Abstract: In electron-atom (or ion) collisions, it is unadvoidable to compute a large number of integrals with seriously oscillatory wavefunctions. Since direct numerical integration are very exhausted and often may fail to reach the required accuracy, analytical methods are necessary. In this paper an improved method is presented for calculating integrals with seriously osillatory in tegrands. The accuracy of phase calculation is improved for the case of wavenumber being different. The analytical expressions of integrals are given for the case of wavenumber being equal. The accury of simulation results are very satisfactory.

Key words: wavefunctions, integrals, seriously oscillatory