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Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
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Publication Date:
NSF-PAR ID:
10133019
Journal Name:
The European Physical Journal C
Volume:
79
Issue:
1
ISSN:
1434-6044
Sponsoring Org:
National Science Foundation
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1. Abstract

We report on a series of detailed Breit-Pauli and Dirac B-spline R-matrix (DBSR) differential cross section (DCS) calculations for excitation of the$$5\,^2\mathrm{S}_{1/2} \rightarrow 5\,^2\mathrm{P}_{1/2}$$$5{\phantom{\rule{0ex}{0ex}}}^{2}{S}_{1/2}\to 5{\phantom{\rule{0ex}{0ex}}}^{2}{P}_{1/2}$and$$5\,^2\mathrm{S}_{1/2}\rightarrow 5\,^2\mathrm{P}_{3/2}$$$5{\phantom{\rule{0ex}{0ex}}}^{2}{S}_{1/2}\to 5{\phantom{\rule{0ex}{0ex}}}^{2}{P}_{3/2}$states in rubidium by 40 eV incident electrons. The early BP computations shown here were carried out with both 5 states and 12 states, while the DBSR models coupled 150 and 325 states, respectively. We also report corresponding results from a limited set of DCS measurements on the unresolved$$5\,^2\mathrm{P}_{1/2,3/2}$$$5{\phantom{\rule{0ex}{0ex}}}^{2}{P}_{1/2,3/2}$states, with the experimental data being restricted to the scattered electron angular range 2–$$10^\circ$$${10}^{\circ }$. Typically, good agreement is found between our calculated and measured DCS for excitation of the unresolved$$5\,^2\mathrm{P}_{1/2,3/2}$$$5{\phantom{\rule{0ex}{0ex}}}^{2}{P}_{1/2,3/2}$states, with best accord being found between the DBSR predictions and the measured data. The present theoretical and experimental results are also compared with predictions from earlier 40 eV calculations using the nonrelativistic Distorted-Wave Born Approximation and a Relativistic Distorted-Wave model.

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2. Abstract The hybrid design of the Pierre Auger Observatory allows for the measurement of the properties of extensive air showers initiated by ultra-high energy cosmic rays with unprecedented precision. By using an array of prototype underground muon detectors, we have performed the first direct measurement, by the Auger Collaboration, of the muon content of air showers between $$2\times 10^{17}$$ 2 × 10 17 and $$2\times 10^{18}$$ 2 × 10 18 eV. We have studied the energy evolution of the attenuation-corrected muon density, and compared it to predictions from air shower simulations. The observed densities are found to be larger than those predicted by models. We quantify this discrepancy by combining the measurements from the muon detector with those from the Auger fluorescence detector at $$10^{{17.5}}\, {\mathrm{eV}}$$ 10 17.5 eV and $$10^{{18}}\, {\mathrm{eV}}$$ 10 18 eV . We find that, for the models to explain the data, an increase in the muon density of $$38\%$$ 38 % $$\pm 4\% (12\%)$$ ± 4 % ( 12 % ) $$\pm {}^{21\%}_{18\%}$$ ± 18 % 21 % for EPOS-LHC , and of $$50\% (53\%)$$ 50 % ( 53 % ) $$\pm 4\% (13\%)$$ ± 4 % ( 13 % ) $$\pm {}^{23\%}_{20\%}$$more »