# Photon-In/Photon-Out X-ray Free-Electron Laser Studies of Radiolysis
## 2 Methods
### X-ray Pump/X-ray Probe  
We now step beyond the ideal case created by impulsive strong-field ionization, i.e., a single ejected electron and a valence hole--basically an electron-hole pair in water--to the situation created by passage of an ionizing X-ray pulse. The X-ray pump/X-ray probe method allows us to extend our earlier study in two important dimensions. First, whereas our previous studies [5; 6] focused on the elementary electron-hole dynamics associated with strong-field ionization from the HOMO in pure liquid water, here we can access ionization from any orbital-more directly mimicking early events in actual radiolysis. Second, the time resolution associated with the earlier study was limited to \(\sim\)100 fs, much too slow to capture correlated hole-proton motions in water, whereas this new X-ray pump/X-ray probe scheme offers sub-femtosecond time-resolution between pump and probe. We note that water is also an excellent testbed for studies of coupled electron-nuclear motion as spatial correlations between nuclear displacement of a light proton and hole can be large [44]. The powerful two-color X-ray pump/X-ray probe schemes at the Linac Coherent Light Source (LCLS) of Stanford Linear Accelerator Center (SLAC) National Accelerator Laboratory [45; 46; 47] provide the means to systematically understand the electronic and nuclear dynamics following valence, inner-valence and core ionization in aqueous systems (Figure 3). An X-ray pump pulse with a photon energy below the 1 s ionization threshold (538.1 eV) can non-resonantly create a hole in any of the valence or inner valence bands, as indicated by the green photons. An X-ray probe pulse can be tuned to selectively probe the dynamics of individual hole states (\(1b_{2},3a_{1},1b_{1}\)) as shown on the left side of Figure 3. The predicted separation of absorption bands is given by the differences in their binding energies in the liquid phase [43]. Based upon estimated oscillator strengths for the \(1s\) transitions to valence hole states, the estimated absorption spectrum is constructed, as shown in the right panel of Figure 3. The relatively small oscillator strength for the \(1s_{1}\to 2a_{1}\) transition is due to dipole selection rules and the symmetries of the respective orbitals. Figure 2: Schematic of optical pump/X-ray probe transient absorption study of water radiolysis. Left: Strong-field laser pump (red photon) ejects an electron from the outermost \(1b_{1}\) orbital. X-ray probe (blue photon) induces the transition from the core 1 s level to the vacancy in the \(1b_{1}\) (\(1a_{1}\to 1b_{1}\)). Right: Absorption spectrum of liquid water for a thickness of 800 nm [42] in gray. Calculated gas phase absorption for H\({}_{2}\)O\({}^{+}\) and OH. Liquid phase binding energies for electrons in the various orbitals [43]. Inset shows the experimental X-ray transient absorption spectrum of the OH(aq) radical. Reproduced from Reference [5]. A schematic of a straightforward X-ray pump/X-ray probe transient absorption configuration is shown in Figure 4. Two independently controlled X-ray pulses with arbitrary central wavelength (250-1600 eV) and pulse delay (0-100 fs) can now be generated at LCLS with the new variable gap soft X-ray undulators and a magnetic chicane located after the eighth undulator. The pulse duration can be adjusted to a few femtoseconds using either low electron bunch charge or an emittance spoiler [48]. While the X-ray bandwidth in self-amplified spontaneous emission (SASE) mode is typically 1% of the central photon energy, and \(\Delta E_{X}\) can be both broader and smoother using the X-ray laser enhanced attosecond pulse (XLEAP) configuration [47], the actual resolution of the transient absorption spectrum will be set by the design of the grating spectrograph--which, for this first application, requires only a moderate resolution of 1/3000 [49]. Normalization of the incident pulse energy is expected on a shot-by-shot basis at the 1% level using extensions of fluorescence intensity monitoring [50].