InternationalReciprocal spaceTables for Crystallography Volume B Edited by U. Shmueli © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. B, ch. 5.3, p. 659
## Section 5.3.5. Effect of external fields on neutron scattering by perfect crystals |

The possibility of acting on neutrons through externally applied fields during their propagation in perfect crystals provides possibilities that are totally unknown in the X-ray case. The theory has been given by Werner (1980) using the approaches (migration of tie points, and Takagi–Taupin equations) that are customary in the treatment of imperfect crystals (see above). Zeilinger *et al.* (1986) pointed out that the effective-mass concept, familiar in describing electrons in solid-state physics, can shed new light on this behaviour: because of the curvature of the dispersion surface at a near-exact Bragg setting, effective masses five orders of magnitude smaller than the rest mass of the neutron in a vacuum can be obtained. Related experiments are discussed below.

An interesting proposal was put forward by Horne *et al.* (1988) on the coupling between the Larmor precession in a homogeneous magnetic field and the spin–orbit interaction of the neutron with nonmagnetic atoms, a term which was dismissed in Section 5.3.2 because its contribution to the scattering length is two orders of magnitude smaller than that of the nuclear term. A resonance is expected to show up as highly enhanced diffracted intensity when a perfect sample is set for Bragg scattering and the magnetic field is adjusted so that the Larmor precession period is equal to the *Pendellösung* period.

### References

Horne, M. A., Finkelstein, K. D., Shull, C. G., Zeilinger, A. & Bernstein, H. J. (1988).*Neutron spin – Pendellösung resonance. Physica B*,

**151**, 189–192.

Werner, S. A. (1980).

*Gravitational and magnetic field effects on the dynamical diffraction of neutrons. Phys. Rev. B*,

**21**, 1774–1789.

Zeilinger, A., Shull, C. G., Horne, M. A. & Finkelstein, K. D. (1986).

*Effective mass of neutrons diffracting in crystals. Phys. Rev. Lett.*

**57**, 3089–3092.