General theoretical approach to Coulombic three-body systems by the hyperspherical formalism

Abstract

Coulombic three-body systems are investigated using the hyperspherical adiabatic approach. By using a suitable variable z=tan(\ensuremath{\alpha}/2) in the angular differential equation for the determination of the potential curves, we are able to obtain stable series-expansion solutions, valid for small and large values of the hyperspherical radius. The analysis of the mathematical singularities of the differential equations in the variable z offers an insight into the physics of the problem and into the determination of stable converging solutions as well. In order to illustrate our investigation, we apply this study to several carefully chosen systems: He, dd\ensuremath{\mu}, ${\mathit{d}}_{2}^{+}$, and excitons bound to a Coulomb center in different semiconductors.