The many levels pairing Hamiltonian for two pairs

dc.creatorBarbaro, M. B.
dc.creatorCenni, R.
dc.creatorMolinari, A.
dc.creatorQuaglia, M. R.
dc.date2003-06-23
dc.date2004-07-08
dc.date.accessioned2026-07-07T05:39:38Z
dc.date.available2026-07-07T05:39:38Z
dc.descriptionWe 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.description35 pages, 6 figures, 2 tables, to be published in EPJA
dc.identifierhttps://arxiv.org/abs/nucl-th/0306062
dc.identifierhttp://arxiv.org/abs/nucl-th/0306062
dc.identifierEur.Phys.J. A22 (2004) 377-390
dc.identifierdoi:10.1140/epja/i2004-10043-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/82032
dc.subjectNuclear Theory
dc.titleThe many levels pairing Hamiltonian for two pairs
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