ﻻ يوجد ملخص باللغة العربية
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 Richardsons 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 $Gtoinfty$ 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.
We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum, is given in
We address the problem of the bosonization of finite fermionic systems with two different approaches. First we work in the path integral formalism, showing how a truly bosonic effective action can be derived from a generic fermionic one with a quar
Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods. Methods: We
We derive the exact $T=0$ seniority-zero eigenstates of the isovector pairing Hamiltonian for an even number of protons and neutrons. Nucleons are supposed to be distributed over a set of non-degenerate levels and to interact through a pairing force
As a first step to derive the IBM from a microscopic nuclear hamiltonian, we bosonize the pairing hamiltonian in the framework of the path integral formalism respecting both the particle number conservation and the Pauli principle. Special attention