An analytical treatment of the energy spectrum of the Van Der Waals potential

The Rydberg states N=20 of the hydrogen atom is considered in two class of potentials; one is the instantaneous-; and the other is true Van Der Waals potential. The energy spectrum is calculated analytically by using the oscillator representation method. The chaotic behavior of Rydberg states is studied over an atom surface distance 50-300 nm. Our investigation show that quantum chaos takes place for the instantaneous Van Der Waals potentials for arbitrary values of the parameter β in the entire region 0<β<√3. In the case of the true potential we demonstrate by means of basis set calculation that the level crossing can be takes place. (author)