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arXiv:quant-ph/0112104 · Few-Body Systems

Scattering of Heavy Charged Particles on Hydrogen Atoms

Rimantas Lazauskas, Jaume Carbonell

Published May 1, 2002• 8 citations
arXivHTMLPDF
DOI
10.1007/s006010200010

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The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2 s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1 s , 2 s , and 3 s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1 s , 2 s , and 3 s states are calculated.
When three particles in three dimensions interact with a short-range potential fine-tuned to an infinite scattering length, they form an infinite sequence of loosely bound states obeying discrete scale invariance known as Efimov states. Here we show that analogous states are formed by three charged particles carrying two equal charges and one opposite charge in one, two, and three dimensions without any fine-tuning. Our finding is based on the Born-Oppenheimer approximation, where an effective inverse-square attraction is induced as a consequence of the dipole-charge interaction between a hydrogenlike heavy-light atom and a far-separated heavy particle. Because the resulting Efimovian states emerge toward the second or higher dissociation threshold, they are to be realized as quasibound states and may be observed by exciting hydrogen molecular ions and trions in excitonic systems. We also consider the same system but with a logarithmic Coulomb potential relevant to quantum vortices in two-dimensional superfluids, where the Efimovian states are shown to emerge as genuine bound states toward the first dissociation threshold.