skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables

Abstract

The traditional approach to nuclear physics encodes phase shift information in a nucleon-nucleon (NN) potential, producing a nucleon-level interaction that captures the sub-GeV consequences of QCD. A further reduction to the nuclear scale is needed to produce an effective interaction for soft Hilbert spaces, such as those employed in the shell model. Here we describe an alternative construction of the effective interaction that is simple and quite precise, proceeding from the QCD scale directly to the nuclear scale. This eliminates the need for constructing and renormalizing the high-momentum NN potential. Instead, continuum phase shifts and mixing angles are used directly at the nuclear scale. The method exploits the analytic continuity in energy of HOBET (Harmonic-Oscillator-Based Effective Theory) to connect bound states to continuum solutions at specific energies. The procedure is systematic, cutoff independent, and convergent, yielding keV accuracy at NNLO or N3LO, depending on the channel. Lepage plots are provided.

Authors:
ORCiD logo;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1559062
Alternate Identifier(s):
OSTI ID: 1580933
Grant/Contract Number:  
SC00046548; AC02-05CH11231; KB0301052; SC0015376
Resource Type:
Published Article
Journal Name:
Physics Letters B
Additional Journal Information:
Journal Name: Physics Letters B Journal Volume: 797 Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Country of Publication:
Netherlands
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Effective theory; Nucleon-nucleon interaction; Phase shifts

Citation Formats

McElvain, K. S., and Haxton, W. C. Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables. Netherlands: N. p., 2019. Web. https://doi.org/10.1016/j.physletb.2019.134880.
McElvain, K. S., & Haxton, W. C. Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables. Netherlands. https://doi.org/10.1016/j.physletb.2019.134880
McElvain, K. S., and Haxton, W. C. Tue . "Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables". Netherlands. https://doi.org/10.1016/j.physletb.2019.134880.
@article{osti_1559062,
title = {Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables},
author = {McElvain, K. S. and Haxton, W. C.},
abstractNote = {The traditional approach to nuclear physics encodes phase shift information in a nucleon-nucleon (NN) potential, producing a nucleon-level interaction that captures the sub-GeV consequences of QCD. A further reduction to the nuclear scale is needed to produce an effective interaction for soft Hilbert spaces, such as those employed in the shell model. Here we describe an alternative construction of the effective interaction that is simple and quite precise, proceeding from the QCD scale directly to the nuclear scale. This eliminates the need for constructing and renormalizing the high-momentum NN potential. Instead, continuum phase shifts and mixing angles are used directly at the nuclear scale. The method exploits the analytic continuity in energy of HOBET (Harmonic-Oscillator-Based Effective Theory) to connect bound states to continuum solutions at specific energies. The procedure is systematic, cutoff independent, and convergent, yielding keV accuracy at NNLO or N3LO, depending on the channel. Lepage plots are provided.},
doi = {10.1016/j.physletb.2019.134880},
journal = {Physics Letters B},
number = C,
volume = 797,
place = {Netherlands},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.physletb.2019.134880

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Nucleon-nucleon effective field theory without pions
journal, July 1999


Sur la détermination des premiers états d'un système de fermions dans le cas dégénéré
journal, September 1958


Variational calculations using low-momentum potentials with smooth cutoffs
journal, August 2006


Form of the effective interaction in harmonic-oscillator-based effective theory
journal, March 2008


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

Is nuclear matter perturbative with low-momentum interactions?
journal, December 2005


The effective interaction of two nucleons in the s-d shell
journal, April 1980


Linked-Cluster Expansions for the Nuclear Many-Body Problem
journal, October 1967


Morphing the Shell Model into an Effective Theory
journal, June 2000


Variational calculations of nuclei with low-momentum potentials
journal, January 2006


Perturbative Effective Theory in an Oscillator Basis?
journal, October 2002


Recent developments in no-core shell-model calculations
journal, May 2009

  • Navrátil, Petr; Quaglioni, Sofia; Stetcu, Ionel
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 8
  • DOI: 10.1088/0954-3899/36/8/083101

Spin–orbit force from lattice QCD
journal, July 2014


Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI
journal, December 2001


Projection operator formalisms and the nuclear shell model
journal, October 2005


Renormalization of Hamiltonians
journal, December 1993


Coupled-cluster computations of atomic nuclei
journal, September 2014


Effective interactions for the three-body problem
journal, July 2004


Structure of finite nuclei and the free nucleon-nucleon interaction
journal, September 1966


Third-order perturbation calculations in nuclear matter for realistic potentials
journal, November 1976


Large-basis ab initio no-core shell model and its application to 12 C
journal, October 2000


Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry
journal, August 2013


Chiral potential renormalized in harmonic-oscillator space
journal, December 2016


Convergence of the Born series with low-momentum interactions
journal, July 2006


Computation of spectroscopic factors with the coupled-cluster method
journal, July 2010


Chiral effective field theory and nuclear forces
journal, June 2011


Similarity renormalization group for nucleon-nucleon interactions
journal, June 2007


No-core shell model in an effective-field-theory framework
journal, September 2007


Modern theory of nuclear forces
journal, December 2009


Low-momentum interaction in few-nucleon systems
journal, December 2004


Diffuse Surface Optical Model for Nucleon-Nuclei Scattering
journal, July 1954


Convergent Theory for Effective Interaction in Nuclei
journal, December 1980

  • Suzuki, K.; Lee, S. Y.
  • Progress of Theoretical Physics, Vol. 64, Issue 6
  • DOI: 10.1143/PTP.64.2091

Coupled-cluster approach to nuclear physics
journal, May 2004


Perturbative renormalization group for Hamiltonians
journal, April 1994


Two-nucleon higher partial-wave scattering from lattice QCD
journal, February 2017


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


Three-nucleon forces from chiral effective field theory
journal, December 2002


Perturbation theory for the effective interaction in nuclei
journal, April 1973


Decoupling in the similarity renormalization group for nucleon-nucleon forces
journal, July 2008


The canonical nuclear many-body problem as an effective theory
journal, July 2001


Nuclear Many-Body Problem
journal, September 1956


The effective interaction in nuclei and its perturbation expansion: An algebraic approach
journal, September 1972


High-precision, charge-dependent Bonn nucleon-nucleon potential
journal, January 2001


Neutron-Proton Scattering with Spin-Orbit Coupling. I. General Expressions
journal, May 1952


Pion-less effective field theory for atomic nuclei and lattice nuclei
journal, November 2018


Off-Shell Effects in Nuclear Matter
journal, February 1971


Family of Hermitian low-momentum nucleon interactions with phase shift equivalence
journal, March 2004


Two Pion versus σ-Meson Exchange Potentials
journal, January 2015

  • Oshima, Sachiko; Fujita, Takehisa; Kanda, Naohiro
  • Journal of Modern Physics, Vol. 06, Issue 07
  • DOI: 10.4236/jmp.2015.67097