{'fraction_non_alphanumeric': 0.01403061224489796, 'fraction_numerical': 0.0, 'mean_word_length': 6.008928571428571, '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}}
Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case

Abstract This work suggests a connection between Landau-Zener transition probabilities between two crossing potentials in the classically accessible WKB regime and Landau-Lifshitz transition probabilities in the classically inaccessible WKB regime. It is based on the uniform Airy (UAi) approximation which represents a generalization of quantum transition probabilities for linear crossing potentials with constant coupling. The performance of the UAi approximation is tested by comparison with distorted-wave probabilities for an exponential potential model and illustrated for potentials that determine the intersection of two ab initio vibronic potential surfaces of the NO-Ar system.