{'fraction_non_alphanumeric': 0.012875536480686695, 'fraction_numerical': 0.0, 'mean_word_length': 5.477777777777778, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Elastic and inelastic atomic scattering in a standing-wave laser field

The motion of a two-level atom in a standing-wave laser field is studied using an approximation to the resolvent operator in the form of a truncated eigenfunction expansion, with the field treated in the occupation-number representation. The formalism provides expressions for the time-dependent S-matrix for transitions into both ground and excited atomic states. The effective Hamiltonian for purely elastic scattering is constructed, allowing for the direct study of scattering in the Bragg regime. Contact with standard treatments of Bragg scattering in terms of Mathieu functions is obtained by imposition of additional approximations. Comparison of numerical results obtained with and without imposition of these approximations provides an indication of their range of validity. The dependence of excitation probabilities on field strength and detuning is studied. These numerical illustrations provide evidence that in cases of physical interest excitation probabilities can be significant and can be reliably estimated for a broad range of field parameters using the present formalism.