Abstract
We propose a practical numerical method for treating the Coulomb interaction in momentum space. The Coulomb potential is regularized by expanding its inner part $r<~R$ as the superposition of the Gaussian functions. This smooth-cutoff Coulomb potential decreases rapidly in momentum space without oscillation. In addition, the partial-wave decomposition can be done analytically without numerical integration. First, the phase shifts are calculated with the regularized Coulomb plus short-range strong potentials. Then, the correct phase shifts or the wave functions can be reconstructed with the aid of coordinate-space calculation from the asymptotic region inward to R. Another possibility is to calculate the logarithmic derivative at R directly by the Fourier transform, which is matched to the point-Coulomb wave functions ${F}_{L}$ and ${G}_{L}.$ This method is examined for calculating the phase shifts of proton-nucleus elastic scattering and found to be accurate over wide energy regions.
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