Abstract
An Angular Correlated Configuration Interaction method is extended and applied to exotic threebody atomic systems with general masses. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two-body coalescence points; (ii) have only linear parameters; (iii) show a fast convergency rate for the energy; (iv) form an orthogonal set. The efficiency of the construction is illustrated by the study a variety of three-body atomic systems [m1− m2− m3z3+ ] with two negatively charged light particles, with 123 diverse masses m1− and m2−, and a heavy positively charged nucleus m3z3+. The calculated ground 11S and several excited n1,3S state energies are compared with those given in the literature, when available. We also present a short discussion on the critical charge necessary to get a stable three-body system supporting two electrons, an electron and a muon, or two muons.
Highlights
Exotic three-body systems, involving electrons, muons and antihydrogen nuclei, are of interest in many branches of physics, including atomic spectroscopy and quantum electrodynamics
The C3-like basis functions are defined as being exact solution of a general three-body Coulomb problem where the non-diagonal terms of the kinetic energy are neglected; the functions naturally satisfy the cusp conditions at the two-body singularities
They are defined as a product of two-body Coulomb wave function multiplied by a Coulomb distortion factor, being in that way the counterpart of the C3 approach used for scattering problems
Summary
Exotic three-body systems, involving electrons, muons and antihydrogen nuclei, are of interest in many branches of physics, including atomic spectroscopy and quantum electrodynamics (see, e.g., the discussion and the references given in the Introduction of [1,2]). A third category, deals with wave functions (typically Hylleraas-type) and energies of quality which are intermediate between the two already mentioned (see, e.g., [22,23,24,25]) All these trial wave functions have separate, and possibly complementary, purposes: obtain very accurate mean quantities (including the energy), search for a solution as formal as possible, or useful for applications such as collision studies. For the latter, it is useful to remind that the evaluation differential cross sections for processes such as double ionization by electron or photon impact [26,27,28,29,30,31,32] involve multi-dimensional numerical integrations; for calculations within the second Born approximation, a complete orthogonal set of wave functions is necessary. This, for example, possibly explains the popularity of Hylleraas-type wave functions, such as that of Kinoshita [22] or simpler versions [23], amongst the collision community
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