Table of contents

Surveys recent theories on the transition between commensurate (C) and incommensurate (I) phases, and on properties of the I phase. The devil's staircase concept for the I phase is described. Differences between theories in two and three dimensions are discussed, together with those on chaotic structures.

In the 'fourth test of general relativity' the gravitational acceleration of celestial bodies-the Earth and the Moon-were experimentally compared in the gravitational field of the Sun. Because such bodies obtain an appreciable fraction of their total mass-energy from their internal gravitational self-energy (5*10^-10 for the Earth), this comparison of free-fall rates measures, among other things, how gravity pulls on gravitational energy and how gravitational energy contributes to the inertial mass of celestial bodies. Using high-precision laser ranging between Earth and reflectors on the Moon's surface, it was found that the Earth and Moon's acceleration in the Sun's gravitational field are the same to one part in 10¹¹. Hypothesising that the gravitational to inertial mass ratio of a celestial body may differ from one by the order of the gravitational self-energy content of the body divided by the total mass-energy: M_G/M_I=1+ eta (U_G/Mc²) eta being a dimensionless constant determined by gravitational theory, the lunar laser ranging experiment limits mod eta mod to less than 1.4*10^-2. This experiment is consistent with general relativity which predicts eta =0, but scalar-metric tensor theories, such as the Brans-Dicke theory, vector-metric tensor theories and two-tensor theories of gravity are inconsistent with this experiment unless sufficient adjustable parameters are used.

The description of transitional nuclei, which have a deformation between spherical and strongly deformed nuclei, is reviewed. The author concentrates on models with a phenomenological core and one or two nucleons moving in its potential. For the core a rigid axial or triaxial rotor, the Bohr-Mottelson model or the interacting boson approximation is used. The motion of the additional nucleons is described as quasiparticles moving in the rotating deformed potential of the core. The properties of the odd nucleons are determined by two forces: (i) the coupling to the quadrupole moments of the core (strong coupling) and (ii) the influence of the Coriolis and centrifugal forces which like to decouple the odd nucleon from the motion of the core (decoupling). Models are presented which can describe at the same time decoupling and strong coupling and the competition between both. The model is applied to odd-mass nuclei, to the two-quasiparticle negative-parity states in even-mass nuclei, to zero- and two-quasiparticle positive-parity states in even-mass nuclei and to doubly odd-mass nuclei. Although it is the Os, Pt and Hg area is emphasised, results for other mass regions are discussed.