Exciton interaction potential in polar crystals

The problem whether polaron effects can lead to a repulsive barrier in the exciton interaction potential is reinvestigated, because this effect is crucial for the possibility of a Bose-Einstein condensation of excitons (rather than of excitonic molecules). The energy for two excitons is calculated accurately as a function of their mean distance in the case of a heavy hole mass by using an integral expansion method of molecular physics. The resulting interaction potential shows for certain polaron radii a very weak repulsive barrier. Taking into account corrections to the Haken potential which have been introduced by Pollmann and Büttner, it is shown that the interaction potential between two excitons in the relative singlet state is always attractive, so that the exciton system is also in polar materials unstable against exciton molecule formation.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Viscosity and optical measurement on fluoride glasses

Scattering loss and viscosity against temperature measurements have been carried out on fluoride glasses. The results indicate for the first time a ?-4 behaviour for scattering loss in the 0.45?0.75 ?m wavelength range. Activation energies for viscous flow were found to be similar for both ZrF4? and HfF4?based glasses.     

Measurement of the differential cross section for πp → πn around the Δ(1232) resonance and test of the charge independence principle

Differential cross sections for the charge-exchange reaction of π⁻ on protons in the region of the Δ(1232) resonance (128 MeV T_π⁻ 246 MeV) are reported. Measurements were performed by detecting the neutron with a time-of-flight technique. The neutron counter efficiency was measured over the entire energy range. Particular care was devoted to eliminating possible sources of systematic error. Statistical errors are of the order of 4%, total errors of the order of 7%. The experimental results are in fair agreement with the most recent phase-shift analysis. Our data satisfy the triangle inequality. An analysis based on recent phase-shift values does not favour violation of charge independence.     

On a fixed-point theorem

Institute of Mathematics, Hanoi. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 30, No. 3, pp. 93–94, July–September, 1996.     

Substrate issues for the growth of mercury cadmium telluride

Close lattice matching and lattice compatibility with mercury cadmium telluride (MCT) make CdTe and related alloys ideal substrate materials for growth of MCT layers for the purpose of making high-performance second-generation infrared detectors. However, the limitations in the properties of CdTe and the difficulties in its bulk growth have prompted extensive research in the area of alternative substrates. Some basic relevant characteristics of substrates such as sapphire, GaAs, and silicon are compared and the possibilities and problems associated with each material are analyzed in the light of the most recent results in the field.     

Soft multihadron production from partonic structure and fragmentation functions

We describe a two-chain model for soft multiparticle production in hadronic collisions. The model is formulated in a parton framework and is consistent with the dual topological scheme for the Pomeron. The sole inputs are valence quark structure functions in the colliding hadrons and parton fragmentation functions, both of which are known from “hard” processes. Our model, which contains no adjustable parameters, reproduces the shape, the energy dependence, and the normalization of inclusive spectra both in the central region and in the fragmentation region. The model provides a natural explanation for the ratio of πp topp cross sections.     

Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals

We give criteria for the Cohen-Macaulay and Gorenstein property of Rees algebras of height 2 non-singular equimultiple prime ideals in terms of explicite representations of the associated graded rings. As consequences, we show that in general, the Cohen-Macaulay resp. Gorenstein property of such Rees algebras does not imply the Cohen-Macaulay resp. Gorenstein property of the base ring and that these properties depend upon the characteristic. Dedicated to the memrory of Professor Lê Van Thiêm Professor Lê Van Thiêm was the first directorof Hanoi Institute of Mathematics