2003/06/30 by M. B. Barbaro, R. Cenni, A. Molinari +1
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #nucl-th
paper · pdf · doi:10.1140/epja/i2004-10043-7
published as Eur.Phys.J. A22 (2004) 377-390 · 35 pages, 6 figures, 2 tables, to be published in EPJA
arxiv created 2004/07/08 · openalex publication_date 2004/11/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 vl, 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→∞ 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.