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}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
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