Multiphoton inner-shell ionization of the carbon atom

We apply time-dependent R-matrix theory to study inner-shell ionization of C atoms in ultra-short high-frequency light fields with a photon energy between 170 and 245 eV. At an intensity of 10$^{17}$ W/cm$^2$, ionization is dominated by single-photon emission of a $2\ell$ electron, with two-photon emission of a 1s electron accounting for about 2-3\% of all emission processes, and two-photon emission of $2\ell$ contributing about 0.5-1\%. Three-photon emission of a 1s electron is estimated to contribute about 0.01-0.03\%. Around a photon energy of 225 eV, two-photon emission of a 1s electron, leaving C$^+$ in either 1s2s2p$^3$ or 1s2p$^4$ is resonantly enhanced by intermediate 1s2s$^2$2p$^3$ states. The results demonstrate the capability of time-dependent R-matrix theory to describe inner-shell ionization processes including rearrangement of the outer electrons.