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.

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

Je t’aime. Moi non plus = I love you. Neither do I. eupinions brief | February 2019

When Emmanuel Macron won the French presidential election with a risky strategy and against all odds in May 2017, spring seemed to break out in Paris. New faces, new dynamics, and the promise to do many things differently and thus better, were in the air and inspired large swathes of the French public. But the protests of the "yellow vests" have in their intensity and perseverance now shaken the last optimist. And they’ve reminded us of how deep the trenches between the political interests in France are – as well as how much energy and effort it takes to navigate them

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