The effect of acoustic nonlinearity on nonlinear wave processes in solids: The inverse problem

The perturbation method is used to study nonlinear acoustic effects in solids that feature elastic, hysteresis, or inelastic nonlinearity. It is found that these media exhibit qualitatively different nonlinearity behavior laws, which facilitates classifying them based on the acoustic nonlinearity type.     

具有交叉对称的李模型下的非弹性振幅

在具有交叉对称的李模型中,写出了非弹性振幅的积分方程组,它们是Omne氏型的。在已知弹性振幅时,这积分方程组是可解的。在适当地写出这方程组时,可证明非齐次项是小的(在某些区域内),因而使解也有取小值的可能。     

Theory of nuclear reactions and decays with allowance for antisymmetrization effects

On the basis of an explicit implementation of the projection-operator method and with due regard to antisymmetrization effects, formulas are constructed for the amplitudes of elastic and inelastic nuclear reactions induced by nucleons and composite particles and for the widths with respect to the nucleonic, alpha-particle, and cluster decays of nuclei. It is shown that equations governing the behavior of elastic-scattering form factors represent generalizations of the equations of the resonating-group model and coincide, provided that ground-state correlations are taken into account, with the analogous equations in the theory of open Fermi systems. It is demonstrated that the nonretarded part of the effective potential of nucleus-nucleus interaction coincides with the Hartree-Fock potential, which has a deep attractive character in accordance with the Levinson theorem, and that the retarded part of the effective potential is determined by the fragmentation of the initial states of colliding nuclei into compound states. It is revealed that the use of different elastic-form-factor representations associated with taking into account antisymmetrization effects leads to the same results for the amplitudes of elastic and inelastic nuclear reactions. The formulas obtained here for the amplitudes of direct inelastic nuclear reactions are found to differ significantly from the corresponding formulas of the distorted-wave method in the Born approximation. Problems that are concerned with the emergence of potential optical resonances for elastic form factors and with their relation to the shell-model wave functions for a compound system are investigated. A new regime of interpolation for the amplitudes of cluster form factors from the shell to the asymptotic region of a decaying nucleus is found. Implications of this interpolation for the calculated alpha-particle and cluster widths and for understanding the nature of superfluid correlations in nuclei are analyzed.     

Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of plasma physics

A new approach to the perturbative analysis of dynamical systems, which can be described approximately by soliton solutions of integrable non-linear wave equations, is employed in the case of small-amplitude solutions of the ion acoustic wave equations of plasma physics. Instead of pursuing the traditional derivation of a perturbed KdV equation, the ion velocity is written as a sum of two components: elastic and inelastic. In the single-soliton case, the elastic component is the full solution. In the multiple-soliton case, it is complemented by the inelastic component. The original system is transformed into two evolution equations: An asymptotically integrable Normal Form for ordinary KdV solitons, and an equation for the inelastic component. The zero-order term of the elastic component is a single-soliton or multiple-soliton solution of the Normal Form. The inelastic component asymptotes into a linear combination of single-soliton solutions of the Normal Form, with amplitudes determined by soliton interactions, plus a second-order decaying dispersive wave. Satisfaction of a conservation law by the inelastic component and of mass conservation by the disturbance to the ion density is determined solely by the initial data and/or boundary conditions imposed on the inelastic component. The electrostatic potential is a first-order quantity. It is affected by the inelastic component only in second order. The charge density displays a triple-layer structure. The analysis is carried out through the third order.     

Relation for the amplitudes of acoustic waves excited by thin elastic plates

Relations between the amplitudes of acoustic waves excited by a thin elastic plate under the effect of external forces and the amplitudes of waves scattered by this plate are obtained. Two cases are considered: when the plate separates acoustic media filling two half-spaces and when it separates acoustic media filling an acoustic waveguide. The energy conservation law is used to derive the identities that determine the relations between the amplitudes of acoustic waves radiated by a thin elastic plate under the action of forces.     

An investigation of the use of the Hedin-Lundqvist exchange and correlation potential in EXAFS data analysis

In real systems, inelastic processes remove photoelectrons from the elastic scattering channel. This reduces the amplitude of the EXAFS. Traditionally the discrepancies between experimental and theoretical amplitudes were treated by including two semi-empirical reduction factors in the data analysis. Some inelastic effects may, however, be modelled more rigorously using a complex exchange and correlation potential, for example the Hedin-Lundqvist (HL) potential used in most EXAFS data-analysis programs. In this paper a systematic study of the effects of the HL potential on the calculated EXAFS amplitudes is presented. Expressions are derived whereby the EXAFS amplitudes may be examined in the presence of an arbitrary complex potential independently to the rest of the EXAFS signal. These results are used to study the effects of the HL potential on EXAFS data analysis in detail.     

Interaction of acoustic waves with cracks: Elastic and inelastic nonlinearity mechanisms on different time scales

The interrelated elastic and inelastic fast and slow effects of acoustic wave interaction with cracks are discussed from a unified point of view. Special attention is given to the dissipative manifestations of the presence of cracks and to the effects of the symmetrically time-reversible slow dynamics observed for acoustically activated cracks. These effects can be more pronounced than the conventionally discussed nonlinear elastic effects (such as higher harmonic generation). Taking into account the main geometric features of cracks, a thermoelastic mechanism is proposed to consistently interpret the experimental data. Consequences of the results of these studies for seismics are discussed, and the possibilities of using the observed effects for nonlinear acoustic diagnostics of cracks are discussed.     

Mutually induced variations in dissipation and elasticity for oscillations in hysteretic materials: non-simplex interaction regimes

Self-action and effects mutually induced by oscillations interacting in hysteretic media are investigated analytically and numerically. Special attention is paid to non-simplex processes for which presence of intermediate extrema results in appearance of minor nested loops inside the main hysteretic stress-strain loop. Non-simplex regimes are typical of interaction of excitations having different frequencies and amplitudes, but comparable strain rates. It is found that, due to transition between the regimes, frequency and amplitude dependencies of the variations in elasticity and dissipation induced by one wave for another one may become non-monotonous. Either additional dissipation or induced transparency may occur in different regimes. The results obtained are important for correct interpretation of experimental data on nonlinear acoustic interactions in rocks and many other microstructured (mesoscopic) solids that are known to exhibit elastic hysteresis and memory properties.     

Straight-line path approximation for high energy elastic and inelastic scattering in quantum gravity

The asymptotic behavior of Planck energy elastic and inelastic amplitudes in quantum gravity is studied by means of the functional integration method. A straight-line path approximation is used to calculate the functional integrals which arise. Closed relativistically invariant expressions are obtained for the two “nucleons” elastic and inelastic amplitudes including the radiative corrections. Under the requirement of “softness” of the secondary gravitons a Poisson distribution for the number of particles emitted in the collision is found. Received: 6 December 1999 / Published online: 6 July 2000     

Unitarizing high-energy scattering amplitudes in field theories I: QED

Using a procedure which incorporates the s-channel unitarity and t-channel unitarity at every step, we calculate the scattering amplitudes of QED in the high-energy limit. We find that all scattering amplitudes, elastic and inelastic, are summarized by a single eikonal formula which is explicitly unitary.     

Inelastic shadowing effects in multiple scattering

The projectile-nucleon scattering amplitudes used as input into multiple scattering theories of projectile-nucleus scattering naturally include the effects of coupling to inelastic (i.e., production) channels. We employ a multichannel separable potential to describe the projectile-nucleon interaction and show that within the fixed nucleon framework we can obtain the nuclear elastic scattering amplitude. This includes terms outside the conventional formalisms, corresponding to intermediate propagation in the inelastic channels both above and below inelastic threshold. We refer to this as inelastic shadowing. In a two-channel approximation, we show that knowledge of the projectile-nucleon elastic scattering phase shifts plus specification of the inelastic threshold energy are sufficient to determine the off-shell coupled-channel transition matrix, implying that the nuclear amplitude can be calculated within this model without any detailed information about the inelastic channels. We study this solution quantitatively for some model problems and for pion scattering, with the general result that inelastic shadowing can be significant whenever the elementary interaction has important channel coupling. For pion scattering in the energy regime characterized by strongly absorptive resonances, we find, for example, that the effect of inelastic shadowing is much more important than that due to two-nucleon correlations.     

High-energy approach for heavy-ion scattering with excitations of nuclear collective states

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach, analytical expressions for elastic and inelastic scattering amplitudes are obtained, where all the orders in the deformation parameters are included. The multistep effect of the 2⁺ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the ¹⁷O ions scattered on different nuclei at about tens of MeV/nucleon or higher are compared with experimental data, and the important role of the Coulomb excitation is established. The text was submitted by the authors in English.     

Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

Results of studying metamorphic rock samples (Outokumpu,Finland Borehole) by the acoustic polarization method

When studying the elastic properties of anisotropic solid media, it is necessary to determine the spatial orientation of the elastic symmetry elements. This is particularly important for randomly inhomogeneous elastically anisotropic media, such as rock. By applying the acoustic polarization method, the possibility of determining the direction of the symmetry elements of deep rock samples extracted from the Outokumpu, Finland borehole was demonstrated. The anisotropy indices of samples were obtained, calculated from the velocity values of longitudinal and transverse waves. Additional inelastic effects were revealed that are widespread in rock.     

Multiparticle unitarity and diffractive amplitudes

Generalizing the results of previous work, an explicit construction of elastic and inelastic diffractive amplitudes through multiparticle unitarity is given starting from a simple parametrization of non-diffractive production amplitudes. The energy dependent interference mechanism which has been previously shown to be essential to produce the diffraction peak in the elastic process is now seen to be also responsible, in a natural way, for the leading particle effect which dominates production yields.     

Selective excitation in kaon-nucleus inelastic scattering

The K⁺ meson (kaon) inelastic excitation of low-lying (E_x = 0–15 MeV) T = 0 collective states in ¹⁶O is theoretically studied as a function of energy and momentum transfer. The distorted wave impulse approximation is used to calculate angular distributions and total inelastic cross sections for exciting the first J^π = 2⁺, 3^?, 4⁺ and 5^? states at lab energies from threshold to 400 MeV. The distortions are represented in a Kisslinger-type optical potential constructed from elementary K⁺-nucleon amplitudes. Total nuclear elastic and reaction K⁺-nucleus cross sections are computed to demonstrate sensitivity to choice in K⁺-nucleon amplitudes. Fermi motion effects are also assessed using a simple averaging procedure. The weak absorption character of the kaon is reflected in the inelastic calculations which predict selective excitation of low spin states at low momentum transfer and high spin states at high momentum transfer.     

Estimates of the unitarity integral

The elastic unitarity integral is studied for amplitudes which satisfy a Mandelstam representation without subtraction. The double spectral functions are taken to belong to function spaces which allow local, even non-integrable, singularities. The existence of fixed point solutions is derived and the additional restrictions due to inelastic unitarity are discussed.     

Antiproton-Nucleus Interaction and Coulomb Effect at High Energies

The Coulomb effect in high energy antiproton-nucleus elastic and inelastic scattering from ¹²C and ¹⁶O is studied in the framework of Glauber multiple scattering theory for five kinetic energies ranged from 0.23 to 1.83 GeV. A microscopic shell-model nuclear wave functions, Woods-Saxon single-particle wave functions, and experimental pN amplitudes are used in the calculations. The results show that the Coulomb effect is of paramount importance for filling up the dips of differential cross sections. We claim that the present result for inelastic scattering of antiproton-¹²C is sufficiently reliable to be a guide for measurements in the very near future. We also believe that antiproton nucleus elastic and inelastic scattering may produce new information on both the nuclear structure and the antinucleon-nucleon interaction, in particular the p-neutron interaction.     

Inelastic phonon interactions at solid–graphite interfaces

The presented model predicts thermal boundary conductance at interfaces where one material comprising the junction is characterized by high elastic anisotropy. In contrast to previous approaches, the current methodology accounts for contributions from inelastic scattering through consideration of multiple-phonon interactions. Inelastic contributions become significant as the temperature, as well as the degree of acoustic mismatch between the materials, increases. Inclusion of the inelastic interactions is necessary for a variety of interfacial systems including the metal–graphite boundary examined here. Improvement is shown over existing approaches that address only elastic scattering as both three- and four-phonon interactions significantly augment the transport.