Uniform analytic approximation of Wigner rotation matrices

We derive the leading asymptotic approximation, for low angle {\theta}, of the Wigner rotation matrix elements $d^j_{m_1m_2}(\theta)$, uniform in $j,m_1$ and $m_2$. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.Comment: 8 pages, 5 figure

Prediction of deviations from the Rutherford formula for low-energy Coulomb scattering of wavepackets

We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part of the incident beam that emerges essentially unscattered. For a model experiment, the scattering of helium nuclei from a thin gold foil, we find the deviation region is magnified for low incident energies (in the keV range), so that a large shadow zone of low probability around the forward direction is expected to be measurable. From a theoretical perspective, the use of wavepackets makes partial wave analysis applicable to this infinite-range potential. It allows us to calculate the everywhere finite probability for a wavepacket to wavepacket transition and to relate this to the differential cross section. Time delays and advancements in the detection probabilities can be calculated. We investigate the optical theorem as applied to this special case.Comment: 21 pages, 8 figures. This version contains clarifications and additional results compared to the previous version. The paper has been accepted for publication in J.Phys.

Cloudphysical Parameters in Dependence on Height above Cloud Base in Different Clouds.

On flights with the DLR icing research aircraft the dependence of aircraft icing on cloudphysical parameters was determined; both for aircraft-referred icing and for normalized icing, as well as for various clouds and locations in clouds. This is done with an improvement of icing predicitons in mind. The species of the cloud and the distance from cloud base are called here cloud parameters; while under cloudphysical parameters are understood liquid water content, temperature, particle size distribution and particle phase. Results from four icing flights are discussed, selected from a total of forty vertical soundings. —The results are arranged in four classes: Stratus/cumulus mixed, stratus; with and without precipitation at the ground

Hello, Goodbye. Bertelsmann Stiftung eupinions brief | January 2020

As the United Kingdom is leaving the European Union all eyes are on the eminent economic effects and future trade negotiations. How the British people feel about the state of their country at this defining moment of their political history has received less attention. In this eupinions brief, we examine how British citizens evaluate the state of their national democracy and the direction of their home country. We also ask what they expect for their personal lives