# Pair condensation in a finite Fermi system

## Abstract

The lowest seniority-zero eigenstates of an exactly solvable multilevel pairing Hamiltonian for a finite Fermi system are examined at different pairing regimes. After briefly reviewing the form of the eigenstates in the Richardson formalism, we discuss a different representation of these states in terms of the collective pairs resulting from the diagonalization of the Hamiltonian in a space of two degenerate time-reversed fermions. We perform a two-fold analysis by working both in the fermionic space of these collective pairs and in a space of corresponding elementary bosons. On the fermionic side, we monitor the variations which occur, with increasing the pairing strength, in the structure of both these collective pairs and the lowest eigenstates. On the bosonic side, after reviewing a fermion-boson mapping procedure, we construct exact images of the fermion eigenstates and study their wave function. The analysis allows a close examination of the phenomenon of pair condensation in a finite Fermi system and gives new insights into the evolution of the lowest (seniority-zero) excited states of a pairing Hamiltonian from the unperturbed regime up to a strongly interacting one.

- Authors:

- Istituto Nazionale di Fisica Nucleare-Sezione di Catania, Via S. Sofia 64, I-95123 Catania (Italy)

- Publication Date:

- OSTI Identifier:
- 20995276

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.75.054314; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOSONS; EIGENSTATES; EXACT SOLUTIONS; EXCITED STATES; FERMIONS; HAMILTONIANS; WAVE FUNCTIONS

### Citation Formats

```
Sambataro, M.
```*Pair condensation in a finite Fermi system*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVC.75.054314.

```
Sambataro, M.
```*Pair condensation in a finite Fermi system*. United States. doi:10.1103/PHYSREVC.75.054314.

```
Sambataro, M. Tue .
"Pair condensation in a finite Fermi system". United States.
doi:10.1103/PHYSREVC.75.054314.
```

```
@article{osti_20995276,
```

title = {Pair condensation in a finite Fermi system},

author = {Sambataro, M.},

abstractNote = {The lowest seniority-zero eigenstates of an exactly solvable multilevel pairing Hamiltonian for a finite Fermi system are examined at different pairing regimes. After briefly reviewing the form of the eigenstates in the Richardson formalism, we discuss a different representation of these states in terms of the collective pairs resulting from the diagonalization of the Hamiltonian in a space of two degenerate time-reversed fermions. We perform a two-fold analysis by working both in the fermionic space of these collective pairs and in a space of corresponding elementary bosons. On the fermionic side, we monitor the variations which occur, with increasing the pairing strength, in the structure of both these collective pairs and the lowest eigenstates. On the bosonic side, after reviewing a fermion-boson mapping procedure, we construct exact images of the fermion eigenstates and study their wave function. The analysis allows a close examination of the phenomenon of pair condensation in a finite Fermi system and gives new insights into the evolution of the lowest (seniority-zero) excited states of a pairing Hamiltonian from the unperturbed regime up to a strongly interacting one.},

doi = {10.1103/PHYSREVC.75.054314},

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

number = 5,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}