Theory of Multi-Photon Ionization of Atoms and Molecules

In this paper we present a density matrix formalism to treat one-photon ionization and multiphoton ionization of atoms and molecules in the presence of an external field. It is shown that Fano's results for one-photon ionization without an external field can easily be obtained from our formulation. For comparison, the Green's function method applied to multiphoton ionization of molecules is also presented.     

Imbedding theorems for spaces of functions with partial derivatives that are summable in various powers

We consider the anisotropic spaces \(W\frac{{\bar l}}{p}(\Omega ),\bar l = \left( {l_1 ,l_2 \ldots ,l_n } \right),l_i > 0,\overline p = \left( {p_1 ,p_2 , \ldots ,p_n } \right),1< p_i< \infty ,i = 1,2, \ldots ,n\) . We extend the class of domains for which imbedding theorems for these spaces have the same form as for E_n. We investigate complete continuity of the corresponding imbedding operators.     

Tautomerism of the Natural Anthraquinones Physcion and Emodin and Their Analogs

The 9,10–1,10-anthraquinoid tautomer was found to be characteristic of physcion and emodin and their analogs in solutions using spectrophotometric, quantum-chemical, and correlation methods. Ionization of these compounds was accompanied by a shift in tautomeric equilibrium. In alkaline solutions 1,10-anthraquinoid anions with a single α-hydroxy that were stabilized by an intramolecular H-bond were formed. Tautomerism occurred in both the ground and excited states of the molecules. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 411–415, September–October, 2005.     

Quantum-chemical and correlation study on the tautomerism and ionization of 1,4,5,8-tetrahydroxy-9,10-anthraquinone and its alkyl-substituted derivatives

1,4,5,8-Tetrahydroxy-9,10-anthraquinone and its alkyl derivatives exist as equilibrium mixtures of prototropic tautomers and rotational isomers differing in the mode of intramolecular hydrogen bonding. Their electronic absorption spectra contain π_l,π* bands corresponding to 9,10-, 1,10-, 1,4-, and (more rarely) 1,5-anthraquinoid structures. Introduction of substituents, solvation, ionization, and complex formation lead to displacement of tautomeric and conformational equilibria, which are responsible for the observed diversity of their absorption spectra.     

Growth and sintering of Pd clusters on alpha-Al2O3(0001)

The growth and sintering of Pd nanoparticles on alpha-Al(2)O(3)(0001) have been studied by noncontact atomic force microscopy (NC-AFM), low-energy ion scattering spectroscopy (LEIS), temperature-programmed desorption (TPD) and x-ray photoelectron spectroscopy (XPS). This is the first study of metal nanoparticles on a well-defined oxide surface where both NC-AFM and LEIS are used for characterization. These prove to be a powerful combination in assessing particle dimensions. The clean alumina surface showed atomically flat, 200-700 nm wide terraces. The sharp step edges are straight (within our resolution) for lengths of >300 nm and have heights in multiples of 0.2 nm. The Pd grows initially as two-dimensional (2D) islands at 300 K, with the transition to 3D particle growth at 0.25 ML (ML=monolayers). Upon heating at 1 K/s, the Pd starts to sinter below 400 K, and sinters at a nearly constant rate with increasing temperature, covering approximately 50% less of the alumina surface by approximately 1000 K, with a doubling in particle diameter and an eightfold decrease in particle number density. By approximately 1000 K, the number density was approximately 9 x 10(11)cm(2) for 0.8 ML of Pd, with an average diameter of 5 nm and an average thickness of 1 nm.     

The effects of SNR on ADC measurements in diffusion-weighted hyperpolarized He-3 MRI

The theoretical dependence of the mean and standard deviation of ADC values on signal-to-noise ratio (SNR) was derived and compared to measured values in porous phantoms and the lungs of human subjects using diffusion-weighted hyperpolarized helium-3 MRI. For SNR values below 15, mean ADC values were highly SNR-dependent due to a combination of noise and choice of noise thresholding. Above SNR values of 15 and for mean ADC values within ranges relevant for evaluating lung disease (<0.6 cm2/s), the mean ADC was largely independent of SNR. The standard deviation, by contrast, was highly dependent on SNR over a much larger range, but this dependence was well predicted by theory, suggesting the histogram of ADC values might be corrected for these stochastic processes to more accurately evaluate disease using restricted diffusion measures in the lungs.