Fourier analysis of the nuclear flux density in diatomic molecules: A complementary tool to map potential-energy curves and to characterize vibrational wave functions

Abstract

Pump-probe spectroscopy has allowed the construction of the nuclear probability density $\ensuremath{\rho}(R,t)$ as a function of the internuclear bond distance $(R)$ and the time $(t)$ in diatomic molecules and consequent deduction of the nuclear flux density $j(R,t)$. Thus, the two observables $[\ensuremath{\rho}(R,t),j(R,t)]$ comprise a very detailed description of the nuclear motion in ultrafast molecular dynamics. Here a Fourier analysis of $j(R,t)$ is proposed and compared with the already existing Fourier analysis of $\ensuremath{\rho}(R,t)$. It is shown that the two power spectra $|\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}}{(R,\ensuremath{\omega};T)|}^{2}$ and $|\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{j}{(R,\ensuremath{\omega};T)|}^{2}$ provide the same information in the frequency domain $\ensuremath{\omega}$, but entirely different information in the spatial domain (i.e., along the $R$ coordinate).