On the scattering of waves by a disk

Zusammenfassung Es wird gezeigt, dass das Problem, die Beugung einer ebenen Welle an einer kreisförmigen Öffnung oder Scheibe zu bestimmen, auf die Lösung von regulären Fredholmschen Integralgleichungen zweiter Art zurückgeführt werden kann. Die Lösungen dieser Integralgleichungen liefern uns für die Scheibe im Falle der Neumannschen Bedingung die radiale Variation der Unstetigkeiten der Wellenfunktion und im Dirichletschen Falle die Unstetigkeiten ihrer normalen Ableitung. Ist das Produkt von Öffnungsradius und Wellenzahl klein, so können die Integralgleichungen gelöst werden. Für die Ableitung der Integralgleichungen verwenden wir einerseits die Poissonsche Darstellung für die Wellenfunktion und andererseits die Fortsetzung der Helmholtzschen Darstellung in die komplexe Ebene.     

Derivation of bonding distance and vibration frequency from field evaporation experiments

This paper extends the analysis of previously reported data, concerning the field evaporation of rhodium atoms that escape as Rh⁺ and are then post-ionised to Rh²⁺. A more general formula is derived for obtaining values of critical distance x^cr from correlated measurements of temperature, field (F), activation energy (Q), and onset appearance energy. A zkT-type correction is included. If prior to evaporation the surface atom is vibrating in an effectively parabolic potential well, and a Gomer-type escape mechanism operates, then experimental plots of $\text{Q}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ versus $\text{1}\text{F}$ and of x^cr versus $\text{Q}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ should be linear. Such plots may be used to obtain estimates of zero-Q evaporation field F^e, electrical bonding distance a, and vibrational force-constant k and frequency v. These formulae and methods are applicable to a range of materials and evaporation situations. For rhodium this paper establishes that escape takes place via a Gomer-type escape mechanism, and deduces the following values: F^e = 61 ± 20 V/nm; a = 0.13 ± 0.035 nm; v = (1.4_+0.5^?0.3) × 10¹²Hz.     

The deposition of energy from reactions of laser excited atoms: Strontium 3P1 with hydrogen halides

The chemical reactions of laser excited Sr^*(³P₁) with HF and HCl are studied in a beam gas arrangement with LlF detection. This is the first experiment reported where both the specific electronic state of the reactant is laser prepared and the specific vibrational states of the products are laser detected. The results show that a large fraction of the available energy is released into vibration of SrX.     

Carbon-13 magnetic resonance study of lanthanide-substituted muscle calcium binding parvalbumins

High resolution natural abundance carbon-13 NMR has been used previously to examine molecular motions and conformational transitions in the muscle calcium binding parvalbumins isolated from mirror carp. [S. J. Opella, D. J. Nelson, and O. Jardetzky, J. Chem. Phys. 64 , 2533 (1976) and D. J. Nelson, S. J. Opella, and O. Jardetzky, Biochemistry 15 , 5552 (1976).] The carbon-13 NMR spectrum of parvalbumin typically reveals the presence of a number of well-resolved resonances from single-carbon sites in the protein. Since accurate assignment of these resonances to specific carbon atoms in the protein is essential before these resonances can be employed as probes of local conformational events, an investigation of the origin of a number of single-carbon resonances has been performed. Carbon-13 NMR on Tb(III)- and Yb(III)-substituted parvalbumin is the principal spectroscopic technique employed; however, results from terbium fluorescence spectroscopy, γ-ray scintillation spectroscopy, and x-ray difference Fourier analysis all contribute to single-carbon site assignment. The principal conclusions drawn from the combined spectroscopic results are that: (1) the downfield carboxyl resonance at 184.6 ppm, previously attributed to Glu-81, whose carboxyl group is involved in an internal ionic bond, originates rather from a carboxyl function coordinating the solvent exposed metal ion, (2) the carbonyl resonance at 168.9 ppm arises from Lys-96, as was previously suggested; and (3) the 11.2 ppm resonance derives from the δ-methyl carbon of Ile-97, a resonance assignment that could not be made previously.