Vibro-rotational states of the two-electron atom. I. Euler angles coordinate basis

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Abstract
The possibility of interpreting doubly excited states of the two-electron atom as vibro-rotational states is discussed in the current literature. In particular the model problem of two particles moving on the sphere was studied by Ezra and Berry (1982). The object of the present series of papers is to perform ab initio analysis of the problem. It begins by the proper choice of variables: Euler angles describing the rotation of both electrons collectively and the dynamical variables-the electron distances from the nucleus and the distance between the electrons. The transition between the Euler angles representation and the conventional one-electron orbitals is generated by the functions describing the free electrons moving on concentric spheres. These functions are calculated with the help of recurrence relations or as a solution of the system of differential equations. The latter approach gives explicit expressions but the solutions are obtained only for some particular cases (Se, Pe, Po and Do states). The motion of two particles of the sphere (Se and Pe states) is studied for some model interaction between them ('the hyperspherical hydrogen-atom model'). The analysis of the wavefunctions shows that the particles are situated primarily on the opposite ends of the sphere diameter. This observation can be used in the development of the ab initio approximate analysis.

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