Table of contents

The (p,n) charge exchange reaction is a powerful tool of nuclear structure physics, with spectroscopic characteristics that are closely related to the free interaction between nucleons. At proton energies in the range of 150-500 MeV, the interaction probes the spin dynamics in the charge exchange process and is particularly sensitive to nuclear pionic fields. At low energies, say less than 50 MeV bombarding energy, the reaction also probes the isovector density. An outstanding success of the reaction as a structural probe is the elucidation of the Gamow-Teller strength function in the nuclear excitation spectrum. However, the total strength found falls short of sum rule predictions by about 40%. Explanations of this quenching have been advanced along two lines, based on subnuclear degrees of freedom or on configuration mixing into high continuum states. Detailed theoretical arguments support the importance of configuration mixing. The subnuclear degrees of freedom may be comparable, but a decisive test is lacking.

A review of the quantised Hall effect is given. The author surveys experiments and theories on the normal and fractional quantum Hall effect including recent developments. As a background to the effect, which is a most remarkable manifestation of the Landau quantisation, the author starts with the description of the two-dimensional electron system in magnetic fields. As a closely related topic, the author also discusses the singular localisation of states specific to systems under the Landau quantisation in two dimensions. The determination of the fine-structure constant including the quantum Hall method is also briefly reviewed. In giving a self-contained account of the effect we emphasise the special features of the quantised Hall effect, which has an aspect of macroscopic quantum phenomenon on the one hand, and invokes, in the presence of electron-electron interactions, a new quantum liquid state on the other.

The problem of microscopic nuclear structure theory in large single particle basis systems is reviewed. Several approaches are discussed, which attempt to approximate the large model spaces numerically inaccessible in complete shell model expansions of the nuclear wavefunctions. All of them use symmetry projected Hartree-Fock-Bogoliubov quasiparticle configurations as basic building blocks of the theory. They differ, however, in the degree of sophistication of the variational procedures which are used to determine the corresponding mean fields as well as the configuration mixing, up to a level, on which the construction of the configuration space itself is entirely left to the dynamics of the considered system. The mathematical formalism underlying these models is briefly summarised and the steps towards a numerical realisation are discussed. In several examples the possibilities and the power of the models are demonstrated and their limitations are shown. The models may provide a powerful tool for the analysis of experimental data as well as for predictions in still unexplored regions. On the other hand they may lead to a much better theoretical understanding of effective nuclear interactions as well as the underlying fundamental forces.