"Optical activity" in the scattering of neutrons from chiral molecules

Neutron "optical activity" or the rotation of the neutron polarization is investigated in the scattering of polarized neutron beams from chiral molecules. A rotation exists to first order in the neutron-electron spin-orbit interaction for randomly oriented target molecules if a total angular momentum $\hslash ({\overrightarrow{\mathrm{j}}}_t+{\overrightarrow{\mathrm{s}}}_t)$ and an orbital angular momentum $h{\overrightarrow{\mathrm{j}}}_t^{*}$ are transferred coherently to a molecular rotator. The first is the angular momentum developed by incident and scattered waves and spinors through a region of interaction with the magnetic fields generated by electrons bound in the "twisted" potentials characteristic of a chiral molecule. The second is the angular momentum developed by incident and scattered waves through a region of interaction with a network of atomic nuclei having the same twist. The magnetic amplitude must be calculated in the first Born distorted-wave approximation. Distortion causes the magnitudes of the magnetic amplitudes to be distinct for $\Delta l=\pm 1$, $\Delta m=\pm 1$, and $\Delta l=\pm 1$, $\Delta m=0\mathrm{}$ partial-wave transitions induced by the magnetic forces, thus preventing their cancellation on rotationally averaging the cross section. This distortion is produced by the nuclear background; thus the rotation is of order $\frac{m_N}{m_e}$ (neutron-to-electron mass ratio) larger than previous estimates based on the use of the second Born plane-wave magnetic amplitude for forward scattering. However, the present rotation exists only at nonzero scattering angles. This is the first example of a rotation of the neutron polarization which is nonvanishing to first order in a spin-orbit interaction. Its strength makes it an important effect in the use of neutrons to probe molecular structure. We check our result by finding the limit of scattering from spin-independent forces. Here the rotation vanishes, and the incoherent limit for the transfer $\hslash {\overrightarrow{\mathrm{j}}}_t=\hslash {\overrightarrow{\mathrm{j}}}_t^{*}$ obtains. This limit is well known from the Fano-Dill or Temkin-Sullivan theory of orbital-angular-momentum transfer to a rotator.