## 3 Results
### Experimental Results  
Good quality spectra were obtained for the four XFEL photon energies of consideration. Spectra were constructed by integrating single photon detections along energy contours on the CCD image, and were then corrected for energy dispersion, solid angle projection, filter transmission and detector response. Figure 5 shows the average spectra obtained for the four XFEL photon energies of consideration, compared with the results from the radiative transfer simulations. The gray regions in the figure indicate the photon energy above which the spectral emission is dominated by bound-free transitions for each case. Note how the simulations agree with the experimental spectra in the slope of the bound-free regions, whereas the bound-bound emission features (at energies lower than those indicated with the gray regions) are not well reproduced by the simulations. This is not surprising, as modelling open shell L-shell spectra of mid- and high-Z elements is a complicated issue that the code-developing community is currently working on (see _Review of the 11 th non-LTE code comparison Workshop_ in preparation). The level of detail necessary to treat all the atomic transitions involved in these spectra requires extremely complicated atomic data, that are usually simplified, which can underestimate the contribution of some transitions to the overall spectra. As described in the previous section, the peak temperature of the plasma (\(T\)) was determined by fitting the bound-free region of each measured spectrum (right of the gray regions in Figure 5), to the function  
\[I=K+I_{0}e^{-E/k_{B}T}, \tag{1}\]  
where \(K\) is a constant introduced to account for any background emission, \(I_{0}\) is a scaling parameter for the spectral intensity, \(E\) is the energy of the emitted photons, and \(k_{B}\) is Boltzmann's constant. We found that variations in the XFEL pulse energy of \(\pm 15\%\), translate into significant variations in the spectral intensity. This is shown in Figure 6, where the spectra from different shots with a XFEL photon energy of 1400 eV are shown together as a function of the pulse energy together with the average spectrum. These intensity variations arise from differences in the temperature of the emitting region of the plasma, as indicated by Equation (1), which allowed us to obtain an estimate of the error introduced in our temperature measurement by the deviations from the nominal laser energy. In Figure 7, we show the comparison between the experimentally obtained temperatures and the peak temperatures predicted by the simulations for the four photon energies of consideration. The triangles represent the peak temperature predicted by Cretin, with the error bars corresponding to variations in this peak temperature with the change of the laser energy. The circles correspond to the temperature obtained from fitting the average spectra for each photon energy, with the error bars corresponding to the standard deviation of the fit parameters. The colored rectangles represent the range of temperatures obtained from individual shots by comparing their absolute spectral bound-free intensity with that of the average spectrum (shown in Figure 6), as given by \(I\propto e^{(-E/kT)}\). Note that, while the temperature obtained from the average spectrum does not correspond in general with the average temperature, owing to the non-linearity of Equation (1), the change in slope of the bound-free emission is monotonic in temperature. Therefore, over a small range of incident intensities, as is the case in this paper, this approximation is valid. Note how, as seen in Figure 6, the slope of the bound-free emission from single shot spectra is very similar among different shots, which is indicative of small changes in the temperature.