Ein verschärfter und verallgemeinerter Satz von Alexandrov

In this paper we prove the following theorem: Suppose that n≥3 and 1≤jn $$(\forall a,b) d(a,b) : = \sum\limits_{\nu = 1}^j { (a_\nu - b_\nu )^2 - \sum\limits_{\nu = j + 1}^n { (a_\nu - b_\nu )^2 .} }$$ If a function f:?ⁿ→?ⁿ satisfies the condition: (*) $$(\forall x,y \in \mathbb{R}^n ) d(f(x),f(y)) = 0 \Leftrightarrow d(x,y) = 0,$$ then f is affine. Moreover, f preserves distances up to a constant factor C≠0, i.e. d(f(x),f(y))=C·d(x,y) for every x,y. In contrast to Alexandrov's result [1] we do not assume that f is bijective, and we also do not assume that j=n?1. A very important part of our proof will be the discussion of a functional equation.     

Determination of the partial electron capture- and spontaneous-fission half-lives of254No

The isotope²⁵⁴No was produced in the fusion reaction⁴⁸Ca +²⁰⁸Pb. Using the velocity filter SHIP and radiochemical techniques it was found that the nuclide²⁵⁴No with a half-life of 55 s decays byα, EC, and spontaneous-fission. Deduced partial half-lives are (61±2) s forα-decay, (550 _?160 ⁺³⁷⁰ ) s for EC and [2.2 _?1.0 ^+2.0 ]×10⁴ s for spontaneous fission.     

The isotopes259106,260106, and261106

In irradiations of²⁰⁷Pb and²⁰⁸Pb, respectively, with⁵⁴Cr theα-decay of the isotopes²⁵⁹106,²⁶⁰106, and²⁶¹106 could be observed for the first time. For²⁶⁰106 a spontaneous fission branch of (50 _?20 ⁺³⁰ )% was observed. The isotopes were identified by genetic relationships of α-decay after separation in-flight with the velocity filter SHIP and implantation into a position-sensitive silicon surface-barrier detector. The measured partial fission halflife of the doubly even isotope²⁶⁰106 of (7.2 _?2.7 ^+4.8 )ms exceeds the predicted values by at least a factor of 40. This result could be explained by the high shell corrections of the ground state mass, derived from the measured α-decay energies. The experimental results show evidence for an island of purely shell stabilized nuclei in the region of deformed isotopes beyond the actinides.     

TR-LII for sizing of carbon particles forming at room temperature

Time-resolved laser-induced incandescence (TR-LII) was applied for the determination of particle sizes during carbon-particle formation from supersaturated atomic carbon vapor that was generated by laser photolysis of carbon suboxide (C₃O₂) at room temperature. Thus, the solid carbon particles were formed under hydrogen-free conditions. The TR-LII technique was used for in situ size measurement of growing carbon particles and samples of final particles were analyzed by transmission electron microscopy (TEM). It was found that the particles grow to a final size of 4–12 nm within 0.02–1 ms. The properties of the obtained particles depend on the initial conditions in the reaction volume, i.e. concentration of carbon suboxide, pressure and type of gas diluter, photolysis wavelength, and laser pulse energy. The comparison of TR-LII and TEM particle sizing results yields information about the effective thermal energy accommodation coefficients for He, Ar, CO, and C₃O₂ molecules on carbon particles. PACS 61.46.Df; 07.60.-j; 78.70.-g     

Metal–Polymer Hybrid Nanoparticles for Correlative High‐Resolution Light and Electron Microscopy

The combination of fluorescence microscopy and electron microscopy promises a deeper insight into the ultrastructural features of cell organelles, e.g., after drug administration. Both methods complement each other and provide, as a correlative approach, a keen insight into the fate of nanoparticles within the cell. Moreover, it represents a promising tool to determine alterations of the cellular environment as a response to particle uptake. However, the availability of suitable correlative markers is mandatory for such correlative approaches. In this contribution, the utilization of poly(ethylene imine) based metal–polymer hybrid particles labeled with small gold nanoparticles and Rhodamine B facilitating the observation of the particles by means of fluorescence as well as by transmission electron microscopy is suggested. Correlative light and electron microscopy is used to study uptake and intracellular fusion processes of endosomal/lysosomal structures.     

Investigation of the fusion reaction27Al+236U→263105 at excitation energies of 57 MeV and 65 MeV

The neutron-deficient isotopes^257,258105 were produced in the reaction²⁷Al+²³⁶u in 6n and 5n evaporation channels, respectively. The evaporation residues emerging from the target were separated in-flight from the projectiles and from products of different nuclear reactions by the electrostatic separator VASSILISSA [1]. The isotopes were then implanted into position-sensitive silicon detectors and identified using the --correlation method. The measured production cross-section is (5n)=(0.45±0.20)nb atE _P =154 MeV and (6n)=(0.075±0.055) nb atE _P =163 MeV. These cross-sections are compared with data measured for the same isotopes in the more symmetrical reaction⁵⁰Ti+²⁰⁹Bi.     

Lamb shift of laser-dressed atomic states

We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.