G.G. Dussel

The nuclear field treatment of some exactly soluble models

Abstract The nuclear field theory is applied to physically meaningful models which are exactly soluble. The particles are coupled through monopole particle-hole and/or pairing forces, which do not mix states with a different number of particles and holes. It is possible to sum up all the field diagrams and, thus, one obtains the exact results in all cases. Therefore, the overcompleteness of the basis and the violations of the Pauli principle are corrected for within the field treatment.

On the many-body foundation of the nuclear field theory

Abstract The equivalence between the description of the many-body finite nuclear system in terms of Feynman diagrams involving only the fermion degrees of freedom and of Feynman diagrams involving fermion and phonon degrees of freedom is proved for intermediate states in the case of a general two-body residual interaction.

A self-consistent description of systems with many interacting bosons

Abstract A self-consistent description for the ground state of many interacting bosons is discussed. The excited bandheads are obtained by solving the TDA and RPA equations. The latter can be used to isolate the spurious states that arise as a consequence of broken symmetries. The rotational moment of inertia is obtained in different approximations. The interband and intraband electromagnetic decay modes are also analyzed. The use of this framework is exemplified describing systems containing bosons with angular momenta l = 0, 2 and 4.

Application of the nuclear field theory to monopole interactions which include all the vertices of a general force

Abstract The field treatment is applied to the monopole pairing and monopole particle-hole interactions in a two-level model. All the vertices of realistic interactions appear, and the problems treated here have most of the complexities of real nuclei. Yet, the model remains sufficiently simple, so that a close comparison with the results of a (conventional) treatment in which only the fermion degrees of freedom are considered is possible. The applicability to actual physical situations appears to be feasible, both for schematic or realistic forces. The advantage of including the exchange components of the interaction in the construction of the phonon is discussed.

Isovector and isoscalar pairing correlations in a solvable model

Abstract A nuclear model in which the nucleons interact via an arbitrary combination of isovector and isoscalar pairing forces is solved by the use of group theory. Collective features of the energy spectra are studied, together with the transfer of nucleon pairs and α-particles. While pair transfer is strongly affected by the relative strength of the two interaction channels, α-transfer is relatively insensitive, but shows slight enhancement when the two interactions have equal strength.

Collective treatment of the pairing Hamiltonian: (II). Charge-independent force — Hamiltonian and symmetries

Abstract We develop a collective treatment of the problem of neutrons and protons interacting throughout a charge-independent pairing force. The Hamiltonian is expressed in terms of six variables, four of them being angular variables defining orientations in isospace and gauge space, while the remaining two variables represent intrinsic deformation. The symmetries of the problem are discussed in terms of the solutions corresponding to the vibrational limit.

Collective treatment of the pairing Hamiltonian: (III). Numerical solutions for the T = 1 case

Abstract Numerical solutions for the T = 1 pairing collective Hamiltonian are obtained. In the first place, the problem of the rigid rotor is solved, for any value of the asymmetry parameter Γ. Secondly, the potential energy surface due to the pairing force is constructed. A model potential, which reproduces the most important features of the pairing-force surface, is diagonalized within the basis corresponding to the six-dimensional harmonic oscillator. Thus, the properties of the collective motion can be followed from the vibrational limit to the different possible rotational limits.

A two-level solvable model involving competing pairing interactions

Abstract A model is considered consisting of nucleons moving in two non-degenerate l -shells and interacting through two pairing residual interactions with ( S , T ) = (1, 0) and (0, 1). These, together with the single particle hamiltonian induce mutually destructive correlations, giving rise to various collective pictures that can be discussed as representing a two-dimensional space of phases. The model is solved exactly using an O(8) ⊗ O(8) group theoretical classification scheme. The transfer of correlated pairs and quartets is also discussed.

Cluster of nucleons as elementary modes of excitation in nuclei

Abstract Conditions which must be fulfilled by clusters of nucleons to qualify as elementary modes of excitation are analysed in terms of simple criteria involving experimental binding energies. It is found that the most complex possible mode is the α-like cluster.

The renormalization of single-particle states in nuclear field theory

Abstract 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.