Fractal dynamics in the ionization of helium Rydberg atoms

We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory. By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization, we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons, and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy. We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons. Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field, and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms. It is shown that, besides the electric and magnetic fields, core scattering is a primary factor in the fractal dynamics.