Nuclear partition functions in the random phase approximation and the temperature dependence of collective states

Green functions techniques at finite temperature are used to calculate nuclear partition functions in the random phase approximation. The theory is shown to yield corrections to the results of functional methods neglecting exchange terms. We discuss the special case of a schematic model for which the level density and the temperature dependence of collective states can be worked out explicitly.     

Broadband tunability of dye lasers

A double compartment dye cell to hold two or more dyes has been found to increase the frequency range of dye lasers. Results are compared with those obtained by mixing the same two dyes in a single cell. The dye cells are transversely pumped by a nitrogen laser. Broadband tunability results from dyes having similar absorption ranges but different Stokes shifts.     

Problem Department

This department aims to provide problems of interest to people engaged in the study of mathematics and science. All readers are invited to both propose and solve problems. In submitting solutions and proposals the following guidelines should be observed.     

Inductions électromagnétiques en relativité générale et principe de Fermat

Sans résumé Mémoire transmis par A. Lichnerowicz     

Spherical functions and invariant differential operators on complex Grassmann manifolds

Proofs are given of two theorems of Berezin and Karpelevi?, which as far as we know never have been proved correctly. By using eigenfunctions of the Laplace-Beltrami operator it is shown that the spherical functions on a complex Grassmann manifold are given by a determinant of certain hypergeometric functions. By application of this result, it is proved that a certain system of operators, fow which explicit expressions are given, generates the algebra of radial parts of invariant differential operators.