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This chapter discusses recent developments in neutron phase-contrast and polarized neutron tomography. Topics covered include theory of phase-contrast imaging, experimental techniques for phase-contrast imaging, and imaging with polarized neutrons.

Neutron beam magnetic resonance experiments with slow neutrons are very similar to corresponding molecular beam experiments. Methods of polarizing neutron beams by total reflection and other means are discussed. The neutron beam experiments that measure the magnetic moment of the neutron are described. Magnetic resonance experiments in which the static magnetic fields are changed from parallel to anti-parallel provide a sensitive upper limit to the neutron electric dipole moment.

This chapter is devoted to the observation of microscopic magnetism, working out in some detail the most commonly used magnetic techniques. The basic aspects of these techniques are only briefly recalled, and indication is given of relevant text books which will give a sound background knowledge. However, it is the goal of the chapter to allow the reader to be able to read the current literature with some acceptable understanding. The magnetic techniques include microSQUID and micro Hall probe techniques and torque magnetometry; specific heat measurements, including equilibrium and out of equilibrium measurements; and magnetic resonance techniques, including EPR, NMR, and muon spin resonance. Mention of neutron techniques, including polarized neutron diffraction and inelastic neutron scattering, will conclude the section.

The description of neutron optical phenomena within the framework of dynamical diffraction theory is described. The coherent wave and optical potential are introduced, and an expression for the complex neutron refractive index in terms of the scattering length density and attenuation coefficient is obtained. The extension to magnetic media and polarized neutrons is covered. Neutron reflectivity is defined, and the wavevector dependence of the reflectivity profile is derived by a transfer matrix method and an optical method. Exact results are compared with the Born approximation. The technique of neutron imaging is described, including neutron radiography and computed tomography. Several optical phenomena that occur in Bragg diffraction from near-perfect crystals, including Pendellösung oscillations, and primary and secondary extinction.

This chapter introduces the basic properties of the neutron and its interactions with matter. The principal methods for neutron production are described, especially reactor and spallation sources. The kinematics of scattering are explained, and a simple interpretation is given in terms of the interference of matter waves. Nuclear scattering is separated into coherent and incoherent contributions, and the neutron scattering length is defined. The concept of the cross-section is introduced, and the total, differential, and partial differential scattering cross-sections, as well as the absorption cross-section, are defined.

The interaction potentials and their spatial Fourer transforms are derived for nuclear and magnetic scattering, as well as for interactions with atomic electric fields. For the nuclear interaction, the Fermi pseudopotential is introduced and the scattering length operator is defined. The neutron spin dependence of the nuclear and magnetic interaction is calculated, and general expressions for spin-dependent scattering are obtained. The longitudinal and XYZ polarization analysis methods are described, and the technique of spherical neutron polarimetry is explained. The Blume-Maleev equation which gives the final neutron polarization for an arbitrary incident polarization are derived.