Atoms in parallel fields: analysis with diffractive periodic orbits

Abstract

We show that fluctuations in the density of states of nonhydrogenic atoms in parallel fields are strongly influenced by diffractive periodic orbits. Unlike typical systems with a diffractive point scatterer, the atomic core of small atoms like lithium and helium is best understood as a combined geometric and diffractive scatterer. Each Gutzwiller (geometric) periodic orbit is paired with a diffractive orbit of the same action. We investigate, particularly, amplitudes for contributions from repetitions, and multiple scattering orbits. We find that periodic orbit repetitions are described by "hybrid" orbits, combining both diffractive and geometric core scatters, and that by including all possible permutations we can obtain excellent agreement between the semiclassical model and accurate fully quantal calculations. For high repetitions, we find even one-scatter diffractive contributions become of the same order as those of the geometric periodic orbit for repetition numbers n approximately Planck's over 2pi(-1/2). Although the contribution of individual diffractive orbits is suppressed by O(Planck's over 2pi(1/2)) relative to the geometric periodic orbits, the proliferation of diffractive orbits with increasing period means that the diffractive effect for the atom can persist in the Planck's over 2pi-->0 limit.