Femtosecond Coulomb Explosion Imaging of Vibrational Wave Functions

Abstract

Because of the nonlinearity of multiphoton ionization, an intense 5 fs pulse is short enough to change the ionization probability from near zero to near unity in less than one-half of a laser period. For ${\mathrm{H}}_2^{+}$ this exposes all parts of the vibrational wave function to the full force of Coulomb repulsion at nearly the same time. By solving the time dependent Schrödinger equation, following both electron and ion motion we show that the initial vibrational wave function $\Psi \left(R\right)$ of ${\mathrm{H}}_2^{+}$ can be reconstructed by using Coulomb's law to map the ion fragment kinetic energy spectrum into $|\Psi \left(R\right){|}^2$.