Fractal dynamics in the ionization of helium Rydberg atoms

Abstract

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.

Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

“…3(a within the framework of the box-counting method. [20] We define the phenomena in the ionization systems as the rhythm attractor with the fractal dimension D f = 0.467 which expresses the irregularity of the rhythm structures. These curves exhibit the same rhythm at the endings of the plots, which are called "rhythm endings" denoting the universality in the ionization process.…”

“…[14][15][16][17][18] With the advancement of laser technology and semiclassical theory, considerable attention has been paid to photoionization microscopy and the ionization dynamics of atoms in external fields. [2,6,7,[19][20][21][22][23][24][25] The chaotic ionization of hydrogen in electric and magnetic fields is described by the Poincaré map. [26][27][28][29] Recently, with the development of chaos and fractal theory in physics, consideration has been given to fractal dynamics in many fields, for example, the fractal dynamics in quantum and semiclassical transport.…”