Dynamics of interatomic Coulombic decay in neon dimers by XUV-pump–XUV-probe spectroscopy

We apply the Monte Carlo wave-packet approach to study the interatomic Coulombic decay (ICD) dynamics of neon dimers after removing a $2s$ electron from one of the Ne atoms by one-photon absorption from an XUV pulse. This method reproduces well both the lifetime for the $2s$ inner-valence vacancy in $\mathrm{Ne}{}_2{}^{+}\left(2s^{-1}\right)$ and the kinetic energy release (KER) spectra for the coincident ${\mathrm{Ne}}^{+}$ and ${\mathrm{Ne}}^{2+}$ fragments following triple ionization, i.e., two photoionizations and one ionization via ICD, of ${\mathrm{Ne}}_2$ measured in an XUV-pump–XUV-probe experiment [K. Schnorr et al., Phys. Rev. Lett. 111, 093402 (2013)]. Comparisons between the calculated and measured nuclear KER spectra give physical insights in the considered process. For example, an analysis of the ratios between the low- and high-energy peaks in the nuclear KER spectra for large delays provides an estimate of the photoionization cross sections for removing a $2p$ electron from the excited states in $\mathrm{Ne}{}_2{}^{+}\left(2s^{-1}\right)$. Such comparisons also allow an estimate for the ICD rates for the $2s$ inner-valence vacancy in the single-site two hole state in $\mathrm{Ne}{{}_2}^{2+}\left(2s^{-1}2p^{-1}\right)$. Finally, the influence of photon statistics of the free electron laser pulses on the nuclear KER spectra is considered.

Figure 1

Selected Born-Oppenheimer potential energy curves as a function of the internuclear distance $R$ for ${\mathrm{Ne}}_2$, as given in Ref. [32]. From bottom to top at $R=5$ a.u., the curves are for the ground state in ${\mathrm{Ne}}_2$, the $2{}^2{\mathrm{\Sigma }}_g^{+}$ and $2{}^2{\mathrm{\Sigma }}_u^{+}$ inner valance ionized states of $\mathrm{Ne}{}_2{}^{+}$, the effective state of the two-site doubly outer-valence-ionized ${\mathrm{Ne}}_2{}^{2+}$, the inner and outer valance doubly ionized state of ${\mathrm{Ne}}_2{}^{2+}$ and the effective state for the two-site triply ionized ${\mathrm{Ne}}_2{}^{3+}$, respectively.

Figure 2

(a) Calculated nuclear KER spectra for coincident ${\mathrm{Ne}}^{2+}$ and ${\mathrm{Ne}}^{+}$ fragments following triple ionization of ${\mathrm{Ne}}_2$ as a function of delay $\tau$ between coherent XUV pump and probe pulses (see text for laser parameters). (b) The solid line shows yields of coincident ${\mathrm{Ne}}^{2+}$ and ${\mathrm{Ne}}^{+}$ pairs integrated over KER values between 3 and 7 eV in (a). The dashed line is an exponential fit of the solid line to extract the lifetime of the ICD in ${\mathrm{Ne}}_2$. (c) Sum of KER spectra for delays between 300 and 420 fs in (a) (see text).

Figure 3

Nuclear KER spectra for different photoionization cross sections ${\sigma }_{2s/2p}$ from the $2{}^2{\mathrm{\Sigma }}_g^{+}$ and $2{}^2{\mathrm{\Sigma }}_u^{+}$ states to ${\mathrm{Ne}}_2{}^{2+}$ at $\tau =400$ fs when the ICD rates are identical to the rates used in Fig. 2.

Figure 4

Nuclear KER spectra under different ICD rates for the ${\mathrm{ICD}}_2$ channel in Fig. 1 at $\tau =400$ fs, i.e., ${\mathrm{\Gamma }}_{{\text{ICD}}_2}=1$, 2, 3, and $4\times {\mathrm{\Gamma }}_{{\text{ICD}}_{1u}}$, respectively. The photoionization cross sections from the $2{}^2{\mathrm{\Sigma }}_g^{+}$ and $2{}^2{\mathrm{\Sigma }}_u^{+}$ states to ${\mathrm{Ne}}_2{}^{2+}$ are taken as ${\sigma }_{2s/2p}=8$ Mb. The other parameters are identical to those in Fig. 2. For better comparison, the measured nuclear KER spectrum at large delays, which was shown in Fig. 2(c) in Ref. [23] (Schorr et al.), is also plotted.

Figure 5

(a) Temporal electric fields for a Gaussian-enveloped coherent pulse and (b)–(e) four random FEL pulses. The laser parameters of the XUV pulses are as follows: $\omega =2.14$ a.u., ${\tau }_p=60$ fs, and $I_0={10}^{12}\text{W}/{\text{cm}}^2$.

Figure 6

(a) Calculated nuclear KER spectra for coincident ${\mathrm{Ne}}^{2+}$ and ${\mathrm{Ne}}^{+}$ fragments following triple ionization of ${\mathrm{Ne}}_2$ as a function of $\tau$ when the applied laser pulses are modeled by the partial coherence method (see text for laser parameters). (b) ${\mathrm{Ne}}^{2+}$ and ${\mathrm{Ne}}^{+}$ yields integrated over all KERs for the delays in (a). (c) Sum of nuclear KER spectra for delays between 300 and 420 fs. The ICD rates for the second ICD channel are taken as $2\times {\mathrm{\Gamma }}_{{\text{ICD}}_{1u}}$ and the photoionization cross sections from the $2{}^2{\mathrm{\Sigma }}_g^{+}$ and $2{}^2{\mathrm{\Sigma }}_u^{+}$ states in $\mathrm{Ne}{}_2{}^{+}$ to ${\mathrm{Ne}}_2{}^{2+}$ are 8 Mb. The other parameters are those used to obtain the results presented in Fig. 2.