On the transition between directed bonding and helium-like angular correlation in a modified Hooke-Calogero model
ETH Zurich, P.O. Box CAB 24, 8092 Zurich, Switzerland
Corresponding author: a email@example.com
Revised: 4 August 2008
Published online: 3 October 2008
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/r2 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.
PACS: 33.15.Dj – Interatomic distances and angles / 03.65.Ge – Solutions of wave equations: bound states
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008