potentials
journal, November 2017


On the pion-deuteron scattering length
journal, June 1978


Three-body interactions among nucleons and pions
journal, November 1992


Neutron Matter at Next-to-Next-to-Next-to-Leading Order in Chiral Effective Field Theory
journal, January 2013


Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions
journal, July 2013


Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions
journal, November 2017


Optimization of quantum Monte Carlo wave functions by energy minimization
journal, February 2007

  • Toulouse, Julien; Umrigar, C. J.
  • The Journal of Chemical Physics, Vol. 126, Issue 8
  • DOI: 10.1063/1.2437215

Ground-state properties of 4 He and 16 O extrapolated from lattice QCD with pionless EFT
journal, September 2017


Model fermion Monte Carlo with correlated pairs. II
journal, October 1997

  • Kalos, M. H.; Schmidt, K. E.
  • Journal of Statistical Physics, Vol. 89, Issue 1-2
  • DOI: 10.1007/BF02770774

Neutron matter at zero temperature with an auxiliary field diffusion Monte Carlo method
journal, August 2003


Unbiased estimators in quantum Monte Carlo methods: Application to liquid He 4
journal, August 1995


Accurate nucleon-nucleon potential with charge-independence breaking
journal, January 1995

  • Wiringa, R. B.; Stoks, V. G. J.; Schiavilla, R.
  • Physical Review C, Vol. 51, Issue 1
  • DOI: 10.1103/PhysRevC.51.38

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991


Volume dependence of N -body bound states
journal, April 2018


An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
journal, October 1950

  • Lanczos, C.
  • Journal of Research of the National Bureau of Standards, Vol. 45, Issue 4
  • DOI: 10.6028/jres.045.026

Low-energy analysis of the nucleon electromagnetic form factors
journal, January 2001