Acceleration of neutrons in the uniform

Acceleration of neutrons in the uniform magnetic field by means of a radio-frequency flipper is well known and successfully used in physical experiments (see, e.g., Ref. [7]). The phenomenon of neutron acceleration in a strong alternating magnetic field (of amplitude ∼0.4T) was observed in Ref. [8]. The acceleration of neutrons in a weak alternating magnetic field (of 0.1–1.0mT) was measured using anomalous behaviour of the velocity dispersion for neutrons, moving in a crystal close to the Bragg directions [9]. The foundations of the neutron acceleration in a laser radiation field were considered in Ref. [10]. Also acceleration and deceleration of neutrons by reflection from moving mirror [11,12] or by Doppler-shifted Bragg diffraction from a moving crystal [13,14] are well-known and used in experiments with ultracold neutrons. Recently a new interest has arisen in the acceleration of neutrons passing through accelerating media [15,16]. This effect was first observed by the authors of Ref. [17] and was described in detail in Ref. [18]. It was noted in Ref. [18] that “the observed effect was a manifestation of quite a general phenomenon – the accelerated medium effect (AME)inherent to waves and particles of different nature”. In Ref. [19], the acceleration and deceleration of neutrons were observed by applying a specific time-of-flight method. In Ref. [20], some new special features of the effect for a birefringent medium were discussed with the applications to neutron spin optics and evolution of flavor states of neutrino, propagating through a free space. The acceleration of the samples in the mentioned experiments reached several tens of g units, and the value of the wnt inhibitor transfer Δ to a neutron with energy fell within the range of (2–6)·10–10eV [18] for ultracold neutrons (UCN), so up to now AME was observed only for UCN and by only one research group (see Refs. [18,20]). Here is a neutron velocity, Δv is a value of a relative neutron-matter velocity variation during the neutron time-of-flight through the sample, n is the refraction index for neutron. In the present paper, a new much more effective mechanism of acceleration effect is proposed [21], which has been tested and confirmed experimentally for cold neutrons passing through the accelerated perfect crystal. An energy transfer to a neutron in this case can be at the level of ∼4⋅10−8eV. This value in contrast to AME is determined by the amplitude Vg of the corresponding harmonic of the nuclear neutron–crystal periodic potential, but not by the value of a relative neutron–crystal velocity variation during the neutron time-of-flight through the crystal. For cold neutron so AME in our case has an order that is negligible in further consideration (V0 is zero harmonic of neutron–crystal interaction potential, i.e. averaged crystal potential). The essence of the crystal acceleration effect is as follows. The crystal refraction index for neutrons in the vicinity of the Bragg resonance sharply depends on the crystal–neutron relative velocity (see further). The neutrons enter into accelerated crystal with one potential of a neutron–crystal interaction and exit with the other potential, so the kinetic energy change at the crystal boundaries will differ, and neutrons will be accelerated or decelerated after passage trough such a crystal, in this case the energy transfer to a neutron being at the level of ∼4·10eV. Neutron wave function significantly modifies for neutrons moving through the crystal under conditions close to the Bragg ones. As a result neutrons concentrate on “nuclear” planes or between them [22,23]. We take the term “nuclear” planes to mean the positions of maxima of periodic nuclear potential for corresponding system of crystallographic planes. The neutron–crystal interaction potential can be written as a sum (the reciprocal lattice vectors expansion) of harmonic potentials (harmonics) corresponding to all nuclear plane systems described by reciprocal lattice vector g normal to the given plane system, g =2π/d(d is an interplanar distance):