Double to tenfold M-shell photoionization of singly charged lanthanum ions
Using the photon-ion merged-beams technique at the PETRA\,III synchrotron light source, we have measured cross sections for double and up to tenfold photoionization of La$^{+}$ ions by a single photon in the energy range 820--1400~eV, where resonances and thresholds occur that are associated with the excitation or ionization of one $M$-shell electron. These cross sections represent experimental benchmark data for the further development of quantum theoretical methods, which will have to provide the bulk of the atomic data required for the modeling of nonequilibrium plasmas such as kilonovae. In the present work, we have upgraded the Jena Atomic Calculator (JAC) and pushed the state-of-the-art of quantum calculations for heavy many-electron systems to new limits. In particular, we have performed large-scale calculations of the La$^+$ photoabsorption cross section and of the deexcitation cascades, which set in after the initial creation of a $3d$ hole. Our theoretical results largely agree with our experimental findings. However, our theoretical product-ion charge state distributions are somewhat narrower than the experimental ones, which is most probably due to the simplifications necessary to keep the cascade calculations tractable.