Calculation of the 1s–2s two-photon excitation cross-section in atomic hydrogen

The two-photon excitation cross-section of atomic hydrogen is calculated using explicit summation over intermediate states within the framework of dipole approximation. The matrix element for two-photon excitation is transformed into finite sums, consisting of the product of a radial and angular part. Nine intermediate states are employed in the calculation of the transition matrix element. The two-photon excitation cross-section obtained for the transition 1s 2 S 1/2 –2s 2 S 1/2 in atomic hydrogen is a good agreement with the literature.