Shell-model coupled-cluster method for open-shell nuclei

Sun, Zhonghao; Morris, Titus D.; Hagen, Gaute; Jansen, Gustav R.; Papenbrock, Thomas

doi:10.1103/PhysRevC.98.054320

Title: Shell-model coupled-cluster method for open-shell nuclei

Abstract

An approach to derive effective shell-model interactions from microscopic nuclear forces is introduced here. The similarity transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a ⁴He core, and compute low-lying states of ^6–8He and ^6–8Li in p-shell model spaces. Our conclusions agree with benchmarks from full configuration interaction.

Authors:

Sun, Zhonghao ^[1];

^[1];

^[2];

^[1]

Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Wed Nov 28 00:00:00 EST 2018

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

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

OSTI Identifier:: 1546557

Alternate Identifier(s):: OSTI ID: 1483714

Grant/Contract Number:: AC05-00OR22725; FG02- 96ER40963; DEFG02-96ER40963

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 98; Journal Issue: 5; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Sun, Zhonghao, Morris, Titus D., Hagen, Gaute, Jansen, Gustav R., and Papenbrock, Thomas. Shell-model coupled-cluster method for open-shell nuclei.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevC.98.054320.

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                    Sun, Zhonghao, Morris, Titus D., Hagen, Gaute, Jansen, Gustav R., & Papenbrock, Thomas. Shell-model coupled-cluster method for open-shell nuclei.  United States.  https://doi.org/10.1103/PhysRevC.98.054320

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                    Sun, Zhonghao, Morris, Titus D., Hagen, Gaute, Jansen, Gustav R., and Papenbrock, Thomas. Wed .  
"Shell-model coupled-cluster method for open-shell nuclei".  United States.  https://doi.org/10.1103/PhysRevC.98.054320.  https://www.osti.gov/servlets/purl/1546557.

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@article{osti_1546557,

  title        = {Shell-model coupled-cluster method for open-shell nuclei},

  author       = {Sun, Zhonghao and Morris, Titus D. and Hagen, Gaute and Jansen, Gustav R. and Papenbrock, Thomas},

  abstractNote = {An approach to derive effective shell-model interactions from microscopic nuclear forces is introduced here. The similarity transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a 4He core, and compute low-lying states of 6–8He and 6–8Li in p-shell model spaces. Our conclusions agree with benchmarks from full configuration interaction.},

  doi          = {10.1103/PhysRevC.98.054320},

  journal      = {Physical Review C},

  number       = 5,

  volume       = 98,

  place        = {United States},

  year         = {Wed Nov 28 00:00:00 EST 2018},

  month        = {Wed Nov 28 00:00:00 EST 2018}

}

Copy to clipboard

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Title: Shell-model coupled-cluster method for open-shell nuclei

Abstract

Citation Formats

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

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

Ab initio no core shell model journal, March 2013

Medium-Mass Nuclei with Normal-Ordered Chiral N N + 3 N Interactions journal, July 2012

Evolution of Shell Structure in Neutron-Rich Calcium Isotopes journal, July 2012

Chiral two- and three-nucleon forces along medium-mass isotope chains journal, June 2014

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Ab initio multireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes journal, October 2014

Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians journal, May 2016

Saturation with chiral interactions and consequences for finite nuclei journal, July 2017

Dawning of the N = 32 Shell Closure Seen through Precision Mass Measurements of Neutron-Rich Titanium Isotopes journal, February 2018

Ab initio path to heavy nuclei journal, September 2014

Structure of the Lightest Tin Isotopes journal, April 2018

Ab Initio Many-Body Calculations of n − H 3 , n − He 4 , p − He 3 , 4 , and n − Be 10 Scattering journal, August 2008

Ab Initio Calculation of the Hoyle State journal, May 2011

Ab initio alpha–alpha scattering journal, December 2015

Neutron and weak-charge distributions of the 48Ca nucleus journal, November 2015

Structure of Ni 78 from First-Principles Computations journal, October 2016

Improved nuclear matter calculations from chiral low-momentum interactions journal, March 2011

Similarity-Transformed Chiral N N + 3 N Interactions for the Ab Initio Description of C 12 and O 16 journal, August 2011

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

Modern theory of nuclear forces journal, December 2009

Chiral effective field theory and nuclear forces journal, June 2011

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

From low-momentum interactions to nuclear structure journal, July 2010

Microscopic Calculation of the Inclusive Electron Scattering Structure Function in O 16 journal, February 2000

Self-consistent Green's function method for nuclei and nuclear matter journal, April 2004

Auxiliary Field Diffusion Monte Carlo Calculation of Nuclei with A ≤ 40 with Tensor Interactions journal, July 2007

Lattice simulations for few- and many-body systems journal, July 2009

Ab initio Gorkov-Green's function calculations of open-shell nuclei journal, January 2013

Many-fermion theory in expS- (or coupled cluster) form journal, February 1978

An overview of coupled cluster theory and its applications in physics journal, January 1991

Coupled-cluster theory in quantum chemistry journal, February 2007

Coupled-cluster computations of atomic nuclei journal, September 2014

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

Status of the Nuclear Shell Model journal, December 1988

The shell model as a unified view of nuclear structure journal, June 2005

New-generation Monte Carlo shell model for the K computer era journal, January 2012

Realistic effective interactions for nuclear systems journal, October 1995

Shell-model calculations and realistic effective interactions journal, January 2009

A folded-diagram expansion of the model-space effective hamiltonian journal, November 1971

Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei journal, June 1970

Convergence Rate of Intermediate-State Summations in the Effective Shell-Model Interaction journal, May 1973

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

Effective interaction for pf -shell nuclei journal, May 2002

New “USD” Hamiltonians for the sd shell journal, September 2006

Ab-initio shell model with a core journal, October 2008

Ab initio effective interactions for s d -shell valence nucleons journal, June 2015

Convergent Theory for Effective Interaction in Nuclei journal, December 1980

Construction of Hermitian Effective Interaction in Nuclei: -- General Relation between Hermitian and Non-Hermitian Forms -- journal, July 1982

Reformulation of Coupled-Cluster Theory for Many-Fermion System on Similarity-Transformation Theory journal, April 1992

Many-body theory in terms of effective interactions and its relation to coupled-cluster method journal, November 1994

Ab Initio Coupled-Cluster Effective Interactions for the Shell Model: Application to Neutron-Rich Oxygen and Carbon Isotopes journal, October 2014

Open s d -shell nuclei from first principles journal, July 2016

Nonperturbative Shell-Model Interactions from the In-Medium Similarity Renormalization Group journal, October 2014

Nucleus-Dependent Valence-Space Approach to Nuclear Structure journal, January 2017

Degenerate many fermion theory in expS form journal, November 1976

Theory of the effective interaction in nuclei journal, October 1979

An extension of the coupled cluster formalism to excited states (I) journal, January 1981

An extension of the coupled cluster formalism to excited states journal, January 1981

Toward open-shell nuclei with coupled-cluster theory journal, May 2011

Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths journal, December 2014

Electron correlations in the Bogoljubov coupled-cluster formalism journal, August 1984

Two-component Fermi systems: II. Superfluid coupled cluster theory journal, September 1988

Multireference Nature of Chemistry: The Coupled-Cluster View journal, December 2011

Many – Body Methods in Chemistry and Physics book, January 2009

A coupled cluster approach with triple excitations journal, December 1984

Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems journal, December 1983

Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations journal, August 2005

Magnus expansion and in-medium similarity renormalization group journal, September 2015

Numerical canonical transformation approach to quantum many-body problems journal, October 2002

Analytic energy derivatives in many‐body methods. I. First derivatives journal, February 1989

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

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

Spherical coupled-cluster theory for open-shell nuclei journal, August 2013

The Shell-Model Code NuShellX@MSU journal, June 2014

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

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

Ab initio no core shell model
journal, March 2013

Medium-Mass Nuclei with Normal-Ordered Chiral $N N + 3 N$ Interactions
journal, July 2012

Evolution of Shell Structure in Neutron-Rich Calcium Isotopes
journal, July 2012

Chiral two- and three-nucleon forces along medium-mass isotope chains
journal, June 2014

Lattice effective field theory for medium-mass nuclei
journal, May 2014

Ab initio multireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes
journal, October 2014

Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians
journal, May 2016

Saturation with chiral interactions and consequences for finite nuclei
journal, July 2017

Dawning of the $N = 32$ Shell Closure Seen through Precision Mass Measurements of Neutron-Rich Titanium Isotopes
journal, February 2018

Ab initio path to heavy nuclei
journal, September 2014

Structure of the Lightest Tin Isotopes
journal, April 2018

Ab Initio Many-Body Calculations of $n − {}^{3}H$ , $n − {}^{4}{He}$ , $p − {}^{3, 4}{He}$ , and $n − {}^{10}{Be}$ Scattering
journal, August 2008

Ab Initio Calculation of the Hoyle State
journal, May 2011

Ab initio alpha–alpha scattering
journal, December 2015

Neutron and weak-charge distributions of the 48Ca nucleus
journal, November 2015

Structure of ${}^{78}{Ni}$ from First-Principles Computations
journal, October 2016

Improved nuclear matter calculations from chiral low-momentum interactions
journal, March 2011

Similarity-Transformed Chiral $N N + 3 N$ Interactions for the Ab Initio Description of ${}^{12}C$ and ${}^{16}O$
journal, August 2011

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

Modern theory of nuclear forces
journal, December 2009

Chiral effective field theory and nuclear forces
journal, June 2011

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

From low-momentum interactions to nuclear structure
journal, July 2010

Microscopic Calculation of the Inclusive Electron Scattering Structure Function in ${}^{16}O$
journal, February 2000

Self-consistent Green's function method for nuclei and nuclear matter
journal, April 2004

Auxiliary Field Diffusion Monte Carlo Calculation of Nuclei with $A \leq 40$ with Tensor Interactions
journal, July 2007

Lattice simulations for few- and many-body systems
journal, July 2009

Ab initio Gorkov-Green's function calculations of open-shell nuclei
journal, January 2013

Many-fermion theory in expS- (or coupled cluster) form
journal, February 1978

An overview of coupled cluster theory and its applications in physics
journal, January 1991

Coupled-cluster theory in quantum chemistry
journal, February 2007

Coupled-cluster computations of atomic nuclei
journal, September 2014

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

Status of the Nuclear Shell Model
journal, December 1988

The shell model as a unified view of nuclear structure
journal, June 2005

New-generation Monte Carlo shell model for the K computer era
journal, January 2012

Realistic effective interactions for nuclear systems
journal, October 1995

Shell-model calculations and realistic effective interactions
journal, January 2009

A folded-diagram expansion of the model-space effective hamiltonian
journal, November 1971

Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei
journal, June 1970

Convergence Rate of Intermediate-State Summations in the Effective Shell-Model Interaction
journal, May 1973

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

Effective interaction for $pf$ -shell nuclei
journal, May 2002

New “USD” Hamiltonians for the $sd$ shell
journal, September 2006

Ab-initio shell model with a core
journal, October 2008

Ab initio effective interactions for $s d$ -shell valence nucleons
journal, June 2015

Convergent Theory for Effective Interaction in Nuclei
journal, December 1980

Construction of Hermitian Effective Interaction in Nuclei: -- General Relation between Hermitian and Non-Hermitian Forms --
journal, July 1982

Reformulation of Coupled-Cluster Theory for Many-Fermion System on Similarity-Transformation Theory
journal, April 1992

Many-body theory in terms of effective interactions and its relation to coupled-cluster method
journal, November 1994

Ab Initio Coupled-Cluster Effective Interactions for the Shell Model: Application to Neutron-Rich Oxygen and Carbon Isotopes
journal, October 2014

Open $s d$ -shell nuclei from first principles
journal, July 2016

Nonperturbative Shell-Model Interactions from the In-Medium Similarity Renormalization Group
journal, October 2014

Nucleus-Dependent Valence-Space Approach to Nuclear Structure
journal, January 2017

Degenerate many fermion theory in expS form
journal, November 1976

Theory of the effective interaction in nuclei
journal, October 1979

An extension of the coupled cluster formalism to excited states (I)
journal, January 1981

An extension of the coupled cluster formalism to excited states
journal, January 1981

Toward open-shell nuclei with coupled-cluster theory
journal, May 2011

Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths
journal, December 2014

Electron correlations in the Bogoljubov coupled-cluster formalism
journal, August 1984

Two-component Fermi systems: II. Superfluid coupled cluster theory
journal, September 1988

Multireference Nature of Chemistry: The Coupled-Cluster View
journal, December 2011

Many – Body Methods in Chemistry and Physics
book, January 2009

A coupled cluster approach with triple excitations
journal, December 1984

Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems
journal, December 1983

Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations
journal, August 2005

Magnus expansion and in-medium similarity renormalization group
journal, September 2015

Numerical canonical transformation approach to quantum many-body problems
journal, October 2002

Analytic energy derivatives in many‐body methods. I. First derivatives
journal, February 1989

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

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

Spherical coupled-cluster theory for open-shell nuclei
journal, August 2013

The Shell-Model Code NuShellX@MSU
journal, June 2014