Transformation and shift of a Gaussian light beam upon reflection from a resonant medium

The specific features of the transformation and shift of a Gaussian beam reflected from a resonant absorbing medium are analyzed numerically. The study is based on the expansion of the field of the incident Gaussian beam into plane-wave components by using the Fourier integral transform. The calculations are performed for a frequency range covering the resonance region. The conditions for the splitting of the profile of the reflected beam and for its negative shift are established.     

Impact of 100 MeV Au on the surface of relaxed Si0.5Ge0.5 alloy films studied by atomic force microscopy

We demonstrate a gradual surface modification process of relaxed Si_0.5Ge_0.5 alloy films by 100 MeV Au beam with fluence varying between 5 × 10¹⁰ and 1 × 10¹² ions/cm² at 80 K by means of atomic force microscopy (AFM). Presence of Ge quantum dots (QDs) was found in the virgin sample. The disappearance of the QDs were noticed when the samples were irradiated with a fluence of 5 × 10¹⁰ ions/cm². Craters were found developing at a fluence of 1 × 10¹¹ ions/cm². Apart from the evolution of the craters, blisters were also detected at a fluence of 1 × 10¹² ions/cm². Variation of the average root mean square value of the surface roughness as a function of fluence was examined.     

Molecular orbital momentum distributions and binding energies for nitric oxide

Binding energy spectra of the valence electrons of the open shell molecule NO have been obtained up to 55 eV at azimuthal angles of 0° and 7° using binary (e, 2e) spectroscopy at an impact energy of 1200 eV. The momentum distribution has been obtained for the least tightly bound (unpaired) electron, removal of which leads to formation of the X ¹Σ⁺ ground state of NO⁺. Momentum distributions have also been measured at 21.0 and 40.5 eV. The measured momentum distributions are compared with several literature wavefunctions of varying complexity. They are found to be in excellent agreement with those calculated using the natural spin orbital wavefunctions of Kouba and Ohrn.     

Einstein vacuum field equations with a single non-null Killing vector

It is shown that, in the case where there is a single non-null Killing vector, the vacuum Einstein field equations imply that there is a Ricci collineation in the quotient 3-space. Using coordinates adapted to the collineation vector, we derive a fourth order partial differential equation involving the metric of the quotient 3-space and we show that if this equation is satisfied, the Ernst potential may be obtained by integrating a total Riccati equation and a straightforward set of total differential equations. We also show that if the collineation vector is null, the metric of the quotient 3-space may be expressed in terms of two real Clebsch potentials. Finally in the special case where the collineation vector is the generator of a timelike homothetic motion we reduce the field equations to a single second order partial differential equation of non-Painlevé type in two independent variables and obtain Petrov type III solution of Robinson-Trautman type.     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

Growth Behavior of CdS Nanoparticles Embedded in Polymer and Sol-Gel Silica Matrices: Relationship with Surface-State Related Luminescence

Chemical techniques were employed to synthesize CdS nanoparticles embedded in polymer (PEG 300) and sol-gel silica matrices. Systematic growth of particles (radius 3–9 nm) was obtained by adjusting post-deposition annealing temperature and time to examine the dependence of surface-state–related luminescence on particle size. Photoluminescence (PL) peak energy showed a linear dependence with a gentle slope in the weak confinement region and a steep slope in the strong confinement region, the divergence being observed near the excitonic Bohr radius for CdS. The empirical relation proposed for the weak confinement region could be used for estimating chemically prepared CdS nanoparticle size with a high degree of reliability from PL peak energy.