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Abstract: Impurity Cr2+ions in the CdSe crystal are studied by tunable EPR spectroscopy in the frequency range of 70–320 GHz. The discovered Jahn–Teller tetragonal distortions of the nearest environment of the chromium ion confirm the results of recent ultrasound studies. The set of spectroscopic parameters that allows obtaining agreement between the calculates and experimental angular and field–frequency dependences of the EPR spectra is determined.

The earlier developed methodology of ultrasonic investigation for determining the parameters of the Jahn–Teller effect (JTE) in impurity centers in crystals is further developed in application to Ni2+impurities in ZnSe : Ni2+. For all normal modes propagating along the [110] axis, the temperature dependences of the attenuation of ultrasound are measured in the frequency range 25–165 MHz. At a temperature of about 13 K, for all these modes, attenuation peaks are observed, which indicate the presence of local distortions of both trigonal and tetragonal types. Following the previously developed method, it is shown that these anomalies of attenuation are caused by the relaxation transitions between equivalent local distortions induced by the JTE at the Ni2+centers. In the tetrahedral environment of selenium, this ion is in the threefold degenerate ground electron state 3T1, in which three types of the JTE can be realized. The data of ultrasonic experiments indicate the realization of the T⊗ (e+ t2) problem, in which the potential energy surface has four equivalent minima of the trigonal type, slightly deformed toward tetragonal saddle points. The trigonal vibronic constants, the stabilization energies of the trigonal minima, and the activation energy of the barriers between them are ev-aluated.

The effects of the interaction of ultrasound with donor delectrons of cobalt impurity atoms at low concentrations in mercury selenide crystals have been investigated. The temperature dependences of the electronic contribution to the absorption coefficient at a frequency of 53 MHz in crystals with cobalt concentrations from 1018to 1020cm−3and in the undoped crystal have been observed experimentally. It has been found that crystals with impurities are characterized by an anomalous nonmonotonic temperature dependence of the absorption coefficient of the slow transverse wave in a narrow temperature range near 10 K. A smooth monotonic temperature dependence has been observed for longitudinal and fast transverse waves. Based on the developed theoretical interpretation, it has been established that the anomaly in the temperature dependence of the absorption coefficient of a slow transverse wave is associated with the hybridization of impurity dstates in the conduction band of the crystal. A comparison of the theoretical and experimental dependences has made it possible to determine the parameters characterizing the hybridized electronic states.

Abstract: The contribution of the Jahn-Teller effect to absorption of an ultrasonic wave by a GaAs crystal doped with copper has been investigated theoretically. The distinguishing feature of the problem under consideration is the existence of two holes in the state of the complex valence band. The magnitude of the tunneling splitting in Jahn-Teller centers has been determined. The theoretical values of the absorption coefficients for the resonant and relaxation types of absorption have been obtained. The magnitudes of these coefficients have been estimated.

Abstract: It was experimentally shown that, in a 3d-impurity-doped ZnSe crystal with the zinc blende structure, nanosized ionic shear displacements of the trigonal (ZnSe : Ni, ZnSe : V) and tetragonal (ZnSe : Cr) types arise at temperatures of 300 and 120 K. As the temperature decreases in the range 100.0–4.2 K, the shear elastic moduli C 44 (ZnSe : Ni) and (C 11–C 12)/2 (ZnSe : Cr) are softened owing to the 3d impurities. A new peak at a frequency of 90 cm−1 appears in the Raman scattering spectrum of ZnSe : Ni at 5 and 20 K.

Abstract: Low-temperature anomalies in absorption of the fast transverse and longitudinal ultrasonic waves are revealed in a ZnSe crystal lightly doped (5.6 × 1018 cm−3) with V2+ ions. These anomalies are interpreted as a manifestation of the Jahn-Teller effect. The temperature dependence of the relaxation time of the impurity 3d electrons is established.

The temperature dependences of the absorption coefficient and phase velocity of 52-MHz ultrasonic waves in iron-doped mercury selenide crystals are studied. The presence of impurities in concentrations of about 1019cm−3is found to initiate the appearance of a resonance peak in the absorption coefficient at a temperature of about 5 K and the corresponding anomaly in the velocity of the slow transverse wave propagating in the 〈110〉 direction. It is shown that the observed effects can be accounted for by the interaction of ultrasound with electrons in the states created in hybridization of the iron impurity donor states with the conduction band states of the crystal. A straightforward theoretical description and quantitative interpretation of these effects are proposed and used to derive data on the hybridized states, which conform with the earlier treatment of the temperature and concentration anomalies of conductivity in the crystals under study.

Abstract: The structure of semiconductor crystals Zn1−x V x2+ Se (x = 0.0018) and Zn1−x Cr x2+ Se (x = 0.0006) was studied for the first time using thermal neutron diffraction at 300 and 120 K. The diffraction patterns of the crystals were revealed to contain diffuse scattering regions near the Bragg reflections of the initial cubic lattice. The experimental results are discussed in combination with earlier obtained data on neutron diffraction and propagation of ultrasonic waves in Zn1−x Ni x2+ Se (x = 0.0025) and Zn1−x Cr x2+ Se (x = 0.0029). The diffuse scattering is shown to be due to nanoscale shear strains of the ZnSe lattice. The character of these strains is determined by Jahn-Teller 3d ions.

Abstract: This paper reports on the results of temperature investigations into the absorption and velocity of ultrasound in ZnSe: Ni and ZnSe: Cr crystals in the frequency range 33–268 MHz. The frequency dependence of the absorption at the maximum is analyzed, and the energy of the excited state of the Ni2+ ions is calculated. The dynamic contribution to the effective elastic modulus is determined, and the results obtained are used to construct the temperature dependences of the relaxed and unrelaxed elastic moduli.

We improve the construction of exact matrix solutions for nonlinear wave equations by using unitary anti-Hermitian and anticommuting matrices. We prove the theorem that constructs the matrix functions unsatisfying the nonlinear wave equation for a set of special potentials. In this case, the graph of complex solution u1has a soliton-like form with a finite number of coils. Exponential representation of matrix solutions unis associated with continuous rotations that can be used for describing intrinsic rotations and state changes of elementary particles. We also prove the theorem on the decomposition of continuous rotation (described by solution u2) onto three simultaneous rotations about coordinate vectors. Each of the three constructed matrix solutions u3is also decomposed into the triplet of elementary matrix solutions.

AbstractA family of the functions, intended for a construction the exact travelling wave solutions of nonlinear partial differential equations, is given. Exact solutions of the Klein‐Gordon equation with a special potential are obtained. The behavior of complex and hypercomplex solutions of the second order is presented.

The fundamental possibilities of applying an approximate method of calculating physical processes — the relative correspondence method — to the indirect measurement of quantities are analyzed. Practical examples are given.

Abstract: In the example of the nonlinear Klein-Gordon equation, we demonstrate that even-indexed hypergeometric solutions admit matrix representations that can be associated with special unitary groups. For the index 2 in particular, this correspondence is shown to be1 :1. For the odd index 3, we show that no anticommuting matrices exist in the class of unitary anti-Hermitian matrices. We also show that the solutions obtained describe going around the potential barrier in the electron-proton transport problem.

Energy dependence of parity non-conservation effects is derived for neutron elastic scattering on nuclei: emission asymmetry and the rotation of the polarization plane for the polarized neutron beam and longitudinal polarization for unpolarized neutrons. Both potential scattering and scattering through the compound-nucleus resonances (multi-level approximation) are taken into account. The expressions obtained are compared with experimental data on thermal neutron scattering.

In a longitudinal magnetic field, oscillations of ellipticity have been found for the propagation of shear ultrasound along the tetragonal axis in superpure indium. A suggested interpretation is based on a theory of magnetoacoustic geometric oscillations taking into account the frequency dispersion.

The theory of twisting nuclear vibrations developed by Holzwarth and Eckart to elucidate the nature of the 2− giant mode is extended to high-multipole, spin-independentM λ,T=0 resonances. Within the framework of the distorted Fermi-surface model the parameters of inertia and stiffness against multipolarity for the nuclear incompressible Fermi-drop are derived. The energies and probabilities of the twistingM λ,T=0 modes calculated in fact without adjustable constants readE(M λ)=ħωF andB(M λ) = γλ Z2A(2λ-4)/3 μ2 fm(2λ-2)respectively. The comparison with data for the 2− resonance and predictions for higher multipoles are presented.

The flow past a sphere as it accelerates in a stream of fluid is studied. Depending on the magnitude and sign of the acceleration the line of boundary-layer separation shifts to the forward or rear stagnation point.

The values of the CP-odd nucleon-nucleon coupling constants arising due to the induced three gluonic operator are estimated for different CP-violating models.

Possible parity-violating effects are considered in ternary fission and estimated for different assumptions regarding the mechanism of the process.

A complex mathematical model of plastic flow of compressible materials is described. The model is versatile and, in the authors' opinion, free from many of the drawbacks of earlier models [9–11]. In particular, it can readily be adapted to analysis of virtually any process of plastic working under conditions of axisymmetric deformation; it enables all mechanical and temperature boundary conditions to be exactly fulfilled in all parts of the boundary S of a plastic flow region; it can be used for studying nonsteady-state processes of plastic working of metals with seats of deformation of complex shape (e.g., axisymmetric forging); it makes it possible to introduce starting data and extract resultant information in a form convenient to the user (production engineer).

A detailed investigation of the recently disco vered magnetoacoustic oscillations of ellipticity has been undertaken in indium single crystals under the non-traditional mutual orientation of the magnetic field H and the ultrasound wave-vector q (close to H‖q). It has been found that oscillations appear in the field dependences of absorption and phase velocity of the circularly polarized ultrasonic waves, and also in those of ellipticity and the angle of rotation of the polarization piane. A description of the phenomenon observed has been given. The oscillations have been shown to be conditioned, unlike the Pippard geometrie oscillations, not only by spatial, but also by frequency dispersion. An analysis of the experimental data points to an electromagnetic nature of the oscillations discussed. Attention is drawn to opportunities to utilize the phenomena to determine the size of the cyclotron trajectory along the magnetic field and to recover the temperature dependence of the relaxation time for the effective electrons.

Abstract: The temperature dependences of the elastic moduli C 44 (C 11 − C 12)/2 and C l = (C 11 + C 12 + 2C 44)/2 of ZnSe : V2+ (impurity concentration, 6 × 1018 cm−3) and ZnSe : Mn2+ (9.4 × 1020 cm−3) are measured in the temperature range 1.4–100.0 K at frequencies of 52 and 156 MHz. The temperature dependences of the adiabatic elastic moduli are derived. It is established that softening of the symmetry modules is observed only in the crystal with an impurity having orbitally degenerate states.

The puzzle of the complete description of (n, ?) angular correlations is discussed. The multi resonance approach is needed for the successful explanation of the recent experimental data.

TheT-violation effects in neutron-deuteron scattering caused byT-noninvariantP-even nucleon-nucleon interaction are discussed.

The previously developed approach to P-nonconservation in nuclear reactions is applied to the investigation of P- and T-noninvariant effects in neutron-induced reactions. Dynamical and resonance enhancement effects for T-noninvariant quantities are considered. The estimate is given of the expected effect in the compound-nucleus p-resonance.