Small-Angle Scattering of Neutrons by Nuclei

The partial-wave phase shifts for the scattering of neutrons by nuclei are considered with some emphasis on large values of orbital angular momentum $l$. It is shown that a rather simple general approximation technique for obtaining the phase shifts follows from the scattering integral equation for the partial-wave amplitudes. This method is used to study the electromagnetic scattering of neutrons by nuclei. It is shown that the first-order approximation for the phase shifts gives a small but non-negligible correction to the Born approximation (zero order) even for large $l$. However, it is shown that higher order approximations tend to reduce the correction significantly. The interference effects between the electromagnetic scattering and the nuclear scattering are also considered. For large $l$ the scattering tends to be dominated by the electromagnetic scattering. However it is found that if the nuclear spin-orbit interaction is sufficiently strong then the nuclear scattering can become important even for large $l$. It is suggested that this effect may be significant in explaining the anomalous small-angle scattering of neutrons by Th, U, and Pu nuclei.