FAST TRACK COMMUNICATION Origin of species dependence of high-energy plateau photoelectron spectra

We analysed the energy and momentum distributions of high-energy ‘plateau’ photoelectrons. These electrons, with energies above 4Up (Up is the ponderomotive energy), have been understood qualitatively as due to the backscattering of laser-induced returning electrons by the target ion. Here, we establish a quantitative rescattering (QRS) theory to show that the species and laser-intensity dependence of the ‘flatness’ of the plateau electrons is entirely determined by the energy and angular dependence of the elastic scattering cross sections between target ions with free electrons. This accurate QRS theory can be used to obtain energy and momentum distributions of plateau electrons without the need of solving the time-dependent Schrödinger equation. (Some figures in this article are in colour only in the electronic version) When atoms or molecules are placed in an intense laser pulse, an electron can be released through either a multiphoton or a tunnelling mechanism. The distinction is based on the Keldysh parameter γ = Ip/2Up, where Ip is the ionization energy, Up = A0 / 4 (atomic units are used unless otherwise specified) is the ponderomotive energy and A0 is the peak value of the vector potential. In the multiphoton regime (γ > 1), the electron spectra exhibit characteristic abovethreshold ionization (ATI) peaks separated by photon energy, with yields decreasing monotonically with increasing electron energy [1]. At higher intensities, in the tunnelling region (γ < 1), the spectra are notably different. First, the ionization yield drops steeply from the threshold, but from about 3 or 4Up onwards, the yield flattens out significantly until about 10Up where it drops precipitously again. The flattened spectral region from 4 to 10Up is called the plateau electrons. Despite this common description, electron spectra in the plateau region are not always flat. The flatness depends on the species and laser intensity. For example, experimental ATI spectra for potassium show strong enhancement in the plateau region, but not for sodium [2]. Similarly, using nearly identical lasers, a clear flat plateau shows up in an Xe target, but not in Kr and Ar [3]. Experimentally, the flatness of plateau electrons has been observed to depend on laser intensities [4] as well. Experimentally, the plateau photoelectrons in ATI spectra from atoms have been studied since 1990s [5–7]. Qualitatively, they are understood based on the rescattering model [8–11]. In this model, electrons that are released earlier by tunnelling ionization can be driven back by the laser field to recollide with the target ion. The plateau electrons are due to elastic largeangle backscattering of the returning electrons by the target ion. Quantitatively, accurate high-energy electron spectra rely on computations carried out by solving the time-dependent Schrödinger equation (TDSE) within the single active electron approximation [12, 13]. However, these theories do not offer the interpretation for the origin of species and laserintensity dependence of the flatness of plateau electrons. In this communication, we present a quantitative rescattering theory (QRS) which shows that the species and laser-intensity dependence of plateau electrons is determined entirely by the electron–ion elastic scattering differential cross sections (DCSs) at large angles. Although such a relation has been 0953-4075/09/061001+05$30.00 1 © 2009 IOP Publishing Ltd Printed in the UK J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 061001 Fast Track Communication