The use of symmetry to correct Larmor phase aberrations in spin echo scattering angle measurement

Spin echo scattering angle measurement (SESAME) is a sensitive interference technique for measuring neutron diffraction. The method uses waveplates or birefringent prisms to produce a phase separation (the Larmor phase) between the "up" and "down" spin components of a neutron wavefunction that is initially prepared in a state that is a linear combination of in-phase up and down components. For neutrons, uniformly birefringent optical elements can be constructed from closed solenoids with appropriately shaped cross sections. Such elements are inconvenient in practice, however, both because of the precision they demand in the control of magnetic fields outside the elements and because of the amount of material required in the neutron beam. In this paper, we explore a different option in which triangular-cross-section solenoids used to create magnetic fields for SESAME have gaps in one face, allowing the lines of magnetic flux to "leak out" of the solenoid. Although the resulting field inhomogeneity produces aberrations in the Larmor phase, the symmetry of the solenoid gaps causes the aberrations produced by neighboring pairs of triangular solenoids to cancel to a significant extent. The overall symmetry of the SESAME apparatus leads to further cancellations of aberrations, providing an architecture that is easy to construct and robust in performance.