# Formulation of functional theory for pairing with particle number restoration

## Abstract

The restoration of particle number within energy density functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and nonprojected densities. As an alternative that might be advantageous for mass models, nuclear dynamics, and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an energy density functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.

- Authors:

- Grand Accelerateur National d'Ions Lourds (GANIL), CEA/DSM-CNRS/IN2P3, Bvd Henri Becquerel, F-14076 Caen (France)
- Universite Bordeaux, Centre d'Etudes Nucleaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan (France)
- (France)

- Publication Date:

- OSTI Identifier:
- 21596555

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. C, Nuclear Physics

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevC.84.014309; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2813

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION MIXING; DENSITY; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; ENERGY DENSITY; MASS; NUCLEAR MODELS; THERMODYNAMICS; TWO-BODY PROBLEM; CALCULATION METHODS; INTERACTIONS; MANY-BODY PROBLEM; MATHEMATICAL MODELS; MATRICES; PHYSICAL PROPERTIES; VARIATIONAL METHODS

### Citation Formats

```
Hupin, Guillaume, Lacroix, Denis, Bender, Michael, and CNRS/IN2P3, Centre d'Etudes Nucleaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan.
```*Formulation of functional theory for pairing with particle number restoration*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVC.84.014309.

```
Hupin, Guillaume, Lacroix, Denis, Bender, Michael, & CNRS/IN2P3, Centre d'Etudes Nucleaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan.
```*Formulation of functional theory for pairing with particle number restoration*. United States. doi:10.1103/PHYSREVC.84.014309.

```
Hupin, Guillaume, Lacroix, Denis, Bender, Michael, and CNRS/IN2P3, Centre d'Etudes Nucleaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan. Fri .
"Formulation of functional theory for pairing with particle number restoration". United States. doi:10.1103/PHYSREVC.84.014309.
```

```
@article{osti_21596555,
```

title = {Formulation of functional theory for pairing with particle number restoration},

author = {Hupin, Guillaume and Lacroix, Denis and Bender, Michael and CNRS/IN2P3, Centre d'Etudes Nucleaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan},

abstractNote = {The restoration of particle number within energy density functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and nonprojected densities. As an alternative that might be advantageous for mass models, nuclear dynamics, and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an energy density functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.},

doi = {10.1103/PHYSREVC.84.014309},

journal = {Physical Review. C, Nuclear Physics},

issn = {0556-2813},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}

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