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# Here are the amplitudes of g harmonics of the

Here are the amplitudes of g-harmonics of the crystal nuclear potential, which are determined by AR-42 HDAC manufacturer scattering amplitudes for crystal elementary cell (structural amplitudes). In general, are complex values, i.e. =expφ.
However, if the crystal is nonabsorbing and centrosymmetric, all phases can be turned to zero at once, i.e. all can be made real, by putting the coordinate origin at the centre of symmetry. When a neutron is moving through the crystal under conditions close to the Bragg ones for a plane system g, only one harmonic with amplitude will be essential and should be taken into account. That is due to a very narrow wavelength width for Bragg reflection of neutrons. For one harmonic, the origin of coordinates can be always placed at its maximum making the amplitude real. Just the same can be done with the crystal electric potential. So for centrosymmetric crystals the positions of \"nuclear\" and \"electric\" planes always coincide.
But if the center of symmetry is absent, the maxima of electric potential for some crystallographic planes will be shifted relative to the nuclear maxima. That will lead to gigantic electric fields, acting on the neutron inside the crystal [23–25], because the neutrons concentrate in the vicinities of the maxima and minima of nuclear potential where electric field is just nonzero in this case. So the whole class of new neutron optics phenomena arises (see, for example, Ref. [26]).

Neutron crystal optics
Interest in neutron optics in the perfect crystals has accelerated in the past few years. It is caused first by new outstanding possibilities for studies of neutron fundamental properties and its interactions. A case in point is, for instance, a search for a neutron electric dipole moment, as well as a search for CP-violating pseudomagnetic forces due to exchange of a pseudoscalar axion-like particle, using neutron optics in crystal [27–32]; these are now the most important tasks.
The admixture of the waves reflected by crystallographic planes to the neutron wave function significantly changes the pattern of neutron propagation in the crystal and leads to new phenomena, which manifest sharply defined resonance character with Bragg (Darvin) width. For example, a small change of the neutron energy within this width (Δ10–5 for thermal and cold neutrons) results in significant changing the neutron mean velocity in crystal (the anomalous velocity dispersion), and so the sharp energy dependence of the neutron-traveltime through the crystal on neutron energy exhibits [33].
In the present paper we discuss one more phenomenon related to the change in the neutron wave function in the crystal, namely the resonant behavior of neutron refractive index (i.e. kinetic energy of neutron inside the crystal) depending on the difference of the initial and Bragg neutron energies. If a neutron passes through the non-absorbing perfect crystal and Bragg conditions are not satisfied for any crystallographic planes, the neutron propagation through the crystal can be described by the refractive index which depends on the V0 amplitude of zero harmonic (average crystal potential). In this paper, a perfect crystal means a crystal with the dispersion of the interplanar distance much less than the intrinsic width of the Bragg reflection. But when the energy or velocity direction of a neutron approaches the Bragg values, the waves reflected by the corresponding plane system start arising. The amplitudes of these waves are determined by the corresponding amplitudes ofpotential harmonics and by the deviations from the exact Bragg condition. When this deviation being more than the harmonic amplitude we can use the perturbation theory [28,34]. In this case if the neutron has an initial energy equal to E0 and the wave vector k0 (E0 = ħk0/2m), its wave function inside the crystal will be written as
where
is the dimensionless parameter of deviation from the exact Bragg condition for some g system of planes; k,kk+g are the wave vectors of incident and reflected waves inside the crystal with the mean refraction index taken into account; and are the unperturbed neutron kinetic energies in states k〉 and k〉,