High-resolution study of theKβ2x-ray spectra induced by proton and photon impact on Zr, Mo, and Pd targets

$K{\beta }_2$ x-ray spectra of Zr, Mo, and Pd induced by photons and 16-, 25-, and 45-MeV protons were measured with a transmission bent crystal spectrometer. The average $M$-shell ionization probabilities were determined with the assumption that the yields in the $K{\beta }_2$ satellite region are due only to the $M$-shell ionization accompanying the removal of the $K$-shell electron. In the case of photoionization, these yields were found to exceed significantly those calculated with the sudden-approximation model for the shakeoff plus shakeup. Likewise, the corresponding yields for collisions with protons exceed those expected for the combined effect of the direct Coulomb ionization and the shake mechanism. The solid-state effects, as well as the direct knockout of the $M$-shell electron by the photoelectron (or the $\delta$ electron), are discussed in view of their possible effect on the line intensity in the satellite region. The direct Coulomb ionization probabilities in near central collisions with protons are determined from the difference of the relative yields of $\mathrm{K}{\beta }_2$ satellites in the proton-and photon-induced ionization. The underlying assumption is that the shake and solid-state effects are independent of the ionizing agent and that the secondary-electron ionization is similar in the two processes. The results are compared with the semiclassical approximation calculations exploiting relativistic hydrogenic and Dirac-Hartree-Fock wave functions.