Systematic calculation of molecular vibrational spectra through a complete Morse expansion

We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard‐Jones oscillator, and to the ab initio potential of the H₂ molecule. Global cm^?1 accuracy is exhibited through the H₂ spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi‐dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Some non-existence results for critical equations on step-two stratified groups

We discuss a non-existence result for a semilinear sub-elliptic Dirichlet problem with critical growth on half-spaces of stratified groups of step two. Our result improves a recent theorem (N. Garofalo, D. Vassilev, Math. Ann. 318 (3) (2000) 453–516). To cite this article: A. Bonfiglioli, F. Uguzzoni, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Superdeformation in142Eu

A rotational band with 15 transitions has been observed in¹⁴²Eu in an experiment with the GASP Ge detector array by the¹¹⁰Pd(³⁷Cl,5_n) reaction. The average energy spacing between the neighbouring transitions is 60 keV, which is similar to the energy spacings in the superdeformed bands in the mass 140 region. The band has a constant dynamic moment of inertia as suggested by Cranked Shell Model calculations.