{'fraction_non_alphanumeric': 0.024806201550387597, 'fraction_numerical': 0.0, 'mean_word_length': 5.333333333333333, '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}}
Approximate Bounds to the Average Electron Momentum Density for Atomic Systems

Approximate bounds to the average electron momentum density ⟨γ⟩ in terms of momentum expectation values ⟨pn⟩ have been derived for atomic systems. These bounds are based on the semiclassical relationships in the Thomas–Fermi model. Meanwhile, approximate bounds to the average electron density ⟨ρ⟩ in terms of the expectation values ⟨rn⟩ have also been obtained employing a similar procedure on the basis of the same model. The quality of the bounds presented is numerically studied and discussed within the Hartree–Fock framework. Atomic units are used throughout.