Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits

Pan, Feng; Zhou, Dan; He, Yingwen; Yang, Siyu; Zhang, Yunfeng; Draayer, J. P.

doi:10.1016/j.physletb.2019.05.053

Title: Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits

Abstract

Exact solution of spherical mean-field plus a special orbit-dependent non-separable pairing Hamiltonian with multi non-degenerate j-orbits, which is related to two previously known hyperbolic Gaudin models, is explored. It is shown that the Hamiltonian with suitable constraints on the pairing interaction parameters turns to be exactly solvable. The extended one-variable Heine-Stieltjes polynomials associated to the Bethe-Gaudin-Richardson ansatz equations of the solution for any number of pairs k are determined. It is shown that the pair excitation energies can be calculated more easily than those of the separable pairing model studied previously. As examples of the solution, pairing excitation energies with the number of pairs up to the half-filling in the ds-shell with 3 j-orbits and in the pf-shell with 4 j-orbits are presented and compared with those of the mean-field plus the general separable, the special separable, and the standard pairing models. It is shown that the pairing excitation energies of the model are close to those of the mean-field plus special separable pairing or general separable pairing model.

Authors:

; Zhou, Dan; He, Yingwen; Yang, Siyu; Zhang, Yunfeng; Draayer, J. P.

Publication Date:: Thu Aug 01 00:00:00 EDT 2019

Research Org.:: Louisiana State Univ., Baton Rouge, LA (United States); Texas A & M Univ., Commerce, TX (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); National Science Foundation (NSF)

OSTI Identifier:: 1527050

Alternate Identifier(s):: OSTI ID: 1610827

Grant/Contract Number:: SC0005248; SC0009971; 11675071; 11375080; OIA-1738287; ACI-1713690

Resource Type:: Published Article

Journal Name:: Physics Letters. B

Additional Journal Information:: Journal Name: Physics Letters. B Journal Volume: 795 Journal Issue: C; Journal ID: ISSN 0370-2693

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics; Non-separable pairing interaction; Exactly solvable models; Bethe-Gaudin-Richardson ansatz

Citation Formats


                    Pan, Feng, Zhou, Dan, He, Yingwen, Yang, Siyu, Zhang, Yunfeng, and Draayer, J. P. Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits.  Netherlands: N. p., 2019. 
Web.  doi:10.1016/j.physletb.2019.05.053.

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                    Pan, Feng, Zhou, Dan, He, Yingwen, Yang, Siyu, Zhang, Yunfeng, & Draayer, J. P. Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits.  Netherlands.  https://doi.org/10.1016/j.physletb.2019.05.053

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                    Pan, Feng, Zhou, Dan, He, Yingwen, Yang, Siyu, Zhang, Yunfeng, and Draayer, J. P. Thu .  
"Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits".  Netherlands.  https://doi.org/10.1016/j.physletb.2019.05.053.

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@article{osti_1527050,

  title        = {Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits},

  author       = {Pan, Feng and Zhou, Dan and He, Yingwen and Yang, Siyu and Zhang, Yunfeng and Draayer, J. P.},

  abstractNote = {Exact solution of spherical mean-field plus a special orbit-dependent non-separable pairing Hamiltonian with multi non-degenerate j-orbits, which is related to two previously known hyperbolic Gaudin models, is explored. It is shown that the Hamiltonian with suitable constraints on the pairing interaction parameters turns to be exactly solvable. The extended one-variable Heine-Stieltjes polynomials associated to the Bethe-Gaudin-Richardson ansatz equations of the solution for any number of pairs k are determined. It is shown that the pair excitation energies can be calculated more easily than those of the separable pairing model studied previously. As examples of the solution, pairing excitation energies with the number of pairs up to the half-filling in the ds-shell with 3 j-orbits and in the pf-shell with 4 j-orbits are presented and compared with those of the mean-field plus the general separable, the special separable, and the standard pairing models. It is shown that the pairing excitation energies of the model are close to those of the mean-field plus special separable pairing or general separable pairing model.},

  doi          = {10.1016/j.physletb.2019.05.053},

  journal      = {Physics Letters. B},

  number       = C,

  volume       = 795,

  place        = {Netherlands},

  year         = {Thu Aug 01 00:00:00 EDT 2019},

  month        = {Thu Aug 01 00:00:00 EDT 2019}

}

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Title: Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits

Abstract

Citation Formats

Exact eigenstates of the pairing-force Hamiltonian journal, March 1964

An exact solution of spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits journal, April 2019

Non-skew-symmetric classical r -matrices and integrable “ p x + i p y ” proton–neutron BCS models journal, November 2012

Colloquium : Exactly solvable Richardson-Gaudin models for many-body quantum systems journal, August 2004

A particle-number-conserving solution to the generalized pairing problem journal, March 1998

Exact solution of the pairing problem for spherical and deformed systems journal, November 2015

Integrable spin-${\frac{1}{2}}$ Richardson–Gaudin XYZ models in an arbitrary magnetic field journal, January 2019

Diagonalisation d'une classe d'hamiltoniens de spin journal, January 1976

Numerical algorithm for the standard pairing problem based on the Heine–Stieltjes correspondence and the polynomial approach journal, October 2014

An exact solution of spherical mean-field plus a special separable pairing model journal, January 2017

A restricted class of exact eigenstates of the pairing-force Hamiltonian journal, February 1963

Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem journal, August 2012

Quantum phase diagram of the integrable p x + i p y fermionic superfluid journal, December 2010

Solutions of nuclear pairing journal, November 2007

New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras journal, January 2005

The extended Heine–Stieltjes polynomials associated with a special LMG model journal, September 2011

Exact solution of the mean-field plus separable pairing model reexamined journal, March 2017

Exact solution of the p x + i p y pairing Hamiltonian by deforming the pairing algebra journal, April 2014

New effective interaction for 0 ℏ ω shell-model calculations in the sd − pf valence space journal, January 2009

Non-skew-symmetric classical r -matrices and integrable cases of the reduced BCS model journal, November 2009

New effective interaction for p f -shell nuclei and its implications for the stability of the N = Z = 28 closed core journal, March 2004

Exactly-solvable models derived from a generalized Gaudin algebra journal, February 2005

Exact eigenstates of the pairing-force Hamiltonian
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An exact solution of spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits
journal, April 2019

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Diagonalisation d'une classe d'hamiltoniens de spin
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journal, October 2014

An exact solution of spherical mean-field plus a special separable pairing model
journal, January 2017

A restricted class of exact eigenstates of the pairing-force Hamiltonian
journal, February 1963

Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
journal, August 2012

Quantum phase diagram of the integrable $p_{x} + i p_{y}$ fermionic superfluid
journal, December 2010

Solutions of nuclear pairing
journal, November 2007

New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras
journal, January 2005

The extended Heine–Stieltjes polynomials associated with a special LMG model
journal, September 2011

Exact solution of the mean-field plus separable pairing model reexamined
journal, March 2017

Exact solution of the $p_{x} + i p_{y}$ pairing Hamiltonian by deforming the pairing algebra
journal, April 2014

New effective interaction for $0 ℏ ω$ shell-model calculations in the $sd − pf$ valence space
journal, January 2009

Non-skew-symmetric classical r -matrices and integrable cases of the reduced BCS model
journal, November 2009

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