Properties of the bound S states (L=0) in Coulomb three-body systems with unit charges

On the validity range of the Born-Oppenheimer approximation: A semiclassical study for all-particle quantization of three-body Coulomb systems

The validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).

Bound state properties of the ground states in the DT+ and T(2)+ ions

Recently developed multibox approach [A.M. Frolov, Phys. Rev. E 64, 036704 (2001)] is used to construct highly accurate, bound state wave functions for the ground states in the heavy adiabatic ions DT+ and T(2)+. The computed variational energies and bound state properties have significantly higher accuracy than results known from earlier computations. Nevertheless, the computed and predicted nucleus-nucleus cusp and nucleus-nucleus delta function differ significantly even for the highly accurate wave functions used in this study.