Weighted divisor sums and Bessel function series,II

On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. In each case, there are three possible interpretations for the double series. In an earlier paper, two of the present authors proved the first identity under one possible interpretation. In the present paper, the second identity is proved under a similar interpretation, with one additional assumption. Moreover, under a second interpretation, entirely different proofs of both identities, depending on weighted (or twisted) divisor sums, are offered. The two identities are intimately connected with the classical circle and divisor problems, respectively.     

Formation of phenol and carbonyls from the atmospheric reaction of OH radicals with benzene

The gas-phase reaction of OH radicals with benzene has been studied in a flow tube operated at 295 +/- 2 K and 950 mbar of synthetic air or O2. Ozonolysis of tetramethylethylene (dark reaction) with a measured OH radical yield of 0.92 +/- 0.08 or photolysis of methyl nitrite in the presence of NO served as the OH sources. For investigations in the presence of NOx, the conditions were chosen so that more than 95% of the OH/benzene adduct reacted with O2 even for the highest NO2 concentration occurring in the experiment. In the absence of NOx, a phenol yield from the reaction of OH radicals with benzene of 0.61 +/- 0.07 was measured by means of long-path FT-IR and UV spectroscopy over a wide range of experimental conditions. This yield was confirmed by measurements performed in the presence of NOx. Detected carbonyls were glyoxal, cis-butenedial and trans-butenedial with formation yields of 0.29 +/- 0.10, 0.08 +/- 0.03 and 0.023 +/- 0.007, respectively, measured in synthetic air and in the presence of NOx. There was no significant difference in the product yields applying both experimental approaches for OH generation (dark reaction or photolysis). Nitrobenzene and o-nitrophenol were detected in traces. The yield of nitrobenzene increased with increasing NOx resulting in a maximum formation yield of 0.007. The detected products in the presence of NOx account for approximately 78% of the reacted carbon. Butenedial yields from benzene degradation are reported for the first time. In the absence of NOx, glyoxal, cis-butenedial and trans-butenedial were also detected, but with distinctly lower yields compared to the experiments with NOx.     

Electronic structure of C60 on Au(887)

We present an analysis of the electronic structure of C60 adsorbed on a vicinal Au(111) surface at different fullerene coverages using photoemission, x-ray absorption, and scanning tunneling microscopy/spectroscopy (STS). STS provides a straightforward determination of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) levels with respect to the Fermi energy. At C60 coverages of 0.5 and 1 ML a 2.7 eV wide HOMO-LUMO gap is found. The near-edge x-ray absorption fine structure (NEXAFS) spectrum for the 0.5 ML C60 nanomesh structure displays a significant intensity at the low energy side of the LUMO exciton peak, which is explained as due to absorption into HOMO-LUMO gap states localized at individual C60 cluster edges. From 0.5 to 1 ML we observe a rigid shift of the HOMO-LUMO peaks in the STS spectra and an almost complete quenching of the gap states feature in NEXAFS.     

Investigation of iron-cobalt alloys by means of electron spectroscopic methods

The results of electron spectroscopic investigations are presented for a number of FeCo alloys. Besides X-ray photoelectron spectroscopy the Auger spectrometry, appearance potential spectroscopy and electron loss spectroscopy are used. From these data conclusions are drawn about the electronic structure of the FeCo alloy system, among other things in the dilute limit.