4 years ago

Density matrix approach to orbital relaxation dynamics in ionization

Density matrix approach to orbital relaxation dynamics in ionization
Hikaru Kitamura
Dynamical response of electrons to a hole generated during ionization is formulated in time domain with the density matrix equations in the time-dependent unrestricted Hartree–Fock approximation. Time evolutions of orbital energies and electron-density distributions are computed for K-shell and M-shell ionizations of a Na atom by taking into account nonlinear coupling of density matrices beyond linear response. When the hole is generated so slowly that the adiabatic theorem is satisfied, the simulation eventually converges to the state of a fully relaxed Na+ ion. A rapid generation of a K-shell hole (within about 1 fs) leads to a breakdown of the adiabatic theorem, triggering a collective oscillation of the electrons with the period of sub-femtoseconds. The shake-up effect associated with strong orbital relaxation in inner-shell ionization is manifested as a mixing of occupied and unoccupied states in the density matrix. When a hole is created in a deep core orbital due to ionization, it attracts the surrounding electrons and modify their orbital shapes. Femtosecond dynamics of such an orbital relaxation process is simulated by the quantum-mechanical density-matrix equations. Nonadiabatic character of the dynamics becomes pronounced for rapid ionization expected in intense X-ray free-electron laser experiments.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/qua.25442

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