The Poisson distribution is a fundamental concept in probability theory and statistics. It is widely used to model the occurrence of rare events across diverse fields, including physics, biology, finance, and medicine. It offers a way to calculate the likelihood of a certain number of events occurring within a specified time period, assuming the events happen independently of one another. The Poisson distribution is commonly used to predict the outcome of random, independent events. In heavy ion-induced nuclear reactions where compound nuclei are formed under conditions of high spin and moderate excitation energy, the investigation of one or multiple neutron emissions is of particular interest. When heavy-ion reactions occur, a random number of neutrons may be released as the target becomes excited by partial or complete absorption of projectile energy, leading to the formation of a highly excited composite system. These neutrons are statistically evaporated to de-excite the compound nucleus (CN). The Poisson distribution function can thus be applied to describe the decay probability of an excited nucleus, particularly for predicting the emission of a specific number of neutrons. In this process, the excess of excitation energy over the binding energy of the released neutrons acts as the continuous variable, and the number of released neutrons serves as the discrete variable. This framework helps us quantify the likelihood of observing a given number of neutrons emitted from an excited nucleus formed in a typical nuclear reaction. In this work, the measured cross-section data for multiple neutron evaporation channels in systems such as 12 C + 165 Ho, 16 O + 169 Tm, 12 C + 128 Te, 16 O + 148 Nd, 19 F + 169 Tm, 16O + 174 Yb, and 12 C + 17 5 Lu reactions have been analyzed using the Poisson distribution. This approach allows all open channels to be treated simultaneously, offering a simplified yet physically meaningful alternative to more elaborate statistical models.
Takar et al. (Thu,) studied this question.