On the Stability Domain of Systems of Three Arbitrary Charges

Ali Krikeb; Andre Martin; Jean-Marc Richard; Tai T. Wu

paper

On the Stability Domain of Systems of Three Arbitrary Charges

arXiv:physics/9812031

Abstract

We present results on the stability of quantum systems consisting of a negative charge $- q_{1}$ with mass $m_{1}$ and two positive charges $q_{2}$ and $q_{3}$ , with masses $m_{2}$ and $m_{3}$ , respectively. We show that, for given masses $m_{i}$ , each instability domain is convex in the plane of the variables $(q_{1} / q_{2}, q_{1} / q_{3})$ . A new proof is given of the instability of muonic ions $(α, p, μ^{-})$ . We then study stability in some critical regimes where $q_{3} ≪ q_{2}$ : stability is sometimes restricted to large values of some mass ratios; the behaviour of the stability frontier is established to leading order in $q_{3} / q_{2}$ . Finally we present some conjectures about the shape of the stability domain, both for given masses and varying charges, and for given charges and varying masses.

Latex, 24 pages, 14 figures (some in latex, some in .eps)