Transition amplitudes and transition probabilities for the two-photon 1s–2s transition in the hydrogen atom and 11s–21s transition in helium atom have been calculated using a partial-closure approach. The dominant term is calculated exactly and the remaining sum over intermediate states is calculated using a mean excitation energy. Our value of the transition amplitudes agree within 2% with the exact results for the hydrogen case. Our value of the transition probability for hydrogen is 8.50 s−1 which is in good accord with its known value 8.226 s−1. For helium, the photon energy distribution of the metastable 21s state is in good agreement with the accurate values. The corresponding transition probability is 53.7 s−1 which is in good agreement with the accurate value 51.3 s−1.
Volume 94, 2020
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