Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

Impurity transport in fractal media in the presence of a degrading diffusion barrier

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t ₀ of emergence of impurity from the barrier and time t _* corresponding to the beginning of degradation. For t ₀ < t _*, degradation processes are immaterial. In the opposite situation, when t ₀ > t _*, the results on time intervals t < t _* can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t _* < t < t ₀ depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t _* < t < t ₀ is very narrow, and the transport regime occurring over time intervals t < t _* passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t _* < t < t ₀ occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t ₀ has two steps, while for t > t ₀, it has only one step. The more remote step for t < t ₀ and the single step for t > t ₀ coincide with the asymptotic form in the problem without a barrier.     

On the Theory of Plasmon Dispersion in Electron-Doped Cuprates

An explicit expression for the dynamic charge susceptibility for electron-doped cuprates has been derived. This expression accurately reproduces the wave vector dependence of the plasmon frequency observed in inelastic X-ray scattering experiments for Nd_{2 – x}Ce_xCuO₄. The imaginary part of the charge susceptibility along the triangular path in the Brillouin zone is plotted. It is demonstrated that the spectral weight of the plasmon mode near q = 0 is negligibly low. The calculated frequencies of the plasmon mode for all wave vectors in the Brillouin zone turn out to lie outside the range of damping related to electron?hole excitations. A formula for the charge susceptibility is derived within the t?t′?t″?J model supplemented by the Coulomb interaction operator and three-site terms. The derivation is performed by the Green’s function technique employing the formalism of composite Hubbard operators and the Mori projection method, which have proved themselves in the analysis of collective spin excitations. The used Fourier transform of the Coulomb interaction corresponds to the monolayer model with a spatially periodic structure, which is embedded in a three-dimensional crystal lattice.     

On the derivation of the Boltzmann-Landau equation from the quantum mechanical hierarchy

The general solution of the equation of motion for the quantum mechanical distribu tion functionf ₂(r ₁ P ₁,r ₂ p ₂;t)in the two particle space is given by means of the Schrödinger scattering functions. A special initial condition leads to the usual Boltzmann equation plus density correction terms, which depend on the scattering matrixt(p′,p). In the long wavelength limit and in lowest order oft(p′,p) the Landau corrections to the simple Boltzmann streaming part are obtained.     

<Emphasis Type="Italic">η</Emphasis><Superscript>7</Superscript>Li Scattering in the <Emphasis Type="Italic">αt</Emphasis>-Cluster Model

The cross sections for elastic and inelastic η-meson scattering on ⁷Li nuclei are obtained on the basis of the αt-cluster representation of the target nucleus. The experimentally known values of the parameters of elastic ηα and αt scattering are used in exactly solving three-body Faddeev equations with separable two-body potentials. The η⁷Li elastic-scattering scattering length found from respective calculations is a_η7Li = ?0.310 ? i0.198 fm.     

Elektron-Photon-Kaskaden in Blei

A Monte-Carlo program has been used for the calculation of electron-photon cascade showers in lead. Bremsstrahlung, electron-electron scattering, multiple scattering, ionization loss, pair creation, Compton effect, and photoelectric effect are taken into account, with empirically corrected values for the cross-sections of these processes. Electrons are followed down toE _e =1,5 MeV and photons toE _γ =0,25. After a comparison of the Monte-Carlo results with available experimental data, the following distributions for electrons and photons are presented for primary electrons incident on lead with energiesE ₀=100, 200, 400 and 1000 MeV and depthst ranging from 0,5 to 25X ₀:

1. 1.
   Number of particles as function of deptht for various cut-off energiesE betweenE _e (orE _γ resp.) up toE=0,9·E ₀. Interpolation formulas are given for the height and position of the maxima of the distributions mentioned before.     
   
   

High-order harmonic generation by atoms in a two-color laser field: Phase control of recombination radiation spectrum and duration

The feasibility of phase control over above-threshold tunnel ionization and subsequent recombination emission in two-frequency laser fields is studied. It is shown that, in such fields, we can control the instants of ionization t₀ (within optical cycle T) and recombination t _k . The conditions that minimize the characteristic times δt₀?T and δt _k ?T, within which effective ionization and recombination occur, were found. Phase control allows recombination radiation to be generated with the selection of a narrow spectral range, while additional high-frequency “background illumination” sets up high harmonic “amplification” conditions. It was shown that special two-frequency pumping with elliptically polarized radiation can generate coherent electromagnetic pulses of attosecond width. The width of the pulses decreases as the intensity of pumping increases and can reach subattosecond values. Experimental generation of such pulses may lead to a breakthrough in the development of new methods for femto-and attosecond diagnostics of fast processes.     

Internal friction in alloys due to plasticity of the diffusion phase transformation

An analytic expression is obtained for the time dependence Q ^?1(t) of internal friction associated with plasticity of a phase transformation. Time dependences Q ^?1(t) of internal friction of the Pb-62Sn and Pb-1.9Sn alloys (wt.%) alloys were studied in the regime of continuous excitation of resonant flexural vibrations. The measurements of the Q ^?1(t) dependences for 1 h at room temperature and a fixed strain amplitude ε₀ ≈ 7 and 19 min) for the Pb-62Sn alloy. For the Pb-1.9Sn alloy under the same conditions, an exponential decrease followed by an internal friction peak (at t _m ≈ 7 min) is observed. It is shown numerically that the above singularities of internal friction are formed by processes of intermittent phase decomposition of Pb-Sn alloys in the cyclic stress field produced by an external load. Experimental data on Q ^?1(t) are used for reconstructing the kinetic curves describing the decomposition (conversion) ratio as a function of time and for calculating the corresponding values of parameters K and n of the Avrami kinetic equation for the Pb-62Sn alloy.     

Ionization potential of a metal cluster containing vacancies

A consistent procedure for determining the ionization potential of a large metal cluster of radius R _{N, v} , consisting of N atoms and N _v vacancies, is proposed. The perturbation theory in small parameters R _v /R _{N, v} and L _v /R _v (Rv and L _v are average distance between vacancies and the length of electron scattering on vacancies, respectively) is constructed in the effective-medium approximation for the electron ground state energy. The effective vacancy potential profile, the electron scattering phase and length are calculated by the Kohn–Sham method for a macroscopic metal in the stable jelly model. The obtained analytical dependences can be useful to analyze the results of photoionization experiments and to determine the size dependence of the vacancy concentration, including that near the melting temperature.     

Compositions,Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N _α (t), N _β (t), t>0, we have that \(N_{\alpha}(N_{\beta}(t)) \stackrel{\mathrm{d}}{=} \sum_{j=1}^{N_{\beta}(t)} X_{j}\), where the X _j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form \(N_{\alpha}(\tau_{k}^{\nu})\), ν∈(0,1], where \(\tau_{k}^{\nu}\) is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ(N(t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.     

Phasenumwandlung zweiter Art als kritische Erscheinung eines inneren Phasengleichgewichtes

It is demonstrated that the transition in a state with two internal phases is a second order phase transition. The term internal phases means phase-like regions inside the system which are not separated by boundaries in the sense of ordinary phase boundaries, and the dimensions and shape of which as well as their properties as such are object of an equilibrium. In a generalization (quasi phases) a long ranged correlation of alternating or periodical character is considered as a typical element of the low temperature state. Such states can be described thermodynamically with the help of a new pair of variablesQ-η. The transition intoQ-η-T is generally analogous to the critical point of ordinary phase transitions inP-V-T, andη ～(?t)^1/3 andC _p～(?t)^?2/3 with a small constant of proportionality are obtained (t=T-T _u). Using the Pippard-relations in the formV-V _γ=(dT _γ/dP) (S-S _γ) the low temperature behaviour of the entropy and density surface as a function ofP andT near the transition line can be completely described. E.g. the saturation magnetization of a ferromagnetic model is derived proportional to (?t)^1/3. Under the action of a magnetic field the transition will be of first order when the saturation magnetization is achieved, without the outer field being analogous toP orQ. Should only one internal phase differ from the high temperature state we obtain an edge point (x=0 analogous to theμ ₁?x-diagram of solutions) with finite jump inC _p andη～({t). A possible relationship to the BCS- model of the supraconductors is indicated.     

The effect of hadronic rindler horizon on hadronization process

In this study by extending the recent suggested mechanisms to hadronization processes, the information loss for QCD matter in hadronic Rindler horizon is found. We notice that for all finite values of quark and gluon energies, all information from all hadronization processes experiences some degree of loss. Then the effect of hedonic Rindler horizon on three jet cross section is explored. It is found that the three jet cross section is rising at y_cut =?0.0002 exhibits a turn-over at moderate value of y_cut =?0.01 and then rapidly decreases as y_cut increases. This model is consistent with OPAL data. Finally, different channels for producing Higgs boson near hadronic Rindler horizon are studied. It is shown that the cross section of Higgs boson produced via gluon fusion and quark interaction near a single Hadronic Rindler Horizon is much larger for higher center of mass energies. This is because an increase in the energy of hadronic Rindler horizon raises the temperature, thus intensifying the thermal radiation of QCD matter.     

<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.     

<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Thermooptical and Dielectric Studies of a Calcium-Induced Ferroelectric Phase in a SrTiO<Subscript>3</Subscript> Incipient Ferroelectric

We have examined temperature changes of the light refraction, birefringence, dielectric permittivity, and dielectric hysteresis loops in Sr_{1 – x}Ca_xTiO₃ single crystals with x = 0.014 (SCT-1.4). The dielectric properties of Sr_{1 – x}Ca_xTiO₃ with x = 0.007 (SCT-0.7) have been studied. We have performed ab initio calculations of equilibrium structures and total energies for three low-temperature phases of SrTiO₃ and CaTiO₃, based on which we have determined an expected symmetry of the ground state of their solid solution and spontaneous polarization directions in a calcium-induced ferroelectric phase in Sr_{1 – x}Ca_xTiO₃. In SCT-1.4, we have separated a spontaneous contribution to the light refraction, which arises due to the spontaneous electrooptical effect caused by the spontaneous polarization and its fluctuations. From the spontaneous contribution to the light refraction, based on a previously developed our phenological approach, we have quantitatively determined for the first time the values and temperature dependences of root-mean-square fluctuations of the order parameter—the polarization P_sh = 〈P _fl ² 〉^1/2(short-range, local polar order) in the ferroelectric phase. From optical and dielectric measurements in SCT-1.4, the average value of spontaneous polarization P_s (the contribution from the long-range order) has been determined. We have estimated the values of P_sh and P_s, which characterize the short- and long-range orders in the ferroelectric phase of SCT-0.7. Separate determination of the values and temperature dependences of P_s and P_sh (which considerably exceeds the value of P_s in the ordered phase) has allowed us to reveal on a quantitative level new particular features of the formation of the induced polar phase in Sr_{1 – x}Ca_xTiO₃.     

The electrical conductance growth of a metallic granular packing

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ _∞ ? Δσ E _α [ ? (t/τ) ^α ], where E _α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g _eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g _eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.