Approximations for modal coupling in scattered fields from orifices

Previous investigations have used Hankel transforms to establish the velocity potentials of the wave fields resulting from arbitrary angle plane wave impingement on a circular orifice in a rigid, thick wall. The scattered field from the orifice is examined, in particular the modal contributions to the amplitude of its velocity potential. For each m,n mode the amplitude is dependent upon the amplitude of the in-orifice waves and a driving term unique to each m,n mode. In establishing the amplitudes of the in-orifice waves, the effects of modal coupling are also considered. In this work these two components of the scattered wave amplitude are investigated on a modal basis and approximations given for coupling effects. These approximations are then used to calculate the scattered field and the results compared with conventional solutions that use full modal coupling.     

Density modulation and superconductivity in a system of fermions

An antisymmetrized product of periodic density modulated one particle functions is investigated as a trial wave function for different local twobody forces. The model is compared with a BCS ground state. For some potentials a lower ground state energy has been found for the density modulated state. In lowest order cluster expansion forces with a hard core have been examined. A liquid-solid transition is indicated for³He at a density near the experimental value.     

Studien zum Vorgang der Wasserstoffübertragung. 36. Mitt. Einfluß von Art und Struktur einiger Leitsalze auf die elektrochemische Spaltung von Diarylsulfonen

Ohne Zusammenfassung     

Influence of short-range correlations on the phonon spectra of f.c.c. helium and neon

The influence of short-range correlations on the phonon spectra of helium at high pressures and of neon is investigated. It is found that a simple cutoff procedure is insufficient. A more appropriate treatment of the hard core might also be necessary for the heavier rare-gas solids at higher temperatures.     

Lattice dynamics of quantum crystals

A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He³ show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results.     

Product studies and laser flash photolysis on alkyl radicals containing two different beta-leaving groups are consonant with the formation of an olefin cation radical.

1-Bromo-2-methoxy-1-phenylpropan-2-yl (3) and 2-methoxy-1-phenyl-1-diphenylphosphatopropan-2-yl (4) were generated under continual photolysis from the respective PTOC precursors in a mixture of acetonitrile and methanol. The radicals undergo heterolytic fragmentation of the substituent in the beta-position to generate the olefin cation radical (5). Z-2-Methoxy-1-phenylpropene (15) is the major product formed in the presence of 1,4-cyclohexadiene, and is believed to result from hydrogen atom transfer to the oxygen of the olefin cation radical, followed by deprotonation. Laser flash photolysis experiments indicate that reaction between 5 and 1,4-cyclohexadiene occurs with a rate constant of approximately 6 x 10(5) M(-1) s(-1). 2,2-Dimethoxy-1-phenylpropane (18) is observed as a minor product. Laser flash photolysis experiments place an upper limit on methanol trapping of 5 at k <1 x 10(3) M(-1) s(-1) and do not provide any evidence for the formation of reactive intermediates other than 5. The use of two PTOC precursors containing different leaving groups to generate a common olefin cation radical enables one to utilize product analysis to probe for the intermediacy of other reactive intermediates. The ratio of 15:18 is dependent upon hydrogen atom donor concentration, but is independent of the PTOC precursor. These observations are consistent with the proposal that both products result from trapping of 5 that is formed via heterolysis of 3 and 4.