Calculation of slowly converging integrals in electron-ion collision problems

For slowly converging integrals encountered in the calculation of electron impact excitation and ionization cross sections, a method of determining integration steps was proposed using the characteristics of Coulomb functions at eta <0. The He + ionization cross sections were calculated in the CBE approximation as an illustration. With the present method, the total integration steps and thus computational time are significantly reduced for a given accuracy.