D.R. Bès

Nuclear field theory

Abstract The nuclear spectrum is described in terms of elementary modes of excitation comprising pairing and surface vibrations and single-particle degrees of freedom. A unified theory of the mutual interweaving of these excitations which makes use of many-body field theoretical concepts is reviewed. The theory is illustrated through the study of the nuclear structure of 209 Bi.

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.

COLLECTIVE TREATMENT OF THE PAIRING HAMILTONIAN. I. FORMULATION OF THE MODEL.

Abstract We develop a treatment of the pairing force problem in terms of two collective variables: the intrinsic deformation α and the gauge angle φ. The comparison between the results obtained solving the corresponding quantum mechanical Hamiltonian and those obtained by an exact diagonalization shows the adequacy of the present approach.

Solution of bohr's collective hamiltonian

Abstract The Bohr collective Hamiltonian is diagonalized within the basis set of states corresponding to the quadrupole vibrator around the spherical equilibrium position. The dependence of the solution on the properties of the basis is discussed. Typical computer times used in the application of the method are given. The minimum number of spherical phonons that is needed in order to represent transition and well-deformed nuclei is also obtained.

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.

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.

Shell-model analysis of pairing excitations in the region 52 ≦ A ≦ 60

Abstract A shell-model diagonalization of a T = 1 residual pairing interaction is performed in the vicinity of 56 Ni for J π = 0 + states. Energies and differential cross sections for two-body transfer processes are compared with experimental values and with the harmonic predictions. Special attention is paid to those reactions which are sensitive to the existence of a phase transition between normal and superconducting systems. Furthermore, it is shown that the assumption of a harmonic non-adiabatic addition phonon explains systematically a number of weak transitions. A list of spectroscopic amplitudes for relevant (and so far unreported) cross sections is included.

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.