To describe the microscopic properties of matter, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms the charge distributions described by the wave function are rarely observed. The hydrogen atom is unique, since it only has one electron and, in a dc electric field, the Stark Hamiltonian is exactly separable in terms of parabolic coordinates (η, ξ, φ). As a result, the microscopic wave function along the ξ coordinate that exists in the vicinity of the atom, and the projection of the continuum wave function measured at a macroscopic distance, share the same nodal structure. In this Letter, we report photoionization microscopy experiments where this nodal structure is directly observed. The experiments provide a validation of theoretical predictions that have been made over the last three decades.
A new photoelectron spectrometer has recently been used to analyze the energy and spatial distribution of photoelectrons produced by multiphoton ionization of rare gases. It is based on the analysis of the image obtained by projecting the expanding electron cloud resulting from the ionization process onto a two-dimensional position sensitive detector by means of a static electric field. In this article, we present the principle of this imaging spectrometer and the relevant equations of motion of the charged particle in this device, together with an inversion method that allows us to obtain the energy and angular distribution of the electrons. We present here the inversion procedure relevant to the case where the electrostatic energy acquired in the static field is large as compared to the initial kinetic energy of the charged particles. A more general procedure relevant to any regime will be described in a following article.
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