The influence of the spin cut-off parameter on the isomeric cross-section ratio of the $(n,2n)$ reaction is studied within the Huizenga-Vandenbosch method, in which the neutron transmission coefficient is evaluated from the optical model, and the spin cut-off parameter is treated for the residual nucleus following the first neutron emission $\left({\sigma }_1\right)$ and that following the second neutron emission $\left({\sigma }_2\right)$ separately. It is found that the isomeric cross-section ratio is definitely sensitive to the spin cut-off parameters, especially the ${\sigma }_2$. Moreover, various formulas of the spin cut-off parameters are compared and applied to calculate the $(n,2n)$ isomeric ratios of a series of nuclei from ${}^{45}\mathrm{Sc}$ to ${}^{198}\mathrm{Hg}$ at $E_n=14$ MeV, and the results are compared with the evaluated values from JENDL-5 and JEFF-3.3, which shows that the method is more reliable in the light- and medium-mass region, and most of the calculated results are described well by the formulas giving the lower spin cut-off parameters than the rigid-body formula, indicating that the effective moment of inertia is less than the rigid body moment of inertia for most nuclei. Furthermore, with the above method the overall isomeric ratios as a function of the incident energy for ${}^{45}\mathrm{Sc}{(n,2n)}^{44m,g}\mathrm{Sc}$, ${}^{85}\mathrm{Rb}{(n,2n)}^{84m,g}\mathrm{Rb}$, and ${}^{120}\mathrm{Te}{(n,2n)}^{119m,g}\mathrm{Te}$ reactions are well described, which shows the validity of the present method in calculating the isomeric ratio of the $(n,2n)$ reaction below 20 MeV.

• Received 13 September 2023
• Accepted 21 November 2023

DOI:https://doi.org/10.1103/PhysRevC.109.014603