Adiabatic hyperspherical representation in barycentric coordinates for helium-like systems

The hyperspherical adiabatic (HSA) representation is introduced in barycentric coordinates for helium-like systems in which isotopic and correlation effects are taken into account exactly. Different methods of forming the HSA basis are considered. The general classification of the HSA basis states is suggested, and examples of correlation diagrams are presented. The complete classification of doubly excited states of two-electron systems is given. Different classification schemes are compared. The convergence of the HSA expansion is investigated numerically. The ground-state energy value of the negative hydrogen ion H- is calculated in the six-channel approximation within an accuracy of 10-5 au.