Vibro-rotational states of the two-electron atom. II: Two interacting particles on the sphere

For pt.I, see ibid., vol.18, p.4349-69 (1985). The problem of two interacting particles moving on a sphere can be considered as a useful model for the analyses, of the feasible vibro-rotational states in the two-electron atom. The object of the authors paper is an ab initio treatment of the problem in contrast to the numerical calculations by Ezra and Berry (1982). The zero-order Hamiltonian is chosen to describe the rotations of the two-particle system as a whole and vibrations over the distance between the particles (or over the angle theta 12). The residual part of the Hamiltonian mixes rotational and vibrational modes and leads to the energy level shifts and splittings. The numerical results prove to be in good agreement with those of Ezra and Berry. The approximate integral of motion is found and its generalisation to the real helium atom case is proposed. Its implications for the classification of the doubly excited states of the two-electron atom are discussed.