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Isotope shifts (ISs) of atomic energy levels are sensitive probes of nuclear structure and new physics beyond the standard model. We present an analysis of the ISs of the cadmium atom (Cd I) and singly charged cadmium ion (Cd II). ISs of the 229 nm, 326 nm, 361 nm and 480 nm lines of Cd I are measured with a variety of techniques; buffer–gas-cooled beam spectroscopy, capturing atoms in a magneto-optic-trap, and optical pumping. IS constants for the D₁and D₂lines of Cd II are calculated with high accuracy by employing analytical response relativistic coupled-cluster theory in the singles, doubles and triples approximations. Combining the calculations for Cd II with experiments, we infer IS constants for all low-lying transitions in Cd I. We benchmark existing calculations via different many-body methods against these constants. Our calculations for Cd II enable nuclear charge radii of Cd isotopes to be extracted with unprecedented accuracy. The combination of our precise calculations and measurements shows that King plots for Cd I can improve the state-of-the-art sensitivity to a new heavy boson by up to two orders of magnitude.

 

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 % ) $$\pm {}^{23\%}_{20\%}$$ ± 20 % 23 % for QGSJetII-04 , is respectively needed.