36,583 research outputs found
Uniform analytic approximation of Wigner rotation matrices
We derive the leading asymptotic approximation, for low angle {\theta}, of
the Wigner rotation matrix elements , uniform in
and . 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
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