Recurrence spectroscopy of atoms in electric fields: Failure of classical scaling laws near bifurcations

The photoabsorption spectra of atoms in a static external electric field shows modulations from {ital recurrences}: electron waves that go out from and return to the vicinity of the atomic core. Closed-orbit theory predicts the amplitudes and phases of these modulations in terms of closed classical orbits. A classical scaling law relates the properties of a closed orbit at one energy and field strength to its properties at another energy and field strength at fixed scaled energy {epsilon}=EF{sup {minus}1/2}. The scaling law states that the recurrence strength of orbits along the electric field axis scale as F{sup 1/4}. We show how this law fails near bifurcations when the effective Planck constant {cflx {h_bar}}{equivalent_to}{h_bar}F{sup 1/4} increases with increasing field at fixed {epsilon}. The recurrences of orbits away from the axis scale as F{sup 1/8} in accordance with the classical prediction. These deviations from the classical scaling law are important in interpreting the recurrence spectra of atoms in current experiments. This leads to an extension of the uniform approximation developed by Gao and Delos [Phys. Rev. A {bold 56}, 356 (1997)] to complex momenta. {copyright} {ital 1998} {ital The American Physical Society}