One-dimensional mappings of the eigenelements of the Schrodinger problem

An approach is proposed for analyzing the inverse spectral problems for the Schrodinger equation based on writing the equation for the analog of the number-of-quanta operator for a harmonic oscillator. This equation makes it possible to determine not only the one-dimensional mapping of the energy eigenvalues but also the linear equation for the point spectrum shift operator of the Schrodinger problem. The solvability conditions of the latter lead to a nonlinear equation that determines the class of allowable potentials. Two classes of potentials regular in R(1) and symmetrical are isolated on the basis of the proposed approach. The first of these leads to equidistant spectra with a gap of arbitrary size and location. The spectrum of the second potential class is a combination of three rigorously equidistant spectra with ground states that are shifted by an arbitrary amount. Generalizations to the case of essentially nonequidistant spectra are shown to be possible.     

Forward particle production in proton–nucleus interactions at momenta of 25 and 50 GeV/<Emphasis Type="Italic">с</Emphasis> and сarbon–nucleus interactions at an energy of 25 GeV per nucleon

Relative yields of high-x _F charged hadrons (π ^±, К^±, р, \(\overline p \), and d) in proton–nucleus interactions at incident-proton momenta of 25 and 50 GeV/c were measured at an angle of 0° in the momentum range between 15 and 40 GeV/c. An upper limit on the forward production of two protons in proton–nucleus interactions at 50 GeV/c was estimated. The properties of a carbon beam with an energy of 25 GeV per nucleon and fragment yields in its interaction with nuclear targets were measured within a short exposure.     

Peculiarities of self-action in second harmonic generation of laser radiation in nonlinear crystals

By using the generalized method of strong interaction of nonlinear waves and computer simulation, an analysis of the influence of self-action effects on second harmonic generation of an intense diverging picosecond pulse is performed. Using the approximation of strong wave interaction, an analytic solution is obtained for frequency conversion of the laser radiation taking into account the pump intensity depletion, the influence of the angular dispersion effect (ADE), and the higher nonlinearities. It is shown that the self-action effects, the ADE, and the linear phase mismatch can compensate for each other, increasing the efficiency of second harmonic generation. Optimum conditions for second harmonic generation in converging and diverging laser beams were found. An asymmetry of the angular dependence of the second harmonic intensity was experimentally observed and theoretically explained. The asymmetry is caused by the reverse energy conversion of the second harmonic into the pump by the influence of the ADE and Kerr nonlinearities.     

A New Method of Strengthening of Ice Blocks Formed under Conditions of Natural Cold

Russian Journal of General Chemistry - With the exploration of the Arctic territories, the use of ice as a construction material to build winter roads, ice crossings, airstrips, and buildings is...     

Polariton spectrum of a bounded antiferromagnet with a center of antisymmetry in an external electric field oriented normally to the surface

The features of transmission of TE and TM polaritons through an interface between magnetic and nonmagnetic media and their localization at the interface in an external dc electric field have been studied. This field is directed along the hard magnetization axis. The magnetic medium is an easy-plane tetragonal antiferromagnet; it is odd with respect to inversion. A magnetic plate and a 1D magnetic photonic crystal in an external dc electric field, oriented normally to the interface, are considered.     

Diffusion locking effect on long-term strength

The diffusion locking effect on the long-term strength of metals is studied in the case of aggressive media. In order to model this effect, the diffusion equation with a variable diffusion coefficient is solved approximately. It is shown that, when determining the long-term strength of metals in aggressive media, it is necessary to take into account the diffusion locking effect.     

Nonlinear localized waves in a medium with nonlocal interaction

Soliton solutions are found for nonlinear integro-differential equations with a type λ/(τ-τ′) kernel used to describe particle tunneling and magnetic and superconducting vortices in a medium with nonlocal interaction. The Fourier transform method is applied to derive asymptotic formulas for even and odd localized solutions. Analytical solutions are found for particular parameter values. A complete pattern is constructed for the behavior of soliton solutions in an arbitrary range of the interaction parameter λ by means of numerical calculations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 366–379, March, 1998.     

Radiative color centers in doped sapphire crystals

Experimental and theoretical results of investigation of the spectral properties of sapphire (α-Al₂O₃) single crystals are analyzed. Crystals grown under different conditions, both nonactivated and activated with impurity ions of the iron group (Cr, V, Mn, Fe, Co, Ni), primarily with chromium ions, were investigated before and after irradiation with photons and high-energy electrons. It is shown that the impurity composition of crystals significantly affects the radiative and optical properties and the character of changes in the electronic state of impurities.     

The nonlinear refractive indices and nonlinear third-order susceptibilities of quadratic crystals

The third-order nonlinear susceptibilities and nonlinear refractive indices of KDP, BBO, and LiNbO₃ crystals at wavelengths of 1064 and 532 nm are measured using the Z-scan technique. The measurements are made for different energies of incident radiation and different focusing conditions and crystal lengths. It is found that, as the angle between the light beam and the principal optic axis of a KDP crystal increases, the nonlinearity drops, with its magnitude at a wavelength of 1064 nm being higher than at 532 nm. For a BBO crystal, the nonlinearity dispersion is normal. The mechanisms of nonlinear losses in KDP, BBO, and LiNbO₃ crystals are identified. The values of the nonlinear susceptibilities thus obtained are analyzed and compared with the results of calculations based on an empirical model and with the data of other authors.