A simple theoretical approach to multiple ionization and its application for 5.1 and 5.5 MeV/u Xq++ Ne collisions

Inner-shell ionization in near-central collisions of 6.7 MeV/amu4He ions with mid-Z atoms

“…From the change in the intensity ratios of different transitions and the energy shift of the X-ray lines, the number of M4, 5 vacancies were determined. They found a remarkable agreement with the geometrical model of Sulik et al [ 11 ].…”

Ionization probability for multiple ionization: An assessment of the geometrical model

“…The degree to which P Sulik [0] falls below P SCA [0] when v 1 ov 2S appears to be only slightly dependent on the Z 1 /Z 2 as the P Sulik [0]/ P SCA [0] calculated for K-shell ionization of 29 Cu, 34 Se, 47 Ag for Z 1 /Z 2 o0.35 (see blue points in Fig. 8) are in close proximity of that ratio calculated for Z 1 =Z 2 ¼ 1 (see blue 2 MeV p -> Ag DATA : Laegsgaard et al [1972] BEA Vriens [1967] BEA Sulik et al [1987] BEA Hansen [1973] SCA Hansteen et al [1975] {P {σBEA, σBEA} / σSCA Fig. 4.…”

“…In our figures, P Sulik [p] is displayed as a step function: P Sulik [0] from the works of Sulik et al ( , 1987 for pop c and 0 otherwise where p c is such that 2p pc o R P Vriens ½pp dp ¼ s Vriens . Since only P Sulik [p] at p ¼ 0 is germane for its assessment vis a vis P SCA [0] and data to be utilized or obtained in studies of multiple ionization, this graphical representation of P Sulik [p] emphasizes its value at p ¼ 0 and is immaterial for p40.…”

“…With the progress in the analysis of highresolution X-ray spectra, it became apparent (see Fig. 5 in Horvat et al, 2005) that the experimentally determined fraction of spectator vacancies in collisions with heavy ions saturates by a factor of 2 below what is calculated by the geometrical model of Sulik et al (1987). This paper focuses on an assessment of the BEA-driven formulas as gauged by the P[0] of the SCA in its simplest straight-line incarnation of Hansteen et al (1975).…”

“…Over the years, a simple formula developed by Sulik et al (1987)-in terms of the scaling variable of the BEAinspired geometrical model for P[0]-has won over the SCA approach. Yet, a review of papers-where the geometrical model is compared with SCA calculations (see Refs.13,51,54,56,[58][59][60] in a recent article by Lapicki et al, 2005)-suggests that P[0] of that model falls below and above the SCA predictions when, respectively, the projectile velocity v 1 is less or greater than the orbital velocity v 2S of the electron ionized from an S shell.…”