Exact non-Born-Oppenheimer wave functions for three-particle Hookean systems with arbitrary masses

A Hookean model of a three-body problem for particles with arbitrary masses and charges where two of them interact with each other through a Coulomb potential and with the third through a harmonic potential is presented. It is shown that a condition relating the masses to the harmonic coupling constants must be satisfied in order to render this problem separable. A general exact analytic solution written in terms of the relative interparticle coordinates is given as well as general expressions for the total and binding energies of this three-body system. We apply these results to examine electronic, muonic, antiprotonic, and pionic families of non-Born-Oppenheimer Hookean systems. The first contains the atoms or atomic ions: Ps(-)(e(+)e(-)e(-)), H-(p(+)e(-)e(-)), D-(d(+)e(-)e(-)), T-(p(+)e(-)e(-)), He-4(he(+2)e(-)e(-)), and the following molecular ions: Ps(2)(+)(e(-)e(+)e(+)), H-2(+)(e(-)p(+)p(+)), HD+(e(-)d(+)p(+)), HT+(e(-)t(+)p(+)), DT+(e(-)d(+)t(+)), D-2(+)(e(-)d(+)d(+)), T-2(+)(e(-)t(+)t(+)). The muonic and antiprotonic families are similar to the electronic ones except that the species are formed replacing e(-) by mu(-) or p(-). The pionic family comprises exotic atoms containing at least one pion. We also apply these results to two-electron three-dimensional spherical quantum dots and for these systems we examine the effect of electronic correlation, particularly on the singlet-triplet transitions and on the collective motion of the electrons and center of mass leading to "floppy"dynamics.