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The ground-state energies of muonium hydride and its isotopes are calculated using a variational method in Hylleraas coordinates. Convergence to a few parts in 109 is achieved, which significantly improves the previous results of Suffczyński, Kotowski and Wolniewicz (2002 Acta Phys. Pol. A 102 351). Expectation values of the interparticle distances are evaluated.

While both isothermal and NFW-based mass models for galaxy clusters are widely adopted in strong-lensing studies, they cannot easily be distinguished based solely on observed positions of arcs and arclets. We compare the magnifications predicted for giant arcs obtained from isothermal and NFW profiles, taking axially-symmetric and asymmetric mass distributions into account. We find that arc magnifications can differ strongly between the two types of density profiles even if the image morphology is well reproduced. Magnifications by lenses with NFW density profiles are usually larger than those for lenses with singular or nearly singular isothermal density profiles, unless the latter have large cores. Asymmetries play an important role. We illustrate our results with the two well-studied clusters MS 2137 and A 370. We confirm earlier results showing that both isothermal and NFW mass models can very well reproduce the observed arcs, radial arcs and other arclets. While the mass model for MS 2137 is not very well constrained, the two types of mass models produce strongly differing critical curves and caustics for A 370. We find that the NFW mass profile is preferred for A 370. We identify new arclet candidates in the field of A 370. Redshift estimates allowed by the lens model are consistent with results in the literature, where available. Three newly found counter-images are suggested to arise from an active, dust-enshrouded star-forming galaxy at z ≈ 1.1.

The dispersion coefficients C 6 for the H(1s)-He(n 1,3 P), H(1s)-Li(n 2 P) and He(1 1 S)-Li(n 2 P) systems with n = 2, 3 are calculated using variational wavefunctions in Hylleraas coordinates.

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