Time-dependent post-collision-interaction effects in THz-field-assisted Auger decay

The effects of postcollision interaction (PCI) in the time evolution of photoinduced Auger decay, assisted by a terahertz (THz) field, is theoretically investigated. We propose a time-dependent model which is based on the quantum-mechanical description of the photoinduced Auger process and quasiclassical description of the PCI. The suggested model is used for calculating the PCI distortion of the Auger spectrum at different temporal overlaps of the exciting extreme ultraviolet pulse and the streaking THz pulse.

Figure 1

Vector potential of the THz field in atomic units (black solid curve) and the XUV pulses (in arbitrary units) used in the calculations as a function of time in fs. The position of the maximum of the x-ray pulse for several delay times used in the calculations is indicated by numbers. The dashed line shows the corresponding THz electric field in atomic units multiplied by ${10}^4$.

Figure 2

The shape of the Auger line calculated with (solid curves) and without (dashed curves) PCI effect for different pulse duration (FWHM) of the exciting XUV pulse: 5 fs (lines 1), 10 fs (lines 2), 20 fs (lines 3). The excess energy is 0.5 eV. The spectral lines are normalized to unity in the maximum, the energy scale is relative to the nominal Auger electron energy, $E_A$.

Figure 3

The shape of the Auger line calculated taking into account the PCI effect for an XUV pulse duration of 5 fs and different excess energies 0.5 eV (line 1), 1.5 eV (line 2), 2.5 eV (line 3), and 10 eV (line 4). The spectral lines are normalized to unity in the maxima, the energy scale is relative to the nominal Auger electron energy, $E_A$. The inner figure shows the absolute energy shift of the peak of each Auger line as a function of the excess energy $E_e$. The dashed line is used to guide the eyes.

Figure 4

Spectra of the Auger decay in the THz field calculated including the PCI effect (solid lines) and without PCI (dashed lines) for an XUV pulse duration of 10 fs, for an excess energy of 1 eV and for different time delays between the XUV and the THz field. The numbers near the peaks indicate the XUV pulse position as shown in Fig. 1. (a) Auger electrons detected in forward direction, (b) Auger electrons detected in the backward direction.

Figure 5

The ratio of the widths of the Auger line calculated for emission in forward and backward directions as a function of delay. The points in the solid curve (upper line) were calculated with PCI, the points in the dashed curve (lower line) without PCI. The parameters of the pulses are the same as in Fig. 4. The lines are drawn to guide the eyes.

Figure 6

(a) The shape of the Auger line in the THz field calculated taking into account the PCI effect for the XUV pulse close to the zero crossing of vector potential (position 1 in Fig. 1), for three different THz frequencies 0.53 THz (solid line), 1.05 THz (dotted line), and 2.1 THz (dashed line). An XUV pulse duration of 10 fs, excess energy of 0.5 eV, and THz field strength of 120 kV/cm have been used in the calculations. (b) shows the same as in (a) but for the time delay corresponding to position 5 in Fig. 1.

Figure 7

The widths of the Auger line calculated for the emission in the forward (solid lines) and the backward (dashed lines) directions as a function of the ratio of the excess and Auger electron energies. The calculations have been performed for the zero crossing point of the THz vector potential. The result of the calculations using the present quantum mechanical model are shown as black lines, the results of the analytical semiclassical model of Ref. [29] are shown as red lines (lighter gray). The calculations have been done for an XUV pulse duration of 5 fs for an excess energy of 1 eV and THz field strength of 60 kV/cm.