Improved version of the eikonal model for absorbing spherical particles

We present a new expression of the scattering amplitude, valid for spherical absorbing objects, which leads to an improved version of the eikonal method outside the diffraction region. Limitations of this method are discussed and numerical results are presented and compared successfully with the Mie theory.Comment: 7 pages, postscript figures available on cpt.univ-mrs.fr, to appear in J. Mod. Optic

Light scattering of large rough particles application to cometary grains

While the electromagnetic field scattered by a spherical particle is classically obtained by the Helmholtz equation, the general case of an arbitrary particle may be investigated in the general framework of the interaction of a wave with a scattering potential. A wave function then satisfies the Schroedinger equation. The general solution of the Schroedinger equation is given. The main disadvantage of this approach are its restriction to large particles and its scalar nature preventing the calculation of the polarization. However, Perrin and Lamy have shown how to avoid the second limitation and retrieve a vectorial description. They proved that in the case of large spheres when the ad hoc assumptions are satisfied, the expression of the scattering amplitude may be approximated by an expansion series in partial waves, i.e., on a discrete basis. The analogy may be generalized, and the ratio of the two components for a rough particle obtained by taking the ratio of the reflectivities for the two directions of polarization. These reflectivities involve the simple and double reflections calculated following the method developed by Wolff for rough surfaces. The theory is further detailed

Optical properties of irregular interstellar grains

In order to study the interaction of light with interstellar grains, the authors represent an irregular particle by a network of interacting dipoles whose polarizability is determined in a first approach by the Clausius-Mossoti relationship. Typically, 10,000 dipoles are considered. In the case of spherical particles, the results from Mie theory are fully recovered. The main interest of this method is to study with good accuracy the implications of surface roughness and/or inhomogeneities on optical properties in the infrared spectral range, particularly of the silicate emission features

Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.Comment: 8 pages, 5 figure

Two-body anticorrelation in a harmonically trapped ideal Bose gas

We predict the existence of a dip below unity in the second-order coherence function of a partially condensed ideal Bose gas in harmonic confinement, signaling the anticorrelation of density fluctuations in the sample. The dip in the second-order coherence function is revealed in a canonical-ensemble calculation, corresponding to a system with fixed total number of particles. In a grand-canonical ensemble description, this dip is obscured by the occupation-number fluctuation catastrophe of the ideal Bose gas. The anticorrelation is most pronounced in highly anisotropic trap geometries containing small particle numbers. We explain the fundamental physical mechanism which underlies this phenomenon, and its relevance to experiments on interacting Bose gases.Comment: 10 pages, 5 figures. v2: Minor changes and corrections to figures and text. To appear in PR

Spatial distribution of unidentified infrared bands and extended red emission in the compact galactic HII region Sh 152

We present visible and near IR images of the compact HII region Sh 152. Some of these images reveal the presence of Extended Red Emission (ERE) around 698 nm and emission from Unidentified Infra Red Bands (UIRBs) at 3.3 and 6.2 micron. Other images show the near infrared (7-12 micron) continuous emission of the nebula. The ERE emission is found to coincide with the ionized region and significantly differ from the UIRBs location. Also some evidence is found in favor of grains as carriers for ERE.Comment: 3 pages, 4 figures, to be published in the proceedings of the colloquium "The universe as seen by ISO" help in Paris, October 20-23, 1998 ; available in html format at http://www.obs-hp.fr/preprints.htm