Highly selective and efficient multiphoton dissociation of polyatomic molecules in multiple-frequency IR-laser fields

An ir multiphoton dissociation (MPD) process in multiple-frequency ir-laser fields has been experimentally realized. A selectivity ofS=10⁴ was obtained in separating¹³C/¹²C isotopes upon multiple-frequency ir multiphoton dissociation (MFMPD) of the CF₂HCl molecule, the dissociation yield¹³ for the¹³CF₂HCl molecule amounting to around 1%. A yield of¹³ was reached at a selectivity ofS=10², and the total laser fluence required for the process was reduced. A new mechanism—sticking of molecules on the lower discrete vibrational levels—responsible for the low MPD yields observed for some molecules is discussed and a technique to eliminate it and thus maximize the dissociation yields is proposed. Ways to improve the selectivity by MFMPD are analyzed and a simple method for obtaining from a single TEA CO₂ laser a multiple-frequency radiation suitable for experimental realization of MFMPD is suggested.     

Quantum-resolved fluorescence excitation spectra of SnO free radical

TheA ¹ –X ^{1 +} system of SnO is studied by laser- induced fluorescence excitation spectroscopy using isotopically enriched tin Sn¹¹⁶. The rotational structure analysis has been carried out for 6-0, 5-0, 2-0 bands. All these spectra were well resolved only with few perturbed lines in 2-0 band. Rotational constantsB ₂,B ₅,B ₆ and henceB _e , _{e e} have been obtained for the Sn¹¹⁶O molecule. An extension of perturbation study on 4-0 band has been made showing the maximum perturbation occurs at different J values for different isotopes.     

Influence of collisional coupling on the energy extraction from theB,C, andD state in KrF

Collisional coupling between theB, C, andD states of KrF is measured in a discharge pumped KrF laser. Detection of the time resolved populations in the three states via measurement of the side fluorescence in theB→X, C→A, andD→X bands is used to record the collisional relaxation from theC andD state to theB state during laser emission. The experimentally determined limits for the collisional coupling times are τ_B-C≦1 ns and τ_B-D,τ_C-D<20 ns at total pressures of 2 bar. Investigation of theB→X fluorescence band shows that the vibrational manifold of theB state is not thermalized during laser emission. TheV-V,T coupling time is estimated to be τ_V-V,T=4±2 ns. The influence of collisional coupling on energy extraction in the KrF laser is discussed.     

Multiple infrared photon absorption in OsO4

Multiple ir photon absorption spectra (MPAS) of OsO₄ are obtained in the range of energy fluencies from 3·10⁻² to 1.26 J/cm². A possible interpretation of MPAS is given on the basis of weak forbidden rovibrational transitions. The stepwise character of the absorption on the laser energy fluence is observed.     

Doppler-free intracavity polarization spectroscopy using elliptically polarized light

The optically induced polarization change was studied in the case of a standing elliptically polarized wave. Using a Zeeman-tuned gas laser at 3.39 μm with an internal methane cell we have demonstrated the influence of the dichroism on the nonlinear absorption signals.     

Spectral line competition in a coaxial electron-beam-pumped high pressure Ar/Xe laser

In order to study the kinetic mechanism of the e-beam pumped Ar/Xe laser, the temporal profiles of individual laser lines during multiline oscillation have been measured as a function of power deposition (1–12MW/cm³) and gas laser pressure (2–14 bar) using a short pulse (30 ns) coaxial electron beam as excitation source. It was found that the optimum output energy at each pressure was obtained at the same specific power deposition.Strong line competition has been observed between the 2.65 and 1.73 m transitions. In order to explain our results we suggest that besides electron collision mixing (ECM) between the 5d and 6p levels of Xe, there is also a redistribution between all 6p levels which strongly favours the lower levels at higher pumping densities.     

SDiff(2) Toda equation — Hierarchy,Tau function,and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS ¹×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.     

Representations of lie groups and multidimensional special functions

This work is devoted to the construction and investigation of two new classes of special functions, related to representations of groups of motions in the spaces of constant curvature as well as the unitary group of large ranks. These are special functions with matrix indices and some types of orthogonal polynomials in several continuous and discrete variables. The functions introduced generalize a number of classical scalar special functions in one variable.     

On Gauss's proof of Seeber's Theorem

Summary Gauss proved Seeber's Theorem, that the determinant of a reduced positive definite ternary quadratic form is at least half the product of its diagonal coefficients, by means of two determinantal identities whose origin has remained unclear. We examine Gauss's method from a general standpoint, as a method whereby, in certain circumstances, a polynomial in several variables may be shown to be non-negative on a convex polytope by representing it as a positive multilinear combination of the linear forms which determine the polytope. We show that Gauss's identities may be obtained in this manner and that the two identities can in fact be replaced by a simpler single identity which also gives Oppenheim's precise minimum for the determinant.