The many levels pairing Hamiltonian for two pairs

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.Comment: 35 pages, 6 figures, 2 tables, to be published in EPJ

On the analytic solution of the pairing problem: one pair in many levels

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 both the strong and weak coupling regimes. Next the displacements of the solutions trapped in between the single particle levels with respect to the unperturbed energies are explored: their dependence upon a suitably defined quantum number is found to undergo a transition between two different regimes.Comment: 30 pages, AMS Latex, 8 figures. Submitted to Phys. Rev.

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.Comment: 20 pages, 4 figure

The pairing Hamiltonian for one pair of identical nucleons bound in a potential well

The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. When the latter are those of an harmonic oscillator well an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels, for any strength of the pairing interaction and for any number of levels. Notably the trapped solutions are labelled through an index upon which they depend parabolically.Comment: 5 pages, 1 postscript figur

A simple model for NN correlations in quasielastic lepton-nucleus scattering

We present a covariant extension of the relativistic Fermi gas model which incorporates correlation effects in nuclei. Within this model, inspired by the BCS descriptions of systems of fermions, we obtain the nuclear spectral function and from it the superscaling function for use in treating high-energy quasielastic electroweak processes. Interestingly, this model has the capability to yield the asymmetric tail seen in the experimental scaling function.Comment: 11 pages, 6 figures, Proceedings of the Twenty Seventh International Workshop on Nuclear Theory, June 23 - 28, 2008, Rila mountains, Bulgari

The generalised relativistic Lindhard functions

We present here analytic expressions for the generalised Lindhard function, also referred to as Fermi Gas polarisation propagator, in a relativistic kinematic framework and in the presence of various resonances and vertices. Particular attention is payed to its real part, since it gives rise to substantial difficulties in the definition of the currents entering the dynamics.Comment: 48 pages, 2 figures, to be published in EPJ

UAV surveying for a complete mapping and documentation of archaeological findings. The early Neolithic site of Portonovo

The huge potential of 3D digital acquisition techniques for the documentation of archaeological sites, as well as the related findings, is almost well established. In spite of the variety of available techniques, a sole documentation pipeline cannot be defined a priori because of the diversity of archaeological settings. Stratigraphic archaeological excavations, for example, require a systematic, quick and low cost 3D single-surface documentation because the nature of stratigraphic archaeology compels providing documentary evidence of any excavation phase. Only within a destructive process each single excavation cannot be identified, documented and interpreted and this implies the necessity of a re- examination of the work on field. In this context, this paper describes the methodology, carried out during the last years, to 3D document the Early Neolithic site of Portonovo (Ancona, Italy) and, in particular, its latest step consisting in a photogrammetric aerial survey by means of UAV platform. It completes the previous research delivered in the same site by means of terrestrial laser scanning and close range techniques and sets out different options for further reflection in terms of site coverage, resolution and campaign cost. With the support of a topographic network and a unique reference system, the full documentation of the site is managed in order to detail each excavation phase; besides, the final output proves how the 3D digital methodology can be completely integrated with reasonable costs during the excavation and used to interpret the archaeological context. Further contribution of this work is the comparison between several acquisition techniques (i.e. terrestrial and aerial), which could be useful as decision support system for different archaeological scenarios. The main objectives of the comparison are: i) the evaluation of 3D mapping accuracy from different data sources, ii) the definition of a standard pipeline for different archaeological needs and iii) the provision of different level of detail according to the user need