Lower and upper bounds on M-shell X-ray production cross sections by heavy ions

In inner-shell ionization by heavy ions, a significant shift of X-ray lines to the higher energy side and broadening of the peaks indicate that simultaneous multiple ionization of the M and higher shells can dramatically change the values of the atomic parameters. 14Si3,4+14Si3,4+ and 16S3,4+16S3,4+ ions in the energy range of 5–10 MeV were used to bombard gold (200 μg/cm2) and bismuth (80 μg/cm2) targets. Eight main M X-ray lines have been detected with a Si(Li) detector. Without a possibility for a realistic way to modify the atomic parameters and an accurate extraction of M-subshell ionization cross sections, theoretical cross sections for M-shell ionization are converted to X-ray production cross sections with two extreme choices that presume (i) no multiple ionization and (ii) the certainty that all shells outer to the M-shell are completely ionized in the full multiple ionization. These choices impose the lower and upper limits on theoretical predictions. The X-ray production data should be bracketed by the bounds calculated with any theory. We test this proposition by comparison of the measured cross sections for production of the main X-ray lines and their sum for the total M-shell X-ray production with the predictions of the First Born and ECUSAR [G. Lapicki, Nucl. Instrum. Meth. B 189 (2002) 8] theories in those two extreme limits. With the extreme assumption of no multiple ionization, the First Born approximation shows overall satisfactory agreement with the data while the ECUSAR theory drastically underpredicts our measurements. With the opposite extreme assumption of the full multiple ionization, the ECUSAR exhibits better agreement with the data than the First Born approximation. While neither agreement suggests sure preference for either of these theories, such extreme conversions – as they would have for of any ionization theories – set the lower and upper bounds on their predictions.