Cocliques of maximal size in the prime graph of a finite simple group

In this paper we continue our investgation of the prime graph of a finite simple group started in http://arxiv.org/abs/math/0506294 (the printed version appeared in [1]). We describe all cocliques of maximal size for all finite simple groups and also we correct mistakes and misprints from our previous paper. The list of correction is given in Appendix of the present paper.Comment: published version with correction

Population of isomers in decay of the giant dipole resonance

The value of an isomeric ratio (IR) in N=81 isotones ($^{137}$Ba, $^{139}$Ce, $^{141}$Nd and $^{143}$Sm) is studied by means of the ($\gamma, n)$ reaction. This quantity measures a probability to populate the isomeric state in respect to the ground state population. In ($\gamma, n)$ reactions, the giant dipole resonance (GDR) is excited and after its decay by a neutron emission, the nucleus has an excitation energy of a few MeV. The forthcoming $\gamma$ decay by direct or cascade transitions deexcites the nucleus into an isomeric or ground state. It has been observed experimentally that the IR for $^{137}$Ba and $^{139}$Ce equals about 0.13 while in two heavier isotones it is even less than half the size. To explain this effect, the structure of the excited states in the energy region up to 6.5 MeV has been calculated within the Quasiparticle Phonon Model. Many states are found connected to the ground and isomeric states by $E1$, $E2$ and $M1$ transitions. The single-particle component of the wave function is responsible for the large values of the transitions. The calculated value of the isomeric ratio is in very good agreement with the experimental data for all isotones. A slightly different value of maximum energy with which the nuclei rest after neutron decay of the GDR is responsible for the reported effect of the A-dependence of the IR.Comment: 16 pages, 4 Fig

Anisoplanatic adaptive optics in parallelized laser scanning microscopy

Inhomogeneities in the refractive index of a biological microscopy sample can introduce phase aberrations, severely impairing the quality of images. Adaptive optics can be employed to correct for phase aberrations and improve image quality. However, conventional adaptive optics can only correct a single phase aberration for the whole field of view (isoplanatic correction) while, due to the highly heterogeneous nature of biological tissues, the sample induced aberrations in microscopy often vary throughout the field of view (anisoplanatic aberration), limiting significantly the effectiveness of adaptive optics. This paper reports on a new approach for aberration correction in laser scanning confocal microscopy, in which a spatial light modulator is used to generate multiple excitation points in the sample to simultaneously scan different portions of the field of view with completely independent correction, achieving anisoplanatic compensation of sample induced aberrations, in a significantly shorter time compared to sequential isoplanatic correction of multiple image subregions. The method was tested in whole Drosophila brains and in larval Zebrafish, each showing a dramatic improvement in resolution and sharpness when compared to conventional isoplanatic adaptive optics

Customized CMOS wavefront sensor

We report on an integrated Hartmann wavefront sensor (WFS) using passive-pixel architecture and pixels clustered as position-sensitive detectors for dynamic wavefront analysis. This approach substitutes a conventional imager, such as a CCD or CMOS imager, by a customized detector, thus improving the overall speed performance. CMOS (complementary-metal- oxide-semiconductor) technology enables on-chip integration of several analog and digital circuitry. The sensor performance depends on the feature size of the technology, noise levels, photosensitive elements employed, architecture chosen and reconstruction algorithm.(undefined

Spin splitting of X-related donor impurity states in an AlAs barrier

We use magnetotunneling spectroscopy to observe the spin splitting of the ground state of an X-valley-related Si-donor impurity in an AlAs barrier. We determine the absolute magnitude of the effective Zeeman spin splitting factors of the impurity ground state to be g$_{I}$= 2.2 $\pm$ 0.1. We also investigate the spatial form of the electron wave function of the donor ground state, which is anisotropic in the growth plane

Shaped-pulse optimisation of coherent soft-x-rays

High-harmonic generation is one of the most extreme nonlinear-optical processes observed to date. By focusing an intense laser pulse into a gas, the light-atom interaction that occurs during the process of ionising the atoms results in the generation of harmonics of the driving laser frequency, that extend up to order ~300 (corresponding to photon energies from 4 to >500eV). Because this technique is simple to implement and generates coherent, laser-like, soft-x-ray beams, it is currently being developed for applications in science and technology including probing of dynamics in chemical and materials systems and for imaging. In this work we demonstrate that by carefully controlling the shape of intense light pulses of 6-8 optical cycles, we can control the interaction of light with an atom as it is being ionised, in a way that improves the efficiency of x-ray generation by an order of magnitude. Furthermore, we demonstrate that it is possible to control the spectral characteristics of the emitted radiation and to channel the interaction between different-order nonlinear processes. The result is an increased utility of harmonic generation as a light source, as well as the first demonstration of optical pulse-shaping techniques to control high-order nonlinear processes.Comment: 16 pages, 3 figure

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Wave function mapping conditions in Open Quantum Dots structures

We discuss the minimal conditions for wave function spectroscopy, in which resonant tunneling is the measurement tool. Two systems are addressed: resonant tunneling diodes, as a toy model, and open quantum dots. The toy model is used to analyze the crucial tunning between the necessary resolution in current-voltage characteristics and the breakdown of the wave functions probing potentials into a level splitting characteristic of double quantum wells. The present results establish a parameter region where the wavefunction spectroscopy by resonant tunneling could be achieved. In the case of open quantum dots, a breakdown of the mapping condition is related to a change into a double quantum dot structure induced by the local probing potential. The analogy between the toy model and open quantum dots show that a precise control over shape and extention of the potential probes is irrelevant for wave function mapping. Moreover, the present system is a realization of a tunable Fano system in the wave function mapping regime.Comment: 6 pages, 6 figure

Partial level density of the n-quasiparticle excitations in the nuclei of the 39< A <201 region

Level density and radiative strength functions are obtained from the analysis of two-step cascades intensities following the thermal neutrons capture. The data on level density are approximated by the sum of the partial level densities corresponding to n quasiparticles excitation. The most probable values of the collective enhancement factor of the level density are found together with the thresholds of the next Cooper nucleons pair breaking. These data allow one to calculate the level density of practically any nucleus in given spin window in the framework of model concepts, taking into account all known nuclear excitation types. The presence of an approximation results discrepancy with theoretical statements specifies the necessity of rather essentially developing the level density models. It also indicates the possibilities to obtain the essentially new information on nucleon correlation functions of the excited nucleus from the experiment.Comment: 29 pages, 8 figures, 2 table