R. Liotta

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.

Nuclear field theory as a method of treating the problem of overcompleteness in descriptions involving elementary modes of both quasi-particles and collective type

Abstract It is shown that the graphical perturbation treatment of nuclear fields (particle-vibration theory) converges to the exact solution, at least in the case of schematic many-body problems. The corresponding rules as well as all the interaction vertices required to obtain this convergence are here presented.

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.

Formfactors for one- and two-nucleon transfer reactions induced by light and heavy ions

Abstract Formfactors and overlaps for light and heavy ion transfer reactions are evaluated including finite range and recoil effects. The treatment of the recoil is based on a separation into a transversal effect, responsible for a modification of the selection rules, and a longitudinal effect related to a scaling of the radial motion. The formfactors for multinucleon transfer can in this formulation be obtained either as products of single-particle overlaps and formfactors or, after transformation to center of mass and relative motion, in terms of cluster type representation. The extension of the nuclear field theory to include transfer reactions is indicated. Some examples of the application of the formfactors to calculations of cross sections by means of distorted wave Born approximation are given with the main emphasis on heavy ion reactions.

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.

Quadrupole moments of the 21+ state of proton-closed-shell nuclei

Abstract The leading order contributions (third order in the particle-vibration coupling vertices) to the static quadrupole moment of the lowest J π =2 + state of Ni, Sn and Pb-isotopes have been calculated in the framework of a graphical perturbation method. The microscopic structure of the 2 + phonon is explicitly taken into account and the Pauli principle is respected up to the order of perturbation in which the quadrupole moments are calculated.

Treatment of the spurious states in nuclear field theory

Abstract It is shown, in the framework of a schematic model, that the nuclear field theory (based on the particle-vibration coupling), is a systematic method to eliminate the spurious states occurring in the descriptions of a many-body system which are based on the concept of elementary modes of excitation.

Elementary modes of excitation in the 204Pb(t, p)206Pb REACTION

Abstract The 204 Pb(t, p) 206 Pb reaction has been performed at a bombarding energy of 20 MeV. Angular distributions using solid-state counters and a magnetic spectrograph were obtained for levels up to 8 MeV of excitation. A strong correlation is found between the recorded 206 Pb spectrum and the spectrum observed in the 206 Pb(t, p) 208 Pb, 207 Pb(t, p) 209 Pb and 208 Pb(t, p) 210 Pb reactions. This correlation provides further support for the existence of multipole pairing quanta. These elementary excitations together with multipole surface modes can then be viewed as the basic building blocks of the spectrum around the closed shell nucleus 208 Pb.

Perturbation treatment of the interaction between single-particle and collective degrees of freedom

Abstract The formalism of Brueckner and Levinson is applied to systems of interacting single-particle and collective degrees of freedom. It is shown how to evaluate the diagrams that contribute to the perturbation expansion, at any order, and it is pointed out which diagrams have to be taken into account in the formalism.