Multiple ionization of helium and krypton by electron impact close to threshold: Appearance energies and Wannier exponents

We determined appearance energy (AE) values AE(Xⁿ⁺/X) for the formation of singly (He⁺) and doubly charged (He²⁺) He ions and multiply charged Kr ions Krⁿ⁺ up to n = 6 following electron impact on He and Kr atoms using a high-resolution electron impact ionization mass spectrometer. The data analysis employs an iterative, non-linear least-squares fitting routine, the Marquart-Levenberg algorithm, in conjunction with either a 2-function or a 3-function fit based on a power threshold law. This allows us to extract the relevant AEs and also the corresponding exponents for a Wannier-type power law from the measured near-threshold data. The values of the AEs determined in this work are compared with other available experimental and with spectroscopic AE values and the extracted exponents p are compared with other available experimental data and with the predictions of the various Wannier-type power law models. One observation is particularly noteworthy, namely the fact that none of the available experimental data seem to support the large values of 'p' predicted by the Wannier-Geltman and the generalized Wannier law for n > 3.