A. I. Frank

Phase modulation of a neutron wave and diffraction of ultracold neutrons on a moving grating

Abstract We report the result of the experiment of UCN diffraction on a moving grating. The resulting spectrum is found to be discrete in good agreement with theory. This purely quantum effect may be interpret as a result of phase modulation of the neutron wave or as diffraction in time. Also, this experiment demonstrates the validity of the Galilean transformation of the neutron wave function in a new and very clear way.

New gravitational experiment with ultracold neutrons

The results of a new neutron gravitation experiment are reported. The change in the energy of a neutron falling to a known height in the Earth’s gravitational field is compensated by an energy quantum ħΘ transferred to the neutron as a result of the phase modulation of the neutron wave. A phase diffraction grating moving across the direction of the propagation of the neutron wave is used as a modulator. The experiment has been carried out with ultracold neutrons Interference filters, neutron analogues of Fabry-Perot interferometers, are used for the spectrometry of ultracold neutrons. The force mggn acting on the neutron in the Earth’s gravitational field has been measured with an accuracy of about 0.2%.

New Experiment on the Observation of the Effect of Accelerating Matter in Neutron Optics

The results of a new experiment on the observation of the effect of accelerating matter in neutron optics are reported. It has been shown that the velocity of neutrons periodically varies when they pass through a harmonically moving refractive sample. The idea of the experiment is based on time focusing, i.e., on the fact that the periodic modulation of the velocity of neutrons leads to the oscillation of the flux density at the observation point. The magnitude of the effect is in reasonable agreement with the theoretical predictions. The experiment has been carried out with ultracold neutrons and a change of ±1 cm/s has been detected in the neutron velocity.

Effect of Accelerated Matter in Neutron Optics

Results of experiments aimed at observing the change in the energy of a neutron traversing an accelerated refractive sample are reported. The experiments were performed with ultracold neutrons, the energy transfer in these experiments being ±(2−6) × 10−10 eV. The results suggest the existence of the effect and agree with theoretical predictions to a precision higher than 10%. A similar effect was previously predicted for the change in the frequency of an electromagnetic wave traversing an accelerated dielectric slab. In all probability, the effect has a very general nature, but it is presently observed only in neutron optics.

Time focusing of nutrons

The possibility of time focusing for very slow neutrons is considered. This focusing may prove very useful in solving the problem of accumulating ultracold neutrons in a trap that are generated by a pulsed source. Diffraction at a phase grating moving across a beam or resonance neutron-spin flip is proposed to implement time-controlled changes in the neutron energy.

A Quantum Time Lens for Ultracold Neutrons

The possibility of creating a time lens, an analogue of the zone plate in X-ray optics, for ultracold neutrons is experimentally demonstrated. The neutron energy was changed by means of a purely quantum effect: the phase modulation of a neutron wave at a variable modulation frequency. The modulator was a phase grating with variable spatial period moving across the neutron beam.

Effect of accelerating matter in neutron optics

The results of an experiment on the observation of a new neutron-optical effect are reported. It has been experimentally shown that the energy of a neutron passing through a refracting sample moving with acceleration changes. The magnitude of the effect is in qualitative agreement with theoretical predictions. The experiment was carried out with ultracold neutrons and the energy transform is equal to ±2 × 10−10 eV.

Dynamic Reflection and Refraction of Neutrons at the Boundaries of Matter Characterized by a Variable Magnetic Induction

Optical phenomena that arise in the interaction of a neutron wave with matter characterized by a variable interaction potential are considered. The time dependence of the potential is assumed to be due to a change in the magnetization vector in matter with time. Since the interaction in question is time-dependent, the neutron energy is not conserved. If a neutron interacts with a sample that has a plane boundary, only the neutron-velocity component orthogonal to the matter boundary changes. Thus, reflected waves are characterized by a reflection angle that is different from the angle of incidence. Waves transmitted through a plane sample can also change direction. The changes in the neutron energy and in the neutron-velocity direction are closely related to the reversal of the neutron-spin projection. The question of whether a slab featuring a rotating magnetization vector can be used as a spin flipper or as a coherent wave splitter is considered.

Neutron Diffraction at a Moving Grating as a Nonstationary Quantum Phenomenon

The observation of the discrete energy spectrum in a new experiment on the diffraction of ultracold neutrons at a moving phase grating is reported. The results are in quantitative agreement with theoretical predictions and can be treated as additional evidence of the validity of the plane-wave representation of the initial neutron state.

Neutron optics of strongly absorbing media and interaction of long-wave neutrons with gadolinium films

The modern state of neutron optics of absorbing media is briefly surveyed. In all probability, there are no physics arguments that would constrain, in the case of strong absorption, the applicability of the commonly accepted Fermi-Foldy dispersion law for neutron waves. In accord with previously known results, it is found that the coefficient of reflection of neutrons from the boundary of a strongly absorbing medium tends to unity with decreasing velocity of neutrons incident on this medium. At low neutron energies peculiar to the case of ultracold neutrons, the complex scattering length for neutron-nucleus interaction proves to be constant, whence it follows that the cross section for neutron capture by a free nucleus obeys the 1/v law. The cross section for the analogous process on nuclei within a medium is described by the 1/v′ law, where v′=ħk′/m, with k′ being the real part of the neutron wave number in the medium. As the incident-neutron velocity v decreases, the velocity v′ in a medium tends to some limiting value. From the coefficient of reflection of cold neutrons that is measured as a function of the wavelength and the angle of incidence, a refined value is found for the real part of the scattering length for neutron interaction with gadolinium nuclei. An experiment was performed where ultracold neutrons were transmitted through thin samples containing natural gadolinium. In analyzing the results of this experiment, use was made of the value found here for the real part of the neutron-nucleus scattering length. The experiment indicates that the imaginary part of the scattering length is a constant or, what is the same, that, for neutron velocities ranging from 4 to about 120 m/s, the 1/v law for the cross section for neutron capture by a free nucleus is valid to within 6%.