Negative molecular ions of azafullerenes and their hydrogenated derivatives

The formation and decay of negative molecular ions of azafullerenes and their hydrogenated derivatives are investigated by mass spectrometry. The mechanisms of resonant electron capture and the lifetimes of negative molecular ions with respect to the electron autodetachment in azafullerene molecules are discussed. A comparative analysis of the data obtained for azafullerenes and hydrogenated fullerene derivatives is carried out.     

Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.     

Realisation and metrological characterisation of thickness standards below 100 nm

High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO₂ on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh     

Arithmetic functions with linear recurrence sequences

We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.     

A large scale double beta and dark matter experiment: On the physics potential of GENIUS

The physics potential of GENIUS, a recently proposed double beta decay and dark matter experiment is discussed. The experiment will allow to probe neutrino masses down to 10^?(2–3) eV. GENIUS will test the structure of the neutrino mass matrix, and therefore implicitly neutrino oscillation parameters comparable or superior in sensitivity to the best proposed dedicated terrestrial neutrino oscillation experiments. If the 10^-3 eV level is reached, GENIUS will even allow to test the large angle MSW solution of the solar neutrino problem. Even in its first stage GENIUS will confirm or rule out degenerate or inverted neutrino mass scenarios, which have been widely discussed in the literature as a possible solution to current hints on finite neutrino masses and also test the ν_e ? ν_μ hypothesis of the atmospheric neutrino problem. GENIUS would contribute to the search for R-parity violating SUSY and right-handed W-bosons on a scale similar or superior to LHC. In addition, GENIUS would largely improve the current 0νββ decay searches for R-parity conserving SUSY and leptoquarks. Concerning cold dark matter (CDM) search, the low background anticipated for GENIUS would, for the first time ever, allow to cover the complete MSSM neutralino parameter space, making GENIUS competitive to LHC in SUSY discovery. If GENIUS could find SUSY CDM as a by-product it would confirm that R-parity must be conserved exactly. GENIUS will thus be a major tool for future non-accelerator particle physics.