{'fraction_non_alphanumeric': 0.02119815668202765, 'fraction_numerical': 0.0027649769585253456, 'mean_word_length': 5.241379310344827, '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}}
The Backward Theory of Stochastic Particle Transport with Multiple Emission Sources

The backward theory of stochastic transport is elaborated for the case of subcritical systems with a source that emits more than one particle in each source emission event. Examples of such sources are spontaneous fission sources, such as 252Cf, and, more important, spallation sources. Possible forms of the source distribution describing e.g. a spallation source in a thin target are discussed. The essence of the theory is the generalization of a formula due to Bartlett, connecting the probability distribution due to a single particle, with that due to a continuous source, to the case of multiple emission sources. From this formula, expressions are derived for first and second order moments of the particle distribution (or the detector count), induced by a multiple source, expressed as integrals over similar moments of the single-particle induced distribution. These expressions are suitable for the calculation of the Feynmann-alpha and Rossi-alpha formulae for multiple emission sources.