Density matrix formalism for femtosecond x-ray absorption and its excitonic enhancement

Abstract

A reduced density matrix (RDM) formalism to simulate the dynamics of core-valence electronic excitation in a metal induced by a femtosecond x-ray laser pulse is presented. The theory is based on the time-dependent unrestricted Hartree–Fock (TDUHF) equation for a one-electron RDM combined with an off-diagonal collision term in the Born approximation (BA), where molecular orbitals (MOs) of a model cluster are used as a basis set. These MOs are calculated with a newly developed semiempirical method in the neglect of diatomic differential overlap approximation that takes into account atomic core structures and valence-orbital hybridization. The off-diagonal component of core-valence RDM is decomposed into a rapidly oscillating factor synchronizing with the x-ray field and a slowly varying envelope; time evolution of the latter yields induced electric polarization and complex electric susceptibility. As a numerical test, K-shell absorption near-edge spectra of copper are computed for a single-shot, weak femtosecond x-ray pulse. It is thereby shown that the attractive interaction between an excited electron and a core hole, described by the exchange part of the self-energy matrix, gives rise to excitonic enhancement of x-ray near-edge absorption. The TDUHF approximation significantly overestimates the excitonic enhancement; additional consideration of the screening of electron-hole interaction by valence electrons in BA leads to a prediction of absorption coefficients comparable to the existing experimental values.