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On the basis of equations obtained in the framework of second-order quantum-mechanical perturbation theory, the standard approach to the calculation of scattering radiation probability is extended to the case of ultrashort laser pulses. We investigate the mechanism of the appearance of plasmon peaks in the spectrum of the plasma form factor for different parameters of the problem. For the case in which scattering on plasmons dominates over scattering on electron density fluctuations caused by chaotic thermal motion, we derive analytical expressions describing the scattering probability of ultrashort laser pulses on plasmons. Together with this, we obtain a simple expression connecting the frequency of scattered radiation and the energy transmitted from the incident pulse to plasmon, and vice versa. In considering the scattering probability, our emphasis is on the dependence on the pulse duration. We assess in detail the trends of this dependence for various relations between pulse carrier frequency and plasmon energy.

The theory of photoionization describing the interaction of x-ray free-electron laser (XFEL) pulses and high-harmonic-generated (HHG) radiation is generalized to ultrashort laser pulses, where the concept of the standard ionization probability per unit time in Fermi’s golden rule and in Einstein’s theory breaks down. Numerical calculations carried out in terms of a generalized photoionization probability for the total duration of pulses in the near-threshold regime demonstrate essentially nonlinear behavior, while absolute values may change by orders of magnitude for typical XFEL and HHG pulses. XFEL self-amplified spontaneous emission pulses are analyzed to reveal general features of photoionization for random and regular spikes: the dependences of the nonlinear photoionization probability on carrier frequency and spike duration are very similar, allowing an analytical expectation value approach that is valid even when there is only limited knowledge of random and regular parameters. Numerical simulations carried out for typical parameters demonstrate excellent agreement.