# Stability domain of systems of three arbitrary charges

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 $(\alpha, p, \mu^-)$. We then study stability in some critical regimes where $q_3\ll q_2$: 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.
Document type :
Journal articles

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Submitted on : Wednesday, January 10, 2001 - 2:29:08 PM
Last modification on : Thursday, November 19, 2020 - 12:58:31 PM
Long-term archiving on: : Tuesday, June 2, 2015 - 11:47:10 AM

### Identifiers

• HAL Id : in2p3-00008004, version 1

### Citation

A. Krikeb, A. Martin, J.-M. Richard, T.T. Wu. Stability domain of systems of three arbitrary charges. Few-Body Systems, Springer Verlag, 2000, 29, pp.237-257. ⟨in2p3-00008004⟩

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