Nonsequential two-photon absorption from the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> shell in solid zirconium

We report the observation of nonsequential two-photon absorption from the $K$ shell of solid Zr (atomic number $Z=40)$ using intense x-ray pulses from the Spring-8 Angstrom Compact Free-Electron Laser (SACLA). We determine the generalized nonlinear two-photon absorption cross section at the two-photon threshold in the range of 3.9--57 $\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}60}\phantom{\rule{4.pt}{0ex}}{\text{cm}}^{4}\phantom{\rule{4.pt}{0ex}}\text{s}$ bounded by the estimated uncertainty in the absolute intensity. The lower limit is consistent with the prediction of 3.1 $\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}60}\phantom{\rule{4.pt}{0ex}}{\text{cm}}^{4}\phantom{\rule{4.pt}{0ex}}\text{s}$ from the nonresonant ${Z}^{\ensuremath{-}6}$ scaling for hydrogenic ions in the nonrelativistic, dipole limit.