Abstract
We developed a method to determine the relaxation time of the innermost vacancies for highly ionized heavy ions moving through the bulk. The method compares the intensities of photons emitted through the front and back sides of a thin metal foil. Using foils with known thickness and x-ray absorption cross sections, we directly obtained the mean x-ray emission depth, and thereafter the mean relaxation time. We present data for the emission depth of highly charged 8.5q keV and 23.5q keV Pbq+ ions (q=53-58) impacting on thin Ta foils. The mean relaxation time of M-shell vacancies is estimated to be between 22 and 68 fs, depending on charge state of the projectile, which is about five times longer relaxation time than reported by Hattas et al. [Phys. Rev. Lett. 82, 4795 (1999)]. The experimental results are supported by a model calculation that combines molecular-orbital calculation for the Pb54+-Ta interaction system with a rate-equation model for inner-shell relaxation.