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On the transition between directed bonding and helium-like angular correlation in a modified Hooke-Calogero model

Müller-Herold, U.

In: The European Physical Journal D, 2008, vol. 49, no. 3, p. 311-315

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    Title
    • On the transition between directed bonding and helium-like angular correlation in a modified Hooke-Calogero model
    Author
    • Müller-Herold, U.. ETH Zurich, P.O. Box CAB 24, 8092, Zurich, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:317948
    Summary
    Angular correlation in three-body systems varies between the limiting cases of slightly perturbed equi-distribution, as in the electronic ground state of helium and directed bond-type bent structure, as in the isolated water molecule. In an exactly solvable modification of the Hooke-Calogero model, it is shown that there is a sharp transition between the two cases if the particles' masses are suitably varied. In the Hooke-Calogero model attraction between different particles is harmonic and the repulsion between equal particles is given by a 1/r 2 potential. The bent structure appears in the angular distribution function if the masses of the two equal particles are below a critical value, which depends on the mass of the third particle. Above the critical value, the angular correlation is of helium type and exhibits a minimum at 0° corresponding to the Coulomb hole and a maximum at 180°. The model thus demonstrates the modulating role of mass in the transition between semi-rigid structure and more diffuse nuclear states