An interpretation of the large shifts of the electronicg-factors of the relaxed excited state (RES) ofF-centres relative to theg-factor of the free electron is given. Theseg-shifts are quantitatively explained by admixture of higher excited states to the RES through the magnetic interaction. This interpretation avoids the serious difficulties and contradictions which arise when one tries to explain theg-factor shifts exclusively within the framework of the vibronic model. As a byproduct new values for the mean radius of the RES wavefunctions are given.

The nuclear quadrupole interaction of the 8+ isomers in206, 208Po was measured in the semimetallic host Bi. The comparison of the extracted electric field gradient eq for PoBi with the values for the neighboring elements Bi and Pb as probe atoms in Bi reveals a very drastic increase from Pb to Bi and to Po by an order of magnitude: eqPbBi∶eqBiBi∶eqPoBi=1.64(10)∶4.8(3)∶16(2)

In the spirit of Haken's theory of phase transition-like phenomena, the Maxwell-Bloch system is reduced to a single nonlinear equation for the electric field through an exact elimination of the atomic dynamics, by means of the Laplace transform technique.

By considering a Potts model on a pseudo-lattice such as a tree or a Husimi tree, it is shown that the analyticity of the free energy in the absence of a field for such systems is due to a graph-theoretical property of these lattices called locality. It is proved that, if this property is destroyed by introducing next-nearest neighbour interactions, then the free energy in the absence of a field is nonanalytic as a function of the nearest-neighbour interaction energy below a critical temperature. An exact relation shows that this nonanalyticity is of the same type (phase transition of continuous order) as that found for the Ising model on a Cayley tree with external field.

The narrow widthsW(≈1 eV) of 5d subbands occurring in a model for 5d electrons in the heavy rare-earth metals are reinterpreted as effective bandwidths for the purpose of determining the equilibrium occupation numbers of 5d subbands. It is shown that, if explicit consideration of interactions between 5d electrons is limited to intraatomic Coulomb interactions without exchange, then, to first order in the intraatomic repulsion energyU between 5d electrons, these effective widths satisfyW=W1-FU. HereW1 is a rectangular-subband equivalent of the overall subband width, andF is a numerical factor, the value of which depends on the local basis states and number of 5d electrons per atom. For the model being discussed it is estimated thatF=0.6±0.4. A valueW 1 B ≈4 eV is inferred forW1 in Gd from results of band-structure calculations. The termFU cannot account for all of the difference betweenW 1 B andW; the discrepancy is attributed to effects of correlation onW1.

We consider the semi-infiniteq-state Potts model in the many component limitq→∞. Both mean field theory and the Migdal-Kadanoff renormalization group scheme are used to obtain an approximate surface free energy. Both methods predict a new low temperature phase where the bulk is ordered while the free surface is disordered.

The conditions for the appearance of a reentrant superconducting phase in granular materials are studied in mean field approximation applied to periodic models. We assume that the relevant low-lying excitation is the transfer of a Cooper pair from a grain to one of its neighbours, and neglect pair breaking. Both on-grain (U) and nearest neighbour (V) Coulomb interactions are taken into account, and the Coulomb problem is treated in Bethe-Peierls approximation. WhenV/U is not too large, reentrance is predicted ifV/U>(4+3z)−1/2 wherez is the coordination number. This result is different from a recent criterion suggested by Simanek, which allows reentrance only in the immediate vicinities of certain discrete values ofV/U.

The transition temperature obtained from recent Monte Carlo calculations for the Quartet Ising model on the fcc lattice deviated by 17% from the exact transition temperatureT SD required by selfduality which we have proven afterwards. Here we use Monte Carlo results of the internal energy, which agree well with low- and high temperature series, to determine entropy and free energy and obtain aT c in excellent agreement (±0.1%) with the exact value. The Quartet model on the hcp lattice is shown to be selfdual too; the rapidly converging series for the fcc and the hcp lattice differ only in higher order.

We show that bistable behaviour in a two-photon resonant system within a cavity may be attributed to interactive mode-pulling via the two-photon optical Kerr effect and also to absorptive bleaching (atomic saturation). The interactive Kerr process may be regarded as giving rise to a new category of optical bistability. Moreover, a mechanism for the recently-predicted tristability can be found in terms of simultaneous competition between the interactive Kerr effect and bleaching.

Using the TDPAC-method with the proble nucleus111Cd the electric quadrupole interaction (QI) in the trigonal semiconductor Te has been investigated in the temperature range 77 K≦T≦655 K. In contrast to most metals the quadrupole frequencyv Q increases with increasing temperature. This is a consequence of the fact that in metals the charge carrier density is temperature independent, whereas in semiconductors it strongly increases with temperature. A comparison between the temperature variation of the quadrupole coupling constantv Q and that of the charge carrier density leads to the conclusion that the QI in Te is governed by changes in the free electron density.