Abstract

Continuous and discrete spectrum states near the ionization limit are considered. The origin of the continuous spectrum narrow resonances is elucidated. We suggest the semiclassical equation for the states near the ionization limit. The way of analytical continuation of the equation for discrete spectrum states into the region of resonances in continuum is pointed out. It is shown that the wave function structure is intermediate between the regular structure and the chaotic one.

Introduction

In the works [1, 2, 3] on the photoexcitation of an Li atom in a magnetic field a number of continuous spectrum narrow resonances as well as discrete spectrum states were observed. The energies of all these states were comparable with the cyclotron frequency ω. The magnetic field was 6.1 T, and corresponding ω = 5.7 cm−1. These are very high Rydberg excitations and therefore the spectrum of an Li atom probably does not differ substantially from that of an H atom. In recent years a number of theoretical works have been devoted to the investigation of an H atom in a magnetic field (see e.g. a review paper [4]). Progress has been achieved in numerical integration of the Schrödinger equation for the continuous spectrum [5, 6, 7]. In Ref. [8] a detailed comparison of experimental data with the results of numerical solution is carried out. There is good agreement after some averaging over the energy.