{'fraction_non_alphanumeric': 0.02266666666666667, 'fraction_numerical': 0.0, 'mean_word_length': 5.705357142857143, '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}}
A new real-space correlated-basis-functions approach for electron correlations of the semiconductor inversion layer

Based on the real-space correlated-basis-functions theory and the collective oscillation behaviour of the electron gas with effective Coulomb interaction, the many-body wavefunction is obtained for the quasi-two-dimensional electron system in the semiconductor inversion layer. The pair-correlation function and the correlation energy of the system have been calculated by the integro-differential method. A comparison with other previous theoretical results is also made. The new theoretical approach and its numerical results show that the pair-correlation functions are definitely positive and satisfy the normalisation condition.