X-ray amplification in intense ultrashort KrF laser–Xe cluster interactions

In earlier work, a time-dependent, ionization dynamic model of a cluster of xenon atoms was constructed [2], [3] in an effort to determine conditions under which the X-ray line amplification data that was observed experimentally at wavelengths between 2.71 and 2.88 Å [1] could be replicated. Model calculations showed that, at laser intensities greater than 10¹⁹ W/cm², the outermost N-shell electrons of xenon would be stripped away by tunnel ionization in less than a femtosecond. They also showed that L-shell electrons within the resulting cluster of Ni-like ions could be photoionized at a sufficient rate as to generate population inversions between these hole states and the states they radiatively decayed into. These inversions only lasted for several femtoseconds, and they were generated early in time when the cluster was being rapidly heated and the cluster's density was rapidly evolving, but was still high. They were seen to depend on the heating and expansion dynamics of the cluster, which had not been modeled in detail in this early work. In this paper, molecular dynamics calculations are described in which the rapidly evolving temperatures and ion densities of an intensely laser-heated cluster are calculated for different peak laser intensities and for two different sized xenon nano-clusters. This data is then used as an input to the ionization dynamic calculations in order to determine the influence of cluster size and of peak laser intensity on the gain coefficient calculations. In these calculations, inner-shell photoionization rates are shaped by the temperature and density dependence of the bremsstrahlung emissions under the assumption that these emissions drive the photoionizations. This shaping produces calculated gain coefficients that agree well with the measured ones.     

Sets of uniqueness for spherically convergent multiple trigonometric series

A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.

     

Leading off-diagonal correction to the form factor of large graphs

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, K(tau), of a generic quantum graph with mixing classical dynamics and time-reversal symmetry. We calculate the contribution from pairs of self-intersecting orbits that differ from each other only in the orientation of a single loop. In the limit of large graphs, these pairs produce a contribution -2tau(2) to the form factor which agrees with random-matrix theory.     

VLPR study of the reaction Br + CH3CHO

The reaction \documentclass{article}\pagestyle{empty}\begin{document}${\rm Br} + {\rm CH}_3 {\rm CHO}\buildrel1\over\rightarrow{\rm HBr} + {\rm CH}_3 {\rm CO}$\end{document} has been studied by VLPR at 300 K. We find k₁ = 2.1 × 10¹² cm³/mol s in excellent agreement with independent measurements from photolysis studies. Combining this value with known thermodynamic data gives k_-1 = 1 × 10¹⁰ cm³/mol s. Observations of mass 42 expected from ketene suggest a rapid secondary reaction: in which step 2 is shown to be rate limiting under VLPR conditions and k₂ is estimated at 10^12.6 cm³/mol s from recent theoretical models for radical recombination. It is also shown that 0 ? E₁ ? 1.4 kcal/mol using theoretical models for calculation of A₁ and is probably closer to the lower limit. Reaction ?1 is negligible under conditions used.     

Wide-band interferometric tuning of a multiatmosphere CO2 laser

We describe the operating characteristics of a compact, frequency tunable, electron-beam-controlled, 15 atmosphere CO₂ laser. Two intracavity Fabry-Perot etalons have been used to obtain laser line narrowing and continuous tuning within the 10.4 μm and 9.4μm bands of the CO₂ gain spectrum. The laser output consists of a 100 nsec pulse (fwhm) with energy up to 100 mJ. The overall laser tuning range is 70 cm^-1 and we have measured a laser linewidth of 0.03 cm^-1.