Strong Absorptions of Thermal Neutrons Caused by Virtual States

Abstract Cross sections of compound nucleus (CN) formation by S-wave neutron scattering, the study of which was begun by Feshbach et al. in a pioneering work, are reanalyzed by the optical model plus the Jost function method (JFM), which is a modern theory for handling bound and unbound continuum states in a unified manner. We have calculated the CN cross section for thermal neutron scattering ($E_n=25.3$ meV) by about 300 stable targets. The enhancements in the CN cross section in specific mass number regions, $A\sim 10, 50$, and 160, which are well known results in the previous optical model analyses, are reproduced by the present calculation. The JFM calculation is applied to investigate the origin of the enhanced CN cross section, and the poles in the scattering matrices (S-matrices) are systematically explored in the complex momentum plane. In JFM, the S-matrix poles representing the virtual states, which are different from the usual resonances described by the Breit–Wigner formula, appear around the origin (zero energy) in the momentum plane in the mass region with the enhanced CN cross section. The present analysis of the S-matrix means that the virtual state strongly enhances the CN cross section. We also discuss the present results in connection with giant resonances and compound nuclear resonances, which were regarded in previous studies as established theories to understand the enhanced absorption of the thermal neutron.