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        {\huge \textbf{Extracting the Electronic Structure of Warm Dense Matter via Resonant Inelastic X-ray Scattering} \par}

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        {\LARGE
        \vspace*{1.5cm}
        \textbf{Alessandro Forte} \\
        \vspace*{0.2cm}
        \Large
        Jesus College\\
        University of Oxford\\
        
        \vspace*{0.2cm}
        Supervised by:\\
        Prof. Sam M. Vinko\\

        \vspace*{0.5cm}
        Thesis Submitted for the Degree of\\
        \textit{Doctor of Philosophy}\\

        \vspace*{0.5cm}
        Hilary Term 2025
        }
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% Dedication
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Dedicata a Giulio e Adriano, che sono nati insieme al mio dottorato
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% Abstract
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    \Large
    \textbf{Extracting the Electronic Structure of Warm Dense Matter via Resonant Inelastic X-ray Scattering}
        
    \vspace{0.2cm}
    \Large
    Alessandro Forte \\
    \large
    \vspace{0.2cm}
    Jesus College, University of Oxford\\
    \vspace{0.05cm}
    \textit{Thesis Submitted for the Degree of Doctor of Philosophy}\\
    \vspace{0.05cm}
    Hilary Term 2025
       
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    \Large
    \textbf{Abstract}
\end{center}
{\normalsize
Understanding how material properties evolve under extreme thermodynamic conditions is essential for advancing our knowledge of matter in such environments, with applications ranging from planetary science to nuclear fusion research. However, the challenges associated with recreating these thermodynamic conditions in laboratory settings, combined with their transient nature, have limited the number of experimental techniques suitable for their study. At the same time, the complexity of High-Energy Density (HED) systems necessitates experimental investigation to benchmark and refine theoretical models. This thesis introduces a novel approach based on Resonant Inelastic X-ray Scattering (RIXS) spectroscopy to measure the electronic density of states (DOS) of materials—a fundamental quantity from which many other material properties can be derived. Unlike traditional techniques such as absorption spectroscopy, RIXS encapsulates information about the global electronic structure of a material in a single spectrum, albeit in a complex form. This feature is particularly advantageous in HED science, where achieving stable and reproducible conditions is inherently difficult. However, this advantage is accompanied by the drawback of a relatively low signal-to-noise ratio (SNR), making the extraction of DOS from RIXS spectra a complex task. To this purpose, I developed a method that combines neural networks with physical modelling to perform this extraction. This approach also deconvolves the source spectrum by correlating it with the RIXS measurements, allowing for the reconstruction of DOS with a resolution that surpasses the limitation given by the source spectrum's bandwidth. The method is first introduced in a general framework as a way to solve complex inverse problems and is subsequently tailored to the RIXS problem. This approach is tested on synthetic RIXS data and its performance is compared with those of more conventional numerical techniques. Additionally, I show that this RIXS-based methodology can also measure the temperature of the probed material. I then apply this method to analyse RIXS spectra from two experiments conducted at the EuXFEL and LCLS facilities. The first experiment investigated warm-dense Fe, FeO, Fe$_2$O$_3$, and gadolinium, extracting their thermodynamic conditions and electronic structures with sufficient resolution to detect the microscopic environment in which ions are embedded and resolve fine details such as bandgaps. The extracted DOS showed good agreement with density functional theory (DFT) calculations. While the investigation of gadolinium primarily showcased the method’s flexibility in analysing various materials through different electronic excitations, the study of iron oxides attracted particular interest due to their distinctive behaviour under high-pressure conditions and their relevance in geophysics. In the other experiment, the DOS of compressed and ambient FeO is extracted, revealing a systematic bandgap closure consistent with theoretical predictions of a insulator-to-metal transition under high compression. The electronic structure evolution was studied in parallel with changes in the crystalline structure, highlighting RIXS’s potential for time-resolved studies of dynamic processes. While these results retrieved the expected trends, higher-quality raw data are required to achieve more precise and conclusive findings. Overall, these results hold promise for this RIXS-based methodology to monitor the evolution of electronic structures in materials undergoing fast dynamic processes, paving the way for innovative diagnostic approaches in this field.



% As a complementary subject, the second chapter of this thesis details methods for constructing spectra from camera images while enhancing their SNR and possibly their resolution. These techniques, while broadly applicable, are particularly valuable for HED science and our investigations, where low signal levels often characterize the data.





% Future experiments, leveraging advancements in experimental technologies, aim to refine these preliminary results. Additionally, we plan to enhance the RIXS methodology and generalize this neural network-based extraction technique to other physical processes.



}




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    \Large
    \textbf{Acknowledgements}

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{\normalsize

There are many people to whom I owe thanks for making this work possible and for accompanying me in these important years of life.

Firstly, I wish to thank my supervisor Sam Vinko for having given me this opportunity, and for his guidance and support throughout these years, both on a scientific and human level. I am especially grateful for the care he took, during many discussions in his office, in helping me grow as a scientist and, more broadly, as a professional, something I must admit I struggled with a bit. 

I would like then to thank all my research group for the helpful feedback they constantly provided during our meetings and, above all, for forgiving all my delays and my not-too-english expressions during presentations. ``The fact is'' that I am not very good with accents. A special thank goes to Tom Gawne, my \textit{star}, to Justin Wark for his always insightful and witty remarks, to Céline Crépisson for her \textit{tireless} support, to Sam Azadi for performing DFT calculations with the ease most people reserve for going to the bathroom, to Karim Alaa El-Din for being my first coauthor and to Pontus Svensson and Thomas Campbell for all our engaging physics discussions, both in and out of the office. A big thank-you as well for sharing your research (especially Paddy with his beautiful presentations), which helped me gain a better overall view of our field, something I believe is really important for any scientist. 

On a personal level, I am grateful to Pontus, the Toms, Hannah, Karim, Charlie and Oliver for these years we spent growing together, learning about each other’s cultures, and sharing unforgettable and funny experiences around the world. In this regard, I extend my sincere thanks to all my external collaborators, who introduced me to the world of research and scientific partnership. None of the experiments would have been possible without their contributions.

% Outside the world of physics, but still within the Oxford sphere, I would like to thank Giuliano, whose genuine joy, abscence of envy, and light-hearted excitement for the happiness of his loved ones I find inspiring and deeply admirable, as well as Riccardo, Pietro, Carlo, Stefano, Katia and Filippo. We discovered our friendship while making life-experiences new to us, and we have been lucky enough to get to know one another across diverse contexts and adventures. I will always keep the memories we created, at times feeling almost like scenes from another life. A thank you also goes to the many nice people I met through football, college, and shared living experiences. You made me discover a different type of life. Lastly, to Mathieu, who has been with me from the very first step we took in Oxford.

Outside the world of physics, but still within the Oxford sphere, I would like to thank Carlo, Stefano, Riccardo, Pietro, Giuliano, Katia and Filippo. We discovered our friendship while making life-experiences new to us, and we have been lucky enough to get to know one another across diverse contexts and adventures. I will always keep the memories we created, at times feeling almost like scenes from another life. A thank you also goes to the many nice people I met through football, college, and shared living experiences. You made me discover a different type of life. Lastly, to Mathieu, who has been with me from the very first step we took in Oxford.

Now going to my \textit{homeworld}, Rome, which everyone who knows me understands I hold dearly in my heart, I would like to thank my mother, my fortress, my father, for all the things he taught me, my elder brother Davide, for the love and esteem he has always given me, my sister-in-law Elisa, for our special brother/sister-in-law relationship, and the two little ones, Giulio and Adriano, whose sweetness brought light even in the darkest moments. My heartfelt thanks also go to the rest of my wonderful and numerous family, and then to all my lifelong friends with whom I grew up. 
I will not list names, first because there are too many of you; and second, because these acknowledgments are already long enough, and if I name one, I will have to name everyone. But be assured that as I write these lines, I am thinking about each of you. I just tell you that you are always with me, and life has proven that physical distance cannot weaken our bond. We will be reunited in the end—it is a promise, or perhaps a threat...
However, two special mentions are in order, one for the beginning and the other for the end of my experience: thanks to Fabi for pushing me to apply to Oxford and to be a bit more ambitious (still in a healthy way)-none of this would have been possible without you. And to Mauro, for showing me what \textit{selfless good} means and for standing by my side during the writing of this thesis, a time that coincided with a tough moment of my life. You are a source of inspiration to me.

Finally, thanks to Bianca that taught me the most important of all things.


%(Eli you as well)

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\noindent \textit{The author would like to thank the Science and Technology Facilities Council (STFC) for their support.}
}

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