The decay probability of a compound nucleus is typically calculated using statistical models such as the Hauser-Feshbach formalism or the Weisskopf-Ewing approximation. These models are commonly employed to describe the decay of excited nuclear states or compound nuclei.
The decay probability depends on various factors, including the excitation energy of the compound nucleus, the available decay channels, and the properties of the particles involved in the decay process.
In the Hauser-Feshbach formalism, the decay probability is determined by considering the competition between different decay channels. It involves the statistical treatment of nuclear reactions, where the compound nucleus is assumed to reach a statistical equilibrium with the surrounding particles before decaying.
The Weisskopf-Ewing approximation, on the other hand, provides an approximate expression for the decay probability by considering the available phase space for the decay process. It assumes that the compound nucleus decays directly into the final states without reaching a statistical equilibrium.
To calculate the decay probability using these models, one typically needs to know the properties of the compound nucleus, such as its excitation energy, the spins and parities of the states involved, the level densities, and the nuclear reaction cross-sections. Experimental data and theoretical models are often used to determine or estimate these quantities.
It's important to note that the decay probability of a compound nucleus is a complex phenomenon, and accurate calculations can be challenging, particularly for heavy or highly excited nuclei. Various approximations and assumptions are made in these models, and experimental measurements are often used to validate and refine the theoretical predictions.