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

As X-ray spectra of multiply ionized atoms are resolved with higher resolution, the number of vacancies in outer shells-used to deduce the probability of ionization at the zero impact parameter P[0]-can be determined with increasing accuracy. The P[0] so extracted, or served as input in X-ray data analyses, has been for over two decades and almost universally compared with, or entered from, the predictions of the geometrical model of Sulik et al. [1984. Charge scaling of ionization probabilities in ion-atom collisions for zero impact parameter. J. Phys. B 17, 3239-3244] which is grounded on the binary encounter approximation (BEA). The validity of P[0] employed in the geometrical model is tested with the straight-line semiclassical approximation (SCA) at p=0. It is shown that the P[0] of Sulik et al. is reasonably close to the semiclassical P[0] when the projectile velocity v1 is in the neighborhood of the velocity of an S-shell electron v2S, but the geometrical model increasingly and significantly under- and overestimates the SCA values when, respectively, v1/v2S<1 and v1/v2S>1. This is consistent with breakdown of the geometrical model as indicated by the recent experiment of Horvat et al. [2005. L X-rays emitted from multiply ionized holmium atoms. Phys. Rev. A 71, 062709].