Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances

Piarulli, M.; Girlanda, L.; Schiavilla, R.; Pérez, R. Navarro; Amaro, J. E.; Arriola, E. Ruiz

doi:10.1103/PhysRevC.91.024003

Title: Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including $Δ$ resonances

Abstract

In this study, we construct a coordinate-space chiral potential, including Δ-isobar intermediate states in its two-pion-exchange component up to order Q³ (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q² and Q⁴, respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constant multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0–300 MeV. For the total 5291 $pp$ and $np$ data in this range, we obtain a Χ² /datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, R_L and R_S respectively, ranging from (R_L,R_S)=(1.2,0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

Authors:

Piarulli, M. ^[1]; Girlanda, L. ^[2]; Schiavilla, R. ^[3]; Pérez, R. Navarro ^[4]; Amaro, J. E. ^[4]; Arriola, E. Ruiz ^[4]

Old Dominion Univ., Norfolk, VA (United States)
Univ. of Salento, Lecce (Italy); INFN-Leece, Leece (Italy)
Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Univ. de Granada, Granada (Spain)

Publication Date:: Thu Feb 26 00:00:00 EST 2015

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1171326

Alternate Identifier(s):: OSTI ID: 1181373

Report Number(s):: JLAB-THY-14-1993; DOE/OR/23177-3257; arXiv:1412.6446
Journal ID: ISSN 0556-2813; PRVCAN; ArticleNumber: 024003

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C, Nuclear Physics

Additional Journal Information:: Journal Volume: 91; Journal Issue: 2; Journal ID: ISSN 0556-2813

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Piarulli, M., Girlanda, L., Schiavilla, R., Pérez, R. Navarro, Amaro, J. E., and Arriola, E. Ruiz. Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevC.91.024003.

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                    Piarulli, M., Girlanda, L., Schiavilla, R., Pérez, R. Navarro, Amaro, J. E., & Arriola, E. Ruiz. Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances.  United States.  https://doi.org/10.1103/PhysRevC.91.024003

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                    Piarulli, M., Girlanda, L., Schiavilla, R., Pérez, R. Navarro, Amaro, J. E., and Arriola, E. Ruiz. Thu .  
"Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances".  United States.  https://doi.org/10.1103/PhysRevC.91.024003.  https://www.osti.gov/servlets/purl/1171326.

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@article{osti_1171326,

  title        = {Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances},

  author       = {Piarulli, M. and Girlanda, L. and Schiavilla, R. and Pérez, R. Navarro and Amaro, J. E. and Arriola, E. Ruiz},

  abstractNote = {In this study, we construct a coordinate-space chiral potential, including Δ-isobar intermediate states in its two-pion-exchange component up to order Q3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q2 and Q4, respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constant multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0–300 MeV. For the total 5291 $pp$ and $np$ data in this range, we obtain a Χ2 /datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, RL and RS respectively, ranging from (RL,RS)=(1.2,0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.},

  doi          = {10.1103/PhysRevC.91.024003},

  journal      = {Physical Review C, Nuclear Physics},

  number       = 2,

  volume       = 91,

  place        = {United States},

  year         = {Thu Feb 26 00:00:00 EST 2015},

  month        = {Thu Feb 26 00:00:00 EST 2015}

}

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Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 9
DOI: 10.1088/1361-6471/ab2b14

Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
journal, May 2018

Reinert, P.; Krebs, H.; Epelbaum, E.
The European Physical Journal A, Vol. 54, Issue 5
DOI: 10.1140/epja/i2018-12516-4

Chiral electroweak currents in nuclei
book, March 2017

Riska, D. O.; Schiavilla, R.
Quarks, Nuclei and Stars
DOI: 10.1142/9789813220669_0021

Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory
journal, January 2020

Piarulli, Maria; Tews, Ingo
Frontiers in Physics, Vol. 7
DOI: 10.3389/fphy.2019.00245

Equations of state for supernovae and compact stars
text, January 2017

Micaela, Oertel,; Matthias, Hempel,; Thomas, Klähn,
American Physical Society
DOI: 10.5451/unibas-ep58112

Nuclear Axial Currents in Chiral Effective Field Theory
text, January 2015

Baroni, A.; Girlanda, L.; Pastore, S.
arXiv
DOI: 10.48550/arxiv.1509.07039

Uncertainty quantification of effective nuclear interactions
preprint, January 2016

Perez, R. Navarro; Amaro, J. E.; Arriola, E. Ruiz
arXiv
DOI: 10.48550/arxiv.1601.08220

Nuclear matter properties from local chiral interactions with $Δ$ isobar intermediate states
text, January 2016

Logoteta, Domenico; Bombaci, Ignazio; Kievsky, Alejandro
arXiv
DOI: 10.48550/arxiv.1609.00649

The falsification of Chiral Nuclear Forces
text, January 2016

Arriola, E. Ruiz; Amaro, J. E.; Perez, R. Navarro
arXiv
DOI: 10.48550/arxiv.1611.02607

Nuclear matter properties with nucleon-nucleon forces up to fifth order in the chiral expansion
text, January 2016

Hu, Jinniu; Zhang, Ying; Epelbaum, Evgeny
arXiv
DOI: 10.48550/arxiv.1612.05433

Perturbation Theory of Nuclear Matter with a Microscopic Effective Interaction
text, January 2017

Benhar, Omar; Lovato, Alessandro
arXiv
DOI: 10.48550/arxiv.1706.00760

Light-nuclei spectra from chiral dynamics
text, January 2017

Piarulli, M.; Baroni, A.; Girlanda, L.
arXiv
DOI: 10.48550/arxiv.1707.02883

Scale dependence of deuteron electrodisintegration
text, January 2017

More, Sushant N.; Bogner, Scott K.; Furnstahl, Richard J.
arXiv
DOI: 10.48550/arxiv.1708.03315

Quantified Gamow Shell Model interaction for $psd$-shell nuclei
text, January 2017

Jaganathen, Y.; Betan, R. M. Id; Michel, N.
arXiv
DOI: 10.48550/arxiv.1710.04727

Historical perspective and future prospects for nuclear interactions
text, January 2017

Machleidt, R.
arXiv
DOI: 10.48550/arxiv.1710.07215

Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation
text, January 2018

Perez, R. Navarro; Schunck, N.; Dyhdalo, A.
arXiv
DOI: 10.48550/arxiv.1801.08615

Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
text, January 2018

Binder, S.; Calci, A.; Epelbaum, E.
arXiv
DOI: 10.48550/arxiv.1802.08584

A new leading contribution to neutrinoless double-beta decay
text, January 2018

Cirigliano, V.; Dekens, W.; de Vries, J.
arXiv
DOI: 10.48550/arxiv.1802.10097

Bayesian optimization in ab initio nuclear physics
text, January 2019

Ekström, A.; Forssén, C.; Dimitrakakis, C.
arXiv
DOI: 10.48550/arxiv.1902.00941

Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
text, January 2020

Piarulli, Maria; Tews, Ingo
arXiv
DOI: 10.48550/arxiv.2002.00032

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Title: Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances

Abstract

Citation Formats

Phase-Shift Analysis of 310-Mev Proton-Proton Scattering Experiments journal, January 1957

Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV journal, August 1993

Construction of high-quality NN potential models journal, June 1994

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

Chiral Two-Pion Exchange and Proton-Proton Partial-Wave Analysis journal, June 1999

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

Determination of the chiral coupling constants c 3 and c 4 in new pp and np partial-wave analyses journal, April 2003

Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV journal, July 2008

Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold journal, December 2013

Coarse-grained NN potential with chiral two-pion exchange journal, February 2014

Statistical error analysis for phenomenological nucleon-nucleon potentials journal, June 2014

Inverse Problems in Quantum Scattering Theory book, January 1989

Single- and coupled-channel radial inverse scattering with supersymmetric transformations journal, June 2014

Towards a model-independent low momentum nucleon–nucleon interaction journal, December 2003

Model-independent low momentum nucleon interaction from phase shift equivalence journal, October 2003

Implicit and explicit renormalization: Two complementary views of effective interactions journal, February 2015

Nuclear Force and Nuclear Physics from Lattice Quantum Chromodynamics journal, September 2012

Determination of the NN π coupling constants in NN partial-wave analyses journal, October 1991

Nuclear forces from chiral lagrangians journal, November 1990

Chiral effective field theory and nuclear forces journal, June 2011

Peripheral nucleon-nucleon phase shifts and chiral symmetry journal, November 1997

Electromagnetic two-body currents of one- and two-pion range journal, December 2008

Effects of Δ-isobar degrees of freedom on low-energy electroweak transitions in few-body nuclei journal, June 1992

Theoretical study of the radiative capture reactions H 2 ( n ,γ ) 3 H and H 2 ( p ,γ ) 3 He at low energies journal, August 1996

Thermal Neutron Captures on d and He 3 journal, November 2010

Weak proton capture on 3 He journal, December 2000

Formalism of nucleon-nucleon elastic scattering experiments journal, January 1978

Nucleon-nucleon phase shift analysis journal, January 1987

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory journal, October 2003

The two-nucleon system at next-to-next-to-next-to-leading order journal, January 2005

Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory journal, January 2015

Bootstrapping the statistical uncertainties of NN scattering data journal, November 2014

Nuclear forces from chiral Lagrangians using the method of unitary transformation (I): Formalism journal, July 1998

Electromagnetic currents and magnetic moments in chiral effective field theory ( χ EFT ) journal, September 2009

Chiral effective field theory analysis of hadronic parity violation in few-nucleon systems journal, June 2014

Peripheral NN-scattering: role of delta-excitation, correlated two-pion and vector meson exchange journal, July 1998

Nuclear forces with Δ excitations up to next-to-next-to-leading order, part I: Peripheral nucleon-nucleon waves journal, May 2007

Improving the convergence of the chiral expansion for nuclear forces - I: Peripheral phases journal, January 2004

Nucleon resonance in nuclei journal, December 1976

The Chiral Effective Pion-Nucleon Lagrangian of Order p4 journal, August 2000

Renormalization of chiral two-pion exchange NN interactions with Δ excitations: Central phases and the deuteron journal, April 2009

Renormalization of chiral two-pion exchange NN interactions with Δ excitations: Correlations in the partial-wave expansion journal, April 2011

Nucleon-mass difference in chiral perturbation theory and nuclear forces journal, October 2004

Isospin-violating nucleon-nucleon forces using the method of unitary transformation journal, October 2005

Electromagnetic Corrections to the One-Pion-Exchange Potential journal, May 1998

Pion-photon exchange nucleon-nucleon potentials journal, April 2006

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

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

Magnetic moment interaction in nucleon-nucleon phase-shift analyses journal, October 1990

Charge symmetry, quarks and mesons journal, October 1990

Nuclear energy density optimization journal, August 2010

Neutron-deuteron breakup experiment at E n = 13 MeV : Determination of the 1 S 0 neutron-neutron scattering length a nn journal, March 2006

Measurement of the neutron-neutron scattering length using the π − d capture reaction journal, May 2008

The deuteron binding energy journal, May 1982

The deuteron asymptotic D-state as a probe of the nucleon-nucleon force journal, September 1983

Asymptotic D -state to S -state ratio of the deuteron journal, March 1990

Hydrogen-Deuterium 1 S − 2 S Isotope Shift and the Structure of the Deuteron journal, January 1998

Quadrupole moment of the deuteron from a precise calculation of the electric field gradient in D 2 journal, August 1979

Electromagnetic structure of A = 2 and 3 nuclei in chiral effective field theory journal, January 2013

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states journal, May 2008

Phase shift analysis of 0 – 30 MeV pp scattering data journal, July 1988

Proton-Proton Effective-Range Theory with Vacuum Polarization journal, October 1960

Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV text, January 2008

Chiral effective field theory and nuclear forces text, January 2011

Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions text, January 2013

Single- and coupled-channel radial inverse scattering with supersymmetric transformations text, January 2014

The chiral effective pion-nucleon Lagrangian of order p^4 text, January 2000

Weak proton capture on 3He text, January 2000

Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction text, January 2001

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory text, January 2003

Improving the convergence of the chiral expansion for nuclear forces I: Peripheral phases text, January 2003

Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves text, January 2007

An accurate nucleon-nucleon potential with charge-independence breaking text, January 1994

Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry text, January 1997

Electromagnetic Corrections to the One-Pion-Exchange Potential text, January 1997

Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism text, January 1998

Peripheral NN-Scattering: Role of Delta-Excitation, Correlated Two-Pion and Vector Meson Exchange text, January 1998

Title: Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including $Δ$ resonances

Phase-Shift Analysis of 310-Mev Proton-Proton Scattering Experiments
journal, January 1957

Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV
journal, August 1993

Construction of high-quality NN potential models
journal, June 1994

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

Chiral Two-Pion Exchange and Proton-Proton Partial-Wave Analysis
journal, June 1999

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

Determination of the chiral coupling constants $c_{3}$ and $c_{4}$ in new $pp$ and $np$ partial-wave analyses
journal, April 2003

Covariant spectator theory of $np$ scattering: Phase shifts obtained from precision fits to data below 350 MeV
journal, July 2008

Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold
journal, December 2013

Coarse-grained NN potential with chiral two-pion exchange
journal, February 2014

Statistical error analysis for phenomenological nucleon-nucleon potentials
journal, June 2014

Inverse Problems in Quantum Scattering Theory
book, January 1989

Single- and coupled-channel radial inverse scattering with supersymmetric transformations
journal, June 2014

Towards a model-independent low momentum nucleon–nucleon interaction
journal, December 2003

Model-independent low momentum nucleon interaction from phase shift equivalence
journal, October 2003

Implicit and explicit renormalization: Two complementary views of effective interactions
journal, February 2015

Nuclear Force and Nuclear Physics from Lattice Quantum Chromodynamics
journal, September 2012

Determination of the NN π coupling constants in NN partial-wave analyses
journal, October 1991

Nuclear forces from chiral lagrangians
journal, November 1990

Chiral effective field theory and nuclear forces
journal, June 2011

Peripheral nucleon-nucleon phase shifts and chiral symmetry
journal, November 1997

Electromagnetic two-body currents of one- and two-pion range
journal, December 2008

Effects of Δ-isobar degrees of freedom on low-energy electroweak transitions in few-body nuclei
journal, June 1992

Theoretical study of the radiative capture reactions ${}^{2}H$ ( n ,γ $)^{3}$ H and ${}^{2}H$ ( p ,γ $)^{3}$ He at low energies
journal, August 1996

Thermal Neutron Captures on $d$ and ${}^{3}{He}$
journal, November 2010

Weak proton capture on $^{3} He$
journal, December 2000

Formalism of nucleon-nucleon elastic scattering experiments
journal, January 1978

Nucleon-nucleon phase shift analysis
journal, January 1987

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory
journal, October 2003

The two-nucleon system at next-to-next-to-next-to-leading order
journal, January 2005

Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
journal, January 2015

Bootstrapping the statistical uncertainties of NN scattering data
journal, November 2014

Nuclear forces from chiral Lagrangians using the method of unitary transformation (I): Formalism
journal, July 1998

Electromagnetic currents and magnetic moments in chiral effective field theory $(χ EFT)$
journal, September 2009

Chiral effective field theory analysis of hadronic parity violation in few-nucleon systems
journal, June 2014

Peripheral NN-scattering: role of delta-excitation, correlated two-pion and vector meson exchange
journal, July 1998

Nuclear forces with Δ excitations up to next-to-next-to-leading order, part I: Peripheral nucleon-nucleon waves
journal, May 2007

Improving the convergence of the chiral expansion for nuclear forces - I: Peripheral phases
journal, January 2004

Nucleon resonance in nuclei
journal, December 1976

The Chiral Effective Pion-Nucleon Lagrangian of Order p4
journal, August 2000

Renormalization of chiral two-pion exchange $NN$ interactions with Δ excitations: Central phases and the deuteron
journal, April 2009

Renormalization of chiral two-pion exchange $NN$ interactions with $Δ$ excitations: Correlations in the partial-wave expansion
journal, April 2011

Nucleon-mass difference in chiral perturbation theory and nuclear forces
journal, October 2004

Isospin-violating nucleon-nucleon forces using the method of unitary transformation
journal, October 2005

Electromagnetic Corrections to the One-Pion-Exchange Potential
journal, May 1998

Pion-photon exchange nucleon-nucleon potentials
journal, April 2006

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

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

Magnetic moment interaction in nucleon-nucleon phase-shift analyses
journal, October 1990

Charge symmetry, quarks and mesons
journal, October 1990

Nuclear energy density optimization
journal, August 2010

Neutron-deuteron breakup experiment at $E_{n} = 13 MeV$ : Determination of the $^{1} S_{0}$ neutron-neutron scattering length $a_{nn}$
journal, March 2006

Measurement of the neutron-neutron scattering length using the $π^{-} d$ capture reaction
journal, May 2008

The deuteron binding energy
journal, May 1982

The deuteron asymptotic D-state as a probe of the nucleon-nucleon force
journal, September 1983

Asymptotic D -state to S -state ratio of the deuteron
journal, March 1990

Hydrogen-Deuterium $1 S - 2 S$ Isotope Shift and the Structure of the Deuteron
journal, January 1998

Quadrupole moment of the deuteron from a precise calculation of the electric field gradient in $D_{2}$
journal, August 1979

Electromagnetic structure of $A = 2$ and 3 nuclei in chiral effective field theory
journal, January 2013

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
journal, May 2008

Phase shift analysis of 0 – 30 MeV pp scattering data
journal, July 1988

Proton-Proton Effective-Range Theory with Vacuum Polarization
journal, October 1960

Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
text, January 2008

Chiral effective field theory and nuclear forces
text, January 2011

Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions
text, January 2013

Single- and coupled-channel radial inverse scattering with supersymmetric transformations
text, January 2014

The chiral effective pion-nucleon Lagrangian of order p^4
text, January 2000

Weak proton capture on 3He
text, January 2000

Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction
text, January 2001

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
text, January 2003

Improving the convergence of the chiral expansion for nuclear forces I: Peripheral phases
text, January 2003

Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
text, January 2007

An accurate nucleon-nucleon potential with charge-independence breaking
text, January 1994

Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
text, January 1997

Electromagnetic Corrections to the One-Pion-Exchange Potential
text, January 1997

Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism
text, January 1998

Peripheral NN-Scattering: Role of Delta-Excitation, Correlated Two-Pion and Vector Meson Exchange
text, January 1998

Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions
journal, January 2018

The falsification of Chiral Nuclear Forces
journal, January 2017