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. As a result, we show that the method can be readily applied to light-nuclei.
- Authors:
-
- Arizona State Univ., Tempe, AZ (United States)
- Trento Institute for Fundamental Physics and Applications, Trento (Italy); Argonne National Lab. (ANL), Argonne, IL (United States)
- Trento Institute for Fundamental Physics and Applications, Trento (Italy); Univ. of Trento, Trento (Italy)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)
- OSTI Identifier:
- 1488383
- Alternate Identifier(s):
- OSTI ID: 1474192
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review C
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
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. https://www.osti.gov/servlets/purl/1488383.
@article{osti_1488383,
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. As a result, we show that the method can be readily applied to light-nuclei.},
doi = {10.1103/PHYsRevC.98.034005},
journal = {Physical Review C},
number = 3,
volume = 98,
place = {United States},
year = {2018},
month = {9}
}
Web of Science
Works referenced in this record:
Three-body interactions among nucleons and pions
journal, November 1992
- Weinberg, Steven
- Physics Letters B, Vol. 295, Issue 1-2
On the Renormalization of the One–Pion Exchange Potential and the Consistency of Weinberg’s Power Counting
journal, October 2012
- Epelbaum, E.; Meißner, Ulf-G.
- Few-Body Systems, Vol. 54, Issue 12
A quantum Monte Carlo method for nucleon systems
journal, January 1999
- Schmidt, K. E.; Fantoni, S.
- Physics Letters B, Vol. 446, Issue 2
Nuclear forces from chiral lagrangians
journal, November 1990
- Weinberg, Steven
- Physics Letters B, Vol. 251, Issue 2
Chiral effective field theory and nuclear forces
journal, June 2011
- Machleidt, R.; Entem, D. R.
- Physics Reports, Vol. 503, Issue 1
Ab Initio Calculation of the Hoyle State
journal, May 2011
- Epelbaum, Evgeny; Krebs, Hermann; Lee, Dean
- Physical Review Letters, Vol. 106, Issue 19
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
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
Nucleon-nucleon scattering from effective field theory
journal, November 1996
- Kaplan, David B.; Savage, Martin J.; Wise, Mark B.
- Nuclear Physics B, Vol. 478, Issue 3
Unbiased estimators in quantum Monte Carlo methods: Application to liquid
journal, August 1995
- Casulleras, J.; Boronat, J.
- Physical Review B, Vol. 52, Issue 5
Low-energy analysis of the nucleon electromagnetic form factors
journal, January 2001
- Kubis, Bastian; Meißner, Ulf-G.
- Nuclear Physics A, Vol. 679, Issue 3-4
Slow Electrons in a Polar Crystal
journal, February 1955
- Feynman, R. P.
- Physical Review, Vol. 97, Issue 3
Local chiral effective field theory interactions and quantum Monte Carlo applications
journal, November 2014
- Gezerlis, A.; Tews, I.; Epelbaum, E.
- Physical Review C, Vol. 90, Issue 5
Modern theory of nuclear forces
journal, December 2009
- Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G.
- Reviews of Modern Physics, Vol. 81, Issue 4
Ground-state properties of 4 He and 16 O extrapolated from lattice QCD with pionless EFT
journal, September 2017
- Contessi, L.; Lovato, A.; Pederiva, F.
- Physics Letters B, Vol. 772
Renormalization of one-pion exchange and power counting
journal, November 2005
- Nogga, A.; Timmermans, R. G. E.; Kolck, U. van
- Physical Review C, Vol. 72, Issue 5
Green’s function Monte Carlo study of light nuclei
journal, November 1987
- Carlson, J.
- Physical Review C, Vol. 36, Issue 5
Renormalization of the interaction with a chiral two-pion-exchange potential: Central phases and the deuteron
journal, November 2006
- Pavón Valderrama, M.; Arriola, E. Ruiz
- Physical Review C, Vol. 74, Issue 5
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
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
journal, March 2016
- Hergert, H.; Bogner, S. K.; Morris, T. D.
- Physics Reports, Vol. 621
Lattice simulations for few- and many-body systems
journal, July 2009
- Lee, Dean
- Progress in Particle and Nuclear Physics, Vol. 63, Issue 1
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
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
Neutron matter at zero temperature with an auxiliary field diffusion Monte Carlo method
journal, August 2003
- Sarsa, A.; Fantoni, S.; Schmidt, K. E.
- Physical Review C, Vol. 68, Issue 2
Chiral perturbation theory: Introduction and recent results in the one-nucleon sector
journal, January 2010
- Scherer, S.
- Progress in Particle and Nuclear Physics, Vol. 64, Issue 1
Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions
journal, November 2017
- Lynn, J. E.; Tews, I.; Carlson, J.
- Physical Review C, Vol. 96, Issue 5
Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991
- Lüscher, Martin
- Nuclear Physics B, Vol. 354, Issue 2-3
Self-consistent Green's functions formalism with three-body interactions
journal, November 2013
- Carbone, Arianna; Cipollone, Andrea; Barbieri, Carlo
- Physical Review C, Vol. 88, Issue 5
Lattice simulations for light nuclei: Chiral effective field theory at leading order
journal, January 2007
- Borasoy, B.; Epelbaum, E.; Krebs, H.
- The European Physical Journal A, Vol. 31, Issue 1
Analyzing the Fierz rearrangement freedom for local chiral two-nucleon potentials
journal, November 2017
- Huth, L.; Tews, I.; Lynn, J. E.
- Physical Review C, Vol. 96, Issue 5
Bethe–Salpeter approach for unitarized chiral perturbation theory
journal, November 2000
- Nieves, J.; Ruiz Arriola, E.
- Nuclear Physics A, Vol. 679, Issue 1
Coupled-cluster computations of atomic nuclei
journal, September 2014
- Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M.
- Reports on Progress in Physics, Vol. 77, Issue 9
Unified Approach for Molecular Dynamics and Density-Functional Theory
journal, November 1985
- Car, R.; Parrinello, M.
- Physical Review Letters, Vol. 55, Issue 22
Comparative study of three-nucleon potentials in nuclear matter
journal, February 2012
- Lovato, Alessandro; Benhar, Omar; Fantoni, Stefano
- Physical Review C, Vol. 85, Issue 2
On the pion-deuteron scattering length
journal, June 1978
- Robilotta, M. R.; Wilkin, C.
- Journal of Physics G: Nuclear Physics, Vol. 4, Issue 6
Volume dependence of N -body bound states
journal, April 2018
- König, Sebastian; Lee, Dean
- Physics Letters B, Vol. 779
Neutron Matter at Next-to-Next-to-Next-to-Leading Order in Chiral Effective Field Theory
journal, January 2013
- Tews, I.; Krüger, T.; Hebeler, K.
- Physical Review Letters, Vol. 110, Issue 3
Quantum Monte Carlo methods for nuclear physics
journal, September 2015
- Carlson, J.; Gandolfi, S.; Pederiva, F.
- Reviews of Modern Physics, Vol. 87, Issue 3
Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions
journal, July 2013
- Gezerlis, A.; Tews, I.; Epelbaum, E.
- Physical Review Letters, Vol. 111, Issue 3
Triton binding energy and neutron-deuteron scattering up to next-to-leading order in chiral effective field theory
journal, August 2017
- Song, Young-Ho; Lazauskas, Rimantas; van Kolck, U.
- Physical Review C, Vol. 96, Issue 2
Works referencing / citing this record:
Electroweak pion production on nuclei within the extended factorization scheme
journal, October 2019
- Rocco, Noemi; Nakamura, Satoshi X.; Lee, T. -S. H.
- Physical Review C, Vol. 100, Issue 4
Neutrino-nucleus cross section within the extended factorization scheme
journal, February 2019
- Rocco, Noemi; Barbieri, Carlo; Benhar, Omar
- Physical Review C, Vol. 99, Issue 2