Ambiguities in the scattering tomography for central potentials

Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering ambiguities that arise in central potentials. We show that scattering is a tomographic projection: the integrated scattering angle is a projection of a scattering function onto the impact parameter. This function depends on the potential, but may be multi-valued, allowing for ambiguities where several potentials share the same scattering data. In addition, multivalued scattering angles also lead to ambiguities. We apply our theory to show that it is in principle possible to construct an invisibility device without infinite phase velocity of light

Neutrino Opacity I. Neutrino-Lepton Scattering

The contribution of neutrino-lepton scattering to the total neutrino opacity of matter is investigated; it is found that, contrary to previous beliefs, neutrino scattering dominates the neutrino opacity for many astrophysically important conditions. The rates for neutrino-electron scattering and antineutrino-electron scattering are given for a variety of conditions, including both degenerate and nondegenerate gases; the rates for some related reactions are also presented. Formulas are given for the mean scattering angle and the mean energy loss in neutrino and antineutrino scattering. Applications are made to the following problems: (a) the detection of solar neutrinos; (b) the escape of neutrinos from stars; (c) neutrino scattering in cosmology; and (d) energy deposition in supernova explosions

Rashba scattering in the low-energy limit

We study potential scattering in a two-dimensional electron gas with Rashba spin-orbit coupling in the limit that the energy of the scattering electron approaches the bottom of the lower spin-split band. Focusing on two spin-independent circularly symmetric potentials, an infinite barrier and a delta-function shell, we show that scattering in this limit is qualitatively different from both scattering in the higher spin-split band and scattering of electrons without spin-orbit coupling. The scattering matrix is purely off-diagonal with both off-diagonal elements equal to one, and all angular momentum channels contribute equally; the differential cross section becomes increasingly peaked in the forward and backward scattering directions; the total cross section exhibits quantized plateaus. These features are independent of the details of the scattering potentials, and we conjecture them to be universal. Our results suggest that Rashba scattering in the low-energy limit becomes effectively one-dimensional.Comment: corrected typo in Eq. (27). 10 pages, 6 figure

Hadronization and final state interaction effects in semi-exclusive Deep Inelastic Scattering off nuclei

Recent calculations of the effects of hadronization and final state interaction (FSI) in semi-exclusive deep-inelastic scattering (DIS) $A(e,e'(A-1))X$ processes are reviewed. The basic ingredient underlying these calculations, {\it viz} the time-dependent effective debris-nucleon cross section is illustrated, and some relevant results on complex nuclei and the deuteron are presented. In the latter case, particular attention is paid to the choice of the kinematics, for such a choice would in principle allow one to investigate both the structure function of a bound nucleon as well as the hadronization mechanisms. It is stressed that a planned experiment at Jlab on the process $D(e,e'p)X$ could be very useful in that respect.Comment: 6 pages, 5 EPS figures. Presented by C. Ciofi degli Atti at the Fourth International Conference on Hadronic Physics, Trieste (Italy), ICTP May 12-16, 2003. To appear in EPJ

Some Results on Inverse Scattering

A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3) Inverse scattering with ''incomplete`` data, 4) Inverse scattering for inhomogeneous Schr\"odinger equation, 5) Krein's inverse scattering method, 6) Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion methods, 7) The Newton-Sabatier and Cox-Thompson procedures are not inversion methods, 8) Resonances: existence, location, perturbation theory, 9) Born inversion as an ill-posed problem, 10) Inverse obstacle scattering with fixed-frequency data, 11) Inverse scattering with data at a fixed energy and a fixed incident direction, 12) Creating materials with a desired refraction coefficient and wave-focusing properties.Comment: 24p

Scattering matrices and expansion coefficients of Martian analogue palagonite particles

We present measurements of ratios of elements of the scattering matrix of Martian analogue palagonite particles for scattering angles ranging from 3 to 174 degrees and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0 to 180 degrees. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty Martian atmosphere.Comment: 34 pages 7 figures 1 tabl

Polariton-polariton scattering in microcavities: A microscopic theory

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wavefunctions is used to calculate the effective scattering matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.Comment: Theoretical paper on polariton-polariton scattering in planar microcavities. The new version contains a slightly modified abstract and a revised introduction. Typos have been corrected wherever spotted. 16 page

Entanglement and Timing-Based Mechanisms in the Coherent Control of Scattering Processes

The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies