The probability $P_n$ of emitting a neutron following $\beta$ decay is critical in many areas of nuclear science, from understanding nucleosynethesis during the $r$ process to control of reactor power levels and nuclear waste management. As it is not always easy to measure or calculate, indirect empirical approaches have been developed to estimate the $P_n$ value from the decay $Q_{\beta }$ value and the neutron separation energy S${}_n$. Here, we present a new prescription incorporating also the half-life $T_{1/2}$, which correlates the known data better and thus improves an estimation of $P_n$ when only $T_{1/2}$, $Q_{\beta }$, and S${}_n$ are known. This new relation can be used to predict $P_n$ values for cases where the half-life is known, thus it can be useful in $r$-process network calculations and in modeling advanced fuel cycles.

• Received 5 September 2012

DOI:https://doi.org/10.1103/PhysRevC.86.041305