## Abstract

In this paper, a model of a paramagnetic impurity in a semiconductor (or of an F' center in an alkali halide) is proposed. It is an exactly soluble form of the quantum-mechanical 3-body problem. Specifically, we deal with 2 interacting particles in any number of dimensions in an attractive external potential, and present the qualitative features of the resulting eigenvalues and eigenfunctions. We find algebraically the conditions for a magnetic moment to appear (e.g., for an F' center to become unstable with respect to an F center) and discover that even a large 2-body electronic repulsion U does not cause a moment to appear when the one-electron bound state orbite about the impurity are sufficiently great. Conversely, in the case of small, tightly bound orbits, beyond a certain value of U, the impurity does in fact become magnetic in the ground state. Using the exact ground-state solution, we show that a perturbation-theoretic expansion in powers of U has a finite radius of convergence.

Original language | English (US) |
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Pages (from-to) | 2045-2052 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 7 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1966 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics