\textbf{Resonant inelastic x-ray scattering study at the oxygen K-edge of corner-shared Sr}$_{\mathbf{2}}$\textbf{CuO}$_{\mathbf{3}}$\textbf{ cuprate}

We present a resonant inelastic x-ray scattering (RIXS) study at the oxygen K-edge of the spin-chain system Sr$_{2}$CuO$_{3}$. We investigate this system using small cluster exact diagonalization calculations for a microscopic model that considers all the orbitals of Cu and O in CuO3-unit cell. Using a canonical parameter set, we compute the XAS and RIXS spectra in comparison to the experiment. This allows us to identify the \textit{dd}- and charge transfer excitations in the observed spectrum. We also infer the presence of several low energy excitations that may be related to phononic and/or magnetic excitations.