<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Energy spectra of developed superfluid turbulence

Turbulence spectra in superfluids are modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. We have found a new state of fully developed turbulence, which occurs in some range of two Reynolds parameters characterizing the superfluid flow. This state displays both the Kolmogorov-Obukhov 5/3-scaling law E_k ∝ k^?5/3 and a new “3-scaling law” E_k ∝ k^?3, each in a well-separated range of k.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Development of high vorticity in incompressible 3D Euler equations: Influence of initial conditions

The incompressible three-dimensional ideal flows develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling ω_max(t) ∝ l(t)^-2/3 between the vorticity maximum and pancake thickness, and provide the leading contribution to the energy spectrum, where the gradual formation of the Kolmogorov interval E _k ∝ k^?5/3 is observed for some initial flows. With the massive numerical simulations, we study the influence of initial conditions on the processes of pancake formation and the Kolmogorov energy spectrum development.     

Hyperfine structure of the <Emphasis Type="Italic">S</Emphasis> levels of the muonic helium ion

Corrections of the α⁵ and α⁶ orders to the energy spectrum of the hyperfine splitting of the 1S and 2S levels of the muonic helium ion are calculated with the inclusion of the electron vacuum polarization effects, nuclear-structure corrections, and recoil effects. The values ΔE ^hfs(1S) = ?1334.56 meV and ΔE ^hfs(2S) = ?166.62 meV obtained for hyperfine splitting values can be considered as reliable estimates for comparison with experimental data. The hyperfine structure interval Δ₁₂ = 8ΔE ^hfs(2S) ? ΔE ^hfs(1S) = 1.64 meV can be used to verify QED predictions.     

Waves in a superlattice with anisotropic inhomogeneities

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on inhomogeneities with anisotropic correlation properties are studied for the first time. The period of the superlattice is modulated by the random function described by the anisotropic correlation function K_?(r) that has different correlation radii, k _∥ ^?1 and k _⊥ ^?1 , along the axis of the superlattice z and in the plane xy, respectively. The anisotropy of the correlation is characterized by the parameter λ=1?k_⊥/k_∥ that can change from λ=0 to λ=1 when the correlation wave number k⊥ changes from k_⊥=k_∥ (isotropic 3D inhomogeneities) to k_⊥=0 (1D inhomogeneities). The correlation function of the superlattice K(r) is developed. Its decreasing part goes to the asymptote L that divides the correlation volume into two parts, characterized by finite and infinite correlation radii. The dependences of the width of the gap in the spectrum at the boundary of the Brillouin zone δν and the damping of waves ξ on the value of λ are studied. It is shown that decreasing L leads to the decrease of δν, and increase of ξ, with the increase of λ.     

Aussagen der Theorie von Kraichnan für die isotrope hydromagnetische Turbulenz

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g _m (k, τ) and the time-correlationsr(k, τ), r _m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE _m (k) obeys aE(k)k ^?2-law in accordance with results ofGolitsyn andMoffatt.     

Spectra and mean energies of prompt neutrons from <Superscript>238</Superscript>U fission induced by primary neutrons of energy in the region <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><20 MeV

The time-of-flight technique is used to measure the ratios R(E, E _n )=N(E, E _n )/N_Cf(E) of the normalized (to unity) spectra N(E, E _n ) of neutrons accompanying the neutron-induced fission of ²³⁸U at primary-neutron energies of E _n =6.0 and 7.0 MeV to the spectrum N_Cf(E) neutrons from the spontaneous fission of ²⁵²Cf. These experimental data and the results of their analysis are discussed together with data that were previously obtained for the neutron-induced fission of ²³⁸U at the primary energies of E _n =2.9, 5.0, 13.2, 14.7, 16.0, and 17.7 MeV.     

Fine and hyperfine structure of <Emphasis Type="Italic">P</Emphasis>-wave levels in muonic hydrogen

Corrections of order α ⁵ and α ⁶ are calculated for muonic hydrogen in the fine-structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and in the hyperfine structure of the 2P _1/2-and 2P _3/2-wave energy levels. The resulting values of ΔE ^fs = 8352.08 μeV, ΔẼ ^hfs(2P _1/2) = 7819.80 μeV, and ΔẼ ^hfs(2P _3/2) = 3248.03 μeV provide reliable guidelines in performing a comparison with relevant experimental data and in more precisely extracting the experimental value of the (2P–2S) Lamb shift in the muonic-hydrogen atom. Original Russian Text ? A.P. Martynenko, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 126–136.     

Relaxation of a 2D MHD flow across a magnetic field (2D hydrodynamic flow) in a bounded region

The problem on magnetohydrodynamic (MHD) flow of a solitary vortex across a magnetic field in a volume confined by rigid walls is solved numerically for large Reynolds numbers (including magnetic Reynolds numbers) and small Alfven-Mach numbers M _A . In this case, the MHD problem is reduced to that of two-dimensional hydrodynamic turbulence. It is shown that sound is not generated by a turbulent medium for small values of M _A ; consequently, this kinetic energy dissipation channel is closed in this case. Calculations show that, in contrast to 3D turbulence, kinetic energy dissipation for 2D turbulence occurs, as expected, over time periods on the order of L²/v(L is the characteristic size of the system and v is the kinematic viscosity). In our calculations with numerical viscosity v～vΔx (Δx is the unit cell size), this corresponds to time values on the order of ～(L/Δx)(L/v). In the kinetic energy spectra for a turbulent flow in a bounded region in the inertial interval (lying between the energy-carrying and viscosity regions), the values of E(k) decrease with increasing wave numbers k at a higher rate than in proportion to k^?3. The volume distribution of vorticity becomes narrower with time (the characteristic values of curlv decrease) and is blurred; for large time periods, the distribution approximately retains its shape as well as asymmetry with respect to positive and negative values, which is associated with the asymmetry of the initial conditions.     

Fine Structure of Beta Decay Strength Function and Anisotropy of Isovector Nuclear Dencity Component Oscillations in Deformed Nuclei

The experimental measurement data on the fine structure of beta-decay strength function S_β(E) in spherical, transitional, and deformed nuclei are analyzed. Modern high-resolution nuclear spectroscopy methods made it possible to identify the splitting of peaks in S_β(E) for deformed nuclei. By analogy with splitting of the peak of E1 giant dipole resonance (GDR) in deformed nuclei, the peaks in S_β(E) are split into two components from the axial nuclear deformation. In this report, the fine structure of S_β(E) is discussed. Splitting of the peaks connected with the oscillations of neutrons against protons (E1GDR), of proton holes against neutrons (peaks in S_β(E) of β⁺/EC-decay), and of protons against neutron holes (peaks in S_β(E) of β^–-decay) is discussed.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Scattering the Geometry of Weighted Graphs

Given two weighted graphs (X, b_k, m_k), k =?1,2 with b₁ ～ b₂ and m₁ ～ m₂, we prove a weighted L¹-criterion for the existence and completeness of the wave operators W_±(H₂, H₁, I_1,2), where H_k denotes the natural Laplacian in ?²(X, m_k) w.r.t. (X, b_k, m_k) and I_1,2 the trivial identification of ?²(X, m₁) with ?²(X, m₂). In particular, this entails a general criterion for the absolutely continuous spectra of H₁ and H₂ to be equal.     

Soliton dynamics in a spin nematic

One-dimensional localized waves, which can be considered as soliton elementary excitations, exist in a magnet with a unit spin and comparable bilinear and biquadratic spin-spin interactions, with which the state of spin nematic is realized. These excitations are characterized by a certain momentum P and a certain energy E. The structure of these solitons has been found, and the E = E(P) dependence, which plays the role of the dispersion law of these soliton elementary excitations, has been constructed. The energy of a soliton with a certain momentum is shown to be lower than that of the quasiparticles of a linear theory. At small momenta, these E = E(P) dependences of the soliton and quasiparticles coincide asymptotically. The dependence of the soliton energy on the soliton momentum is a periodic function with a period P ₀ = π?/a, whose value does not depend on exchange integrals and depends only on a single crystal parameter, namely, the interatomic distance a. These soliton excitations have common features with the so-called Lieb states, which are well known in many condensed matter models.     

Anisotropic characteristics of the kraichnan direct cascade in two-dimensional hydrodynamic turbulence

The statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution 8192 × 8192) in the presence of pumping and viscous-like damping. It is shown that quasi-shocks of vorticity and their Fourier partnerships in the form of jets introduce an essential influence in turbulence leading to strong angular dependencies for correlation functions. The energy distribution as a function of modulus k for each angle in the inertial interval has the Kraichnan behavior, ~k ^–4, and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum E _k = C _Kη^2/3k^–3, where η is the enstrophy flux and the Kraichnan constant C _K ? 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S ₃ ^L which, as for the isotropic turbulence, gives the same scaling with respect to the separation length R and η, S ₃ ^L = C ₃ηR ³, but the average over the angles and time differs from its isotropic value.     

de Haas-van Alphen oscillations with non-parabolic dispersions

de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form S(E) ∝ E ^α for a given energy E. The case α = 1 stands for the parabolic energy dispersion. It is demonstrated that the periodicity of the magnetic oscillations in inverse field can depend notably on the temperature. We evaluated analytically the Fourier spectrum of these oscillations to evidence the frequency shift and smearing of the main peak structure as the temperature increases.     

Calculation of the energy dependence of the fusion cross section and total cross sections for peripheral reactions on the basis of an analysis of data on elastic heavy-ion scattering: Strongly bound ions

A method is proposed for calculating the energy dependence of the fusion cross section (in general, the sum of the cross sections for complete and incomplete fusion, quasifission, and reactions of deep-inelastic scattering) σ _F (E) and the total cross section for peripheral (or quasielastic) reactions, σ _D (E). The method is based on an analysis of a limited set of angular distributions for the elastic scattering in a given pair of nuclei. The predictive power of the method is illustrated by considering the ¹⁶O + ²⁰⁸Pb, ¹⁶O + ⁴⁰Ca, and ¹⁶O + ²⁸Si systems. For each of these systems, the calculations were performed at energies in the range extending from subbarrier values to those exceeding the barrier height substantially. The results of the calculations are found to be in good agreement with relevant experimental data, whereby the reliability of the method is confirmed. By virtue of this, it is proposed to employ the method to study the energy dependences σ _F (E) and σ _D (E) in collisions involving unstable nuclei, for which it is difficult to determine experimentally the above dependences because of a low intensity of secondary beams.