An effective method to calculate the electron impact excitation cross sections of helium from ground state to a final channel in the whole energy region

The electron impact excitation (EIE) cross sections of an atom/ion in the whole energy region are needed in many research fields, such as astrophysics studies, inertial confinement fusion researches and so on. In the present work, an effective method to calculate the EIE cross sections of an atom/ion in the whole energy region is presented. We use the EIE cross sections of Helium as an illustration example. The optical forbidden 11S - n1S (n = 2 - 4) and optical allowed 11S - n1P (n = 2 - 4) excitation cross sections are calculated in the whole energy region using a scheme that combines the partial wave R-matrix method and the first Born approximation. The calculated cross sections are in good agreement with the available experimental measurements. Based on these accurate cross sections of our calculation, we find that the ratios between the accurate cross sections and Born cross sections are nearly the same for different excitation final states in the same channel. According to this interesting property, a universal correction function is proposed to calculate the accurate EIE cross sections with the same computational efforts of the widely used Born cross sections, which should be very useful in the related application fields. The Correction Function data for [1s2] 11S – [1sns] n1S and [1s2] 11S – [1snp] n1P transitions are presented in TABLE I and II respectively. And an interpolation Fortran program CF.f that reproduces all the data in TABLE I and II are provided. Besides, we also propose an analytical formula for the Correction Function to facilitate different application requirements using Eqs. (1) and TABLE III.