[en] Short communication. 8 refs

[en] This paper studies the effects of the large N limit in the LMG model has on the calculation of eigenvalues, its 1/N corrections, and on the evolution of correlations in the exact wave function. The evolution of single particle properties in the Time Dependent Hartree-Fock (TDHF) approximation is discussed and compared with the exact evolution

[en] The BCS equations are derived by means of the summation of a particular set of diagrams. For any finite value of π/Ω (where π is the number of pairs of particles and Ω is the degeneracy of the system), these diagrams yield the smallest contribution in powers of Ω^-1. To this order, there is no fluctuation in the number of particles. (Auth.)

[en] The shifts in the energies of pairing vibrations due to the presence of valence nucleons are described in simple terms. Calculations are reported for the Z = 50 isotopes and N = 82 isotones and compared with experiment

[en] As a model for a deformed nucleus the many level pairing model (picket fence model with 100 levels) is considered in four approximations and compared to the exact solution given by Richardson long time ago. It is found that, as usual, the number projected BCS method improves over standard BCS but that it is much less accurate than the more sophisticated many-body-approaches which are Coupled Cluster Theory (CCT) in its SUB2 version or Self-Consistent Random Phase Approximation (SCRPA)

[en] The collective lines in a given diagram are renormalized by including higher order processes. The problem is cast into the form of a conventional linear algebraic matrix equation that allows a simple treatment of the normalization conditions. It is shown that the states entering in the renormalization of the phonons become improper initial or final states, if dressed phonons are used in the intermediate states. A simple extension of this argument allows one to justify one of the rules given in the formulation of the NFT. (Auth.)

No abstract available

[en] The single-particle states are renormalized by taking into account the emission and subsequent absorption of a phonon to all orders of perturbation theory. The Ward identity provides a useful normalization condition to the new dressed excitations. Other orthonormalization properties are interpreted in terms of anticommutation and energy weighted sum rules. A two-level model with a monopole phonon is treated in detail as an example. (Auth.)

[en] The principal series approximation is used in the analysis of deformed nuclei. (A.C.A.S.)

[en] A full quantum mechanical treatment is applied to a residual (symmetry restoring) hamiltonian in a deformed basis, in a simple case (two-dimensional rotor). Intrinsic excitation energies, moments of inertia and matrix elements between members of a rotational band are calculated. The results reproduce the exact values to the required order of an expansion in powers of Omega^-1, where Omega is the degeneracy of the system. The lowest order is correctly given by the usual semiclassical approximations. (orig.)