The many levels pairing Hamiltonian for two pairs
| dc.creator | Barbaro, M. B. | |
| dc.creator | Cenni, R. | |
| dc.creator | Molinari, A. | |
| dc.creator | Quaglia, M. R. | |
| dc.date | 2003-06-23 | |
| dc.date | 2004-07-08 | |
| dc.date.accessioned | 2026-07-07T05:39:38Z | |
| dc.date.available | 2026-07-07T05:39:38Z | |
| dc.description | We address the problem of two pairs of fermions living on an arbitrary number of single particle levels of a potential well (mean field) and interacting through a pairing force. The associated solutions of the Richardson's equations are classified in terms of a number $v_l$, which reduces to the seniority $v$ in the limit of large values of the pairing strength $G$ and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the $G\to\infty$ limit. We express analytically, through the moments of the single particle levels distribution, the collective mode energy and the two critical values $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ of the coupling which can exist on a single particle level with no pair degeneracy. Notably $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ merge when the number of single particle levels goes to infinity, where they coincide with the $G_{\rm cr}$ (when it exists) of a one pair system, not envisioned by the Richardson theory. In correspondence of $G_{\rm cr}$ the system undergoes a transition from a mean field to a pairing dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes finding out that the former, for $G>G_{\rm cr}^{-}$, come close to the BCS predictions, whereas the latter display a divergence at $G_{\rm cr}$, signaling the onset of a long range off-diagonal order in the system. | |
| dc.description | 35 pages, 6 figures, 2 tables, to be published in EPJA | |
| dc.identifier | https://arxiv.org/abs/nucl-th/0306062 | |
| dc.identifier | http://arxiv.org/abs/nucl-th/0306062 | |
| dc.identifier | Eur.Phys.J. A22 (2004) 377-390 | |
| dc.identifier | doi:10.1140/epja/i2004-10043-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/82032 | |
| dc.subject | Nuclear Theory | |
| dc.title | The many levels pairing Hamiltonian for two pairs | |
| dc.type | text |