Impact of three-body forces on elastic nucleon-nucleus scattering observables

Vorabbi, Matteo; Gennari, Michael; Finelli, Paolo; Giusti, Carlotta; Navrátil, Petr; Machleidt, Ruprecht

doi:10.1103/physrevc.103.024604

Title: Impact of three-body forces on elastic nucleon-nucleus scattering observables

Abstract

In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon ( $N N$ ) $t$ matrix and the nuclear density of the target. In the calculations $N N$ and three-nucleon ( $3 N$ ) chiral interactions were used for the target density and only the $N N$ interaction for the $N N t$ matrix. The purpose of this study is to achieve another step towards the calculation of a more consistent OP introducing the $3 N$ force also in the dynamic part of the OP. The full treatment of the $3 N$ interaction is beyond our present capabilities. Thus, here it is approximated with a density dependent $N N$ interaction obtained after the averaging over the Fermi sphere. In practice, in our model the $3 N$ force acts as a medium correction of the bare $N N$ interaction used to calculate the $t$ matrix. Even if the $3 N$ force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results. We consider as case studies the elastic scattering of nucleons off ${}_{12}C$ and ${}_{16}O$ . We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the $3 N$ interaction in the dynamic part of the OP. Conclusions: Our analysis indicates that the contribution of the $3 N$ force in the $t$ matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the $3 N$ force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.

Authors:

^[1]; Gennari, Michael ^[2];

^[3];

^[4];

^[5];

^[6]

Brookhaven National Lab. (BNL), Upton, NY (United States). National Nuclear Data Center (NNDC)
Univ. of Victoria, BC (Canada); TRIUMF, Vancouver, BC (Canada)
Univ. degli Studi di Bologna (Italy); National Inst. of Nuclear Physics (INFN), Bologna (Italy)
Univ. degli Studi di Pavia (Italy); National Inst. of Nuclear Physics (INFN), Pavia (Italy)
TRIUMF, Vancouver, BC (Canada)
Univ. of Idaho, Moscow, ID (United States)

Publication Date:: Tue Feb 02 00:00:00 EST 2021

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Univ. of Idaho, Moscow, ID (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); Natural Sciences and Engineering Research Council of Canada (NSERC); National Research Council of Canada (NRC)

OSTI Identifier:: 1765667

Alternate Identifier(s):: OSTI ID: 1820915

Report Number(s):: BNL-221004-2021-JAAM
Journal ID: ISSN 2469-9985; TRN: US2206266

Grant/Contract Number:: SC0012704; AC02-98CH10886; FG02-03ER41270; SAPIN-2016-00033

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. C

Additional Journal Information:: Journal Volume: 103; Journal Issue: 2; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; direct reactions; nucleon induced nuclear reactions

Citation Formats


                    Vorabbi, Matteo, Gennari, Michael, Finelli, Paolo, Giusti, Carlotta, Navrátil, Petr, and Machleidt, Ruprecht. Impact of three-body forces on elastic nucleon-nucleus scattering observables.  United States: N. p., 2021. 
Web.  doi:10.1103/physrevc.103.024604.

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                    Vorabbi, Matteo, Gennari, Michael, Finelli, Paolo, Giusti, Carlotta, Navrátil, Petr, & Machleidt, Ruprecht. Impact of three-body forces on elastic nucleon-nucleus scattering observables.  United States.  https://doi.org/10.1103/physrevc.103.024604

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                    Vorabbi, Matteo, Gennari, Michael, Finelli, Paolo, Giusti, Carlotta, Navrátil, Petr, and Machleidt, Ruprecht. Tue .  
"Impact of three-body forces on elastic nucleon-nucleus scattering observables".  United States.  https://doi.org/10.1103/physrevc.103.024604.  https://www.osti.gov/servlets/purl/1765667.

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@article{osti_1765667,

  title        = {Impact of three-body forces on elastic nucleon-nucleus scattering observables},

  author       = {Vorabbi, Matteo and Gennari, Michael and Finelli, Paolo and Giusti, Carlotta and Navrátil, Petr and Machleidt, Ruprecht},

  abstractNote = {In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon (NN) t matrix and the nuclear density of the target. In the calculations NN and three-nucleon (3N) chiral interactions were used for the target density and only the NN interaction for the NN t matrix. The purpose of this study is to achieve another step towards the calculation of a more consistent OP introducing the 3N force also in the dynamic part of the OP. The full treatment of the 3N interaction is beyond our present capabilities. Thus, here it is approximated with a density dependent NN interaction obtained after the averaging over the Fermi sphere. In practice, in our model the 3N force acts as a medium correction of the bare NN interaction used to calculate the t matrix. Even if the 3N force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results. We consider as case studies the elastic scattering of nucleons off C12 and O16. We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the 3N interaction in the dynamic part of the OP. Conclusions: Our analysis indicates that the contribution of the 3N force in the t matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the 3N force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.},

  doi          = {10.1103/physrevc.103.024604},

  journal      = {Physical Review. C},

  number       = 2,

  volume       = 103,

  place        = {United States},

  year         = {Tue Feb 02 00:00:00 EST 2021},

  month        = {Tue Feb 02 00:00:00 EST 2021}

}

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Title: Impact of three-body forces on elastic nucleon-nucleus scattering observables

Abstract

Citation Formats

Comparison between optical-model potentials in G -matrix folding method and improved local-density approximation method journal, August 2020

Microscopic global optical potential for nucleon-nucleus systems in the energy range 50–400 MeV journal, March 2019

Structure of A = 10 – 13 Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory journal, July 2007

Quantifying uncertainties in neutron- α scattering with chiral nucleon-nucleon and three-nucleon forces journal, August 2020

Irreducible nonlocality of optical model potentials based on realistic NN interactions journal, November 2018

Erratum: Microscopic calculations based on chiral two- and three-nucleon forces for proton- and 4 He -nucleus scattering [Phys. Rev. C 92 , 024618 (2015)] journal, November 2017

Ab initio no core shell model journal, March 2013

Optical model analysis of 200 MeV p→ + 16 O elastic scattering data measured to large momentum transfers journal, January 1985

Elastic scattering of 200 MeV polarized protons from C 1 2 , 1 3 and the optical potential journal, February 1981

Inelastic excitation of C 12 and N 14 by 122 MeV protons and implications for the effective nucleon-nucleon interaction journal, June 1980

Effective field theory of nuclear forces journal, January 1999

Optical potentials derived from nucleon-nucleon chiral potentials at N 4 LO journal, October 2017

Colloquium : Three-body forces: From cold atoms to nuclei journal, January 2013

Ab initio folding potentials for nucleon-nucleus scattering based on no-core shell-model one-body densities journal, April 2019

Microscopic optical potential from chiral nuclear forces journal, August 2013

Optical potential from first principles journal, February 2017

Pion Theory of Three-Body Forces journal, March 1957

Energy dependence and surface contribution of the folding-model optical potential for nucleon-nucleus scattering at energies up to 1 GeV/nucleon journal, July 2019

Pauli rearrangement potential for a scattering state with the nucleon-nucleon interaction in chiral effective field theory journal, November 2018

Dispersive optical model analysis of Pb 208 generating a neutron-skin prediction beyond the mean field journal, April 2020

SWANLOP: Scattering waves off nonlocal optical potentials in the presence of Coulomb interactions journal, February 2021

Exact scattering waves off nonlocal potentials under Coulomb interaction within Schrödinger's integro-differential equation journal, February 2019

Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces journal, February 2019

Extension of TALYS to 1 GeV journal, April 2014

Introduction to Chiral Perturbation Theory book, January 2003

Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion journal, September 2015

Multiple scattering theory of proton elastic scattering at intermediate energies journal, July 1992

Full-folding optical potentials in elastic proton-nucleus scattering journal, March 1990

Ab initio leading order effective potentials for elastic nucleon-nucleus scattering journal, September 2020

Measurement of neutron elastic scattering cross sections for C 12 , Ca 40 , and Pb 208 at energies from 65 to 225 MeV journal, November 2004

In-medium full-folding optical model for nucleon-nucleus elastic scattering journal, July 1995

Chiral Dynamics in Nucleons and Nuclei journal, June 1995

Discrepancy between experimental and theoretical β-decay rates resolved from first principles journal, March 2019

Application of multiple scattering theory to lower-energy elastic nucleon-nucleus scattering journal, March 1995

Coupled-Cluster Computations of Optical Potential for Medium-Mass Nuclei journal, July 2020

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

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

Local three-nucleon interaction from chiral effective field theory journal, November 2007

Proton elastic scattering on calcium isotopes from chiral nuclear optical potentials journal, July 2019

Coupled-cluster computations of atomic nuclei journal, September 2014

Recent developments for the optical model of nuclei journal, March 2019

Ab Initio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei journal, January 2017

Proton-nucleus elastic scattering: Comparison between phenomenological and microscopic optical potentials journal, December 2018

Off-shell structures of nucleon-nucleon t matrices and their influence on nucleon-nucleus elastic scattering observables journal, March 1998

Chiral symmetry and three-nucleon forces journal, January 1999

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

Effective interaction for O 16 ( p , p ’) at E p =318 MeV journal, March 1991

Microscopic calculations based on chiral two- and three-nucleon forces for proton- and He 4 -nucleus scattering journal, August 2015

Chiral EFT based nuclear forces: achievements and challenges journal, July 2016

Ab Initio Study of Ca 40 with an Importance-Truncated No-Core Shell Model journal, August 2007

Nuclear forces from chiral lagrangians journal, November 1990

Large-angle proton-nucleus scattering shows no evidence for intermediate Δ states journal, April 1985

Chiral effective field theory and nuclear forces journal, June 2011

Proton scattering from C 12 between 120 and 200 MeV and the optical potential journal, February 1983

Three-nucleon forces journal, September 2014

Density dependence in the two-nucleon effective interaction at 135 MeV journal, April 1989

Validity of local density prescriptions for microscopic calculations of proton nucleus elastic scattering journal, December 1994

Erratum: Nonrelativistic full-folding model of nucleon elastic scattering at intermediate energies journal, October 1990

Microscopic formulation of medium contributions to the first-order optical potential journal, December 1993

Proton inelastic scattering to the dilute α -cluster condensed 0 2 + state at E x = 7 . 654 MeV in C 12 journal, May 2010

Neutron elastic scattering on calcium isotopes from chiral nuclear optical potentials journal, June 2020

Local and global nucleon optical models from 1 keV to 200 MeV journal, January 2003

Modern theory of nuclear forces journal, December 2009

Nonrelativistic full-folding model of nucleon elastic scattering at intermediate energies journal, May 1990

Role of nuclear densities in nucleon elastic scattering journal, August 1990

Full-folding optical potentials for elastic nucleon-nucleus scattering based on realistic densities journal, October 1997

Erratum: Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory [Phys. Rev. Lett. 103 , 102502 (2009)] journal, January 2019

Microscopic optical potentials for calcium isotopes journal, October 2018

Propagator modifications in elastic nucleon-nucleus scattering within the spectator expansion journal, October 1995

Off-shell effects from meson exchange in the nuclear optical potential journal, August 1989

Effective interaction for O 16 ( p , p ’) and Ca 40 ( p , p ’) at E p =200 MeV journal, April 1993

Ab Initio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei journal, August 2019

Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory journal, September 2009

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

Double-folding potentials from chiral effective field theory journal, July 2018

Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order journal, May 2015

Importance truncation for large-scale configuration interaction approaches journal, June 2009

Comparison between optical-model potentials in $G$ -matrix folding method and improved local-density approximation method
journal, August 2020

Microscopic global optical potential for nucleon-nucleus systems in the energy range 50–400 MeV
journal, March 2019

Structure of $A = 10 - 13$ Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory
journal, July 2007

Quantifying uncertainties in neutron- $α$ scattering with chiral nucleon-nucleon and three-nucleon forces
journal, August 2020

Irreducible nonlocality of optical model potentials based on realistic NN interactions
journal, November 2018

Erratum: Microscopic calculations based on chiral two- and three-nucleon forces for proton- and $^{4} He$ -nucleus scattering [Phys. Rev. C 92 , 024618 (2015)]
journal, November 2017

Ab initio no core shell model
journal, March 2013

Optical model analysis of 200 MeV p→ $+^{16}$ O elastic scattering data measured to large momentum transfers
journal, January 1985

Elastic scattering of 200 MeV polarized protons from ${}^{12, 13}C$ and the optical potential
journal, February 1981

Inelastic excitation of ${}^{12}C$ and ${}^{14}N$ by 122 MeV protons and implications for the effective nucleon-nucleon interaction
journal, June 1980

Effective field theory of nuclear forces
journal, January 1999

Optical potentials derived from nucleon-nucleon chiral potentials at $N^{4} LO$
journal, October 2017

Colloquium : Three-body forces: From cold atoms to nuclei
journal, January 2013

Ab initio folding potentials for nucleon-nucleus scattering based on no-core shell-model one-body densities
journal, April 2019

Microscopic optical potential from chiral nuclear forces
journal, August 2013

Optical potential from first principles
journal, February 2017

Pion Theory of Three-Body Forces
journal, March 1957

Energy dependence and surface contribution of the folding-model optical potential for nucleon-nucleus scattering at energies up to 1 GeV/nucleon
journal, July 2019

Pauli rearrangement potential for a scattering state with the nucleon-nucleon interaction in chiral effective field theory
journal, November 2018

Dispersive optical model analysis of ${}^{208}{Pb}$ generating a neutron-skin prediction beyond the mean field
journal, April 2020

SWANLOP: Scattering waves off nonlocal optical potentials in the presence of Coulomb interactions
journal, February 2021

Exact scattering waves off nonlocal potentials under Coulomb interaction within Schrödinger's integro-differential equation
journal, February 2019

Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces
journal, February 2019

Extension of TALYS to 1 GeV
journal, April 2014

Introduction to Chiral Perturbation Theory
book, January 2003

Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion
journal, September 2015

Multiple scattering theory of proton elastic scattering at intermediate energies
journal, July 1992

Full-folding optical potentials in elastic proton-nucleus scattering
journal, March 1990

Ab initio leading order effective potentials for elastic nucleon-nucleus scattering
journal, September 2020

Measurement of neutron elastic scattering cross sections for ${}^{12}C$ , ${}^{40}{Ca}$ , and ${}^{208}{Pb}$ at energies from $65 to 225 MeV$
journal, November 2004

In-medium full-folding optical model for nucleon-nucleus elastic scattering
journal, July 1995

Chiral Dynamics in Nucleons and Nuclei
journal, June 1995

Discrepancy between experimental and theoretical β-decay rates resolved from first principles
journal, March 2019

Application of multiple scattering theory to lower-energy elastic nucleon-nucleus scattering
journal, March 1995

Coupled-Cluster Computations of Optical Potential for Medium-Mass Nuclei
journal, July 2020

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

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

Local three-nucleon interaction from chiral effective field theory
journal, November 2007

Proton elastic scattering on calcium isotopes from chiral nuclear optical potentials
journal, July 2019

Coupled-cluster computations of atomic nuclei
journal, September 2014

Recent developments for the optical model of nuclei
journal, March 2019

Ab Initio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei
journal, January 2017

Proton-nucleus elastic scattering: Comparison between phenomenological and microscopic optical potentials
journal, December 2018

Off-shell structures of nucleon-nucleon $t$ matrices and their influence on nucleon-nucleus elastic scattering observables
journal, March 1998

Chiral symmetry and three-nucleon forces
journal, January 1999

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

Effective interaction for ${}^{16}O$ ( p , p ’) at $E_{p}$ =318 MeV
journal, March 1991

Microscopic calculations based on chiral two- and three-nucleon forces for proton- and ${}^{4}{He}$ -nucleus scattering
journal, August 2015

Chiral EFT based nuclear forces: achievements and challenges
journal, July 2016

Ab Initio Study of ${}^{40}{Ca}$ with an Importance-Truncated No-Core Shell Model
journal, August 2007

Nuclear forces from chiral lagrangians
journal, November 1990

Large-angle proton-nucleus scattering shows no evidence for intermediate $Δ$ states
journal, April 1985

Chiral effective field theory and nuclear forces
journal, June 2011

Proton scattering from ${}^{12}C$ between 120 and 200 MeV and the optical potential
journal, February 1983

Three-nucleon forces
journal, September 2014

Density dependence in the two-nucleon effective interaction at 135 MeV
journal, April 1989

Validity of local density prescriptions for microscopic calculations of proton nucleus elastic scattering
journal, December 1994

Erratum: Nonrelativistic full-folding model of nucleon elastic scattering at intermediate energies
journal, October 1990

Microscopic formulation of medium contributions to the first-order optical potential
journal, December 1993

Proton inelastic scattering to the dilute $α$ -cluster condensed $0_{2}^{+}$ state at $E_{x} = 7.654$ MeV in ${}^{12}C$
journal, May 2010

Neutron elastic scattering on calcium isotopes from chiral nuclear optical potentials
journal, June 2020

Local and global nucleon optical models from 1 keV to 200 MeV
journal, January 2003

Modern theory of nuclear forces
journal, December 2009

Nonrelativistic full-folding model of nucleon elastic scattering at intermediate energies
journal, May 1990

Role of nuclear densities in nucleon elastic scattering
journal, August 1990

Full-folding optical potentials for elastic nucleon-nucleus scattering based on realistic densities
journal, October 1997

Erratum: Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory [Phys. Rev. Lett. 103 , 102502 (2009)]
journal, January 2019

Microscopic optical potentials for calcium isotopes
journal, October 2018

Propagator modifications in elastic nucleon-nucleus scattering within the spectator expansion
journal, October 1995

Off-shell effects from meson exchange in the nuclear optical potential
journal, August 1989

Effective interaction for ${}^{16}O$ ( p , p ’) and ${}^{40}{Ca}$ ( p , p ’) at $E_{p}$ =200 MeV
journal, April 1993

Ab Initio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei
journal, August 2019

Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory
journal, September 2009

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

Double-folding potentials from chiral effective field theory
journal, July 2018

Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
journal, May 2015

Importance truncation for large-scale configuration interaction approaches
journal, June 2009

Novel applications of the dispersive optical model
journal, February 2017

Spectra and binding energy predictions of chiral interactions for ${}^{7}{Li}$
journal, June 2006

Accurate nuclear radii and binding energies from a chiral interaction
journal, May 2015