Double resonance interference in third-order light mixing

The first observation of interference effects between two sharp resonant contributions to the third-order nonlinear susceptibility χ₍₃₎ (ω₃=ω₀+ω₁?ω₂) is reported. Using two tunable near ir frequencies, ω₀=ω₁ and ω₂, the was seen in crystalline CuCl when 2ω₁ and ω₁?ω₂ were close to the sharp Z₃ exciton at 3.21 eV and the 210 cm^-1 Raman line, respectively. Three different tunable visible frequencies were used to observe similar interference effects in a benzene-cyclohexane mixture when ω₀?ω₂ and ω₁?ω₂ were close to the 992 cm^-1 Raman line of benzene and the 801 cm^-1 Raman line of cyclohexane, respectively.     

Der Grundzustand der Urfermionen im Gitterraum

The energy of the Dirac sea of interacting urfermions in a lattice space withZ ³ points is calculated using Heisenberg's Hamiltonian and a two-particle approximation which is a variational calculation with the test function ¦?〉=e ⁱη¦D ₀〉; ¦D ₀〉 is the Dirac sea without interaction,η=(ψ ^° ψ) a bilinear expression of the urfermion creation and annihilation operators. The same result is obtained by a BCS-calculation. Beyond that, we derive simple lower and upper bounds for the energy. Excited states are considered consisting of a particle-antiparticle pair with the energyE=2√ω ²+M ². The massM and the interaction constantW are connected by the equation (4W)^?1=Z ^?3∑(ω ²+M ²)^?1/2. For usual masses 4W～√Z/1 (1 a nuclear length). Methods are discussed to improve the results.     

Total cross section forZ 0 production in electron proton collisions

We present an exact calculation of the total cross section π_tot of theZ ⁰ production ine ^?1+p→e ^?+Z ⁰+X processes. We find a total cross section π_tot?1.0·10^?36cm² for an energy in the center of mass of 300 GeV and aZ ⁰ mass of 90GeV, which is quite a measurable result in somee ^?1 proton collider experiments, like HERA or SPS/LEP.     

Bi-solitons for a class of non-linear equations with quadratic non-linearity. II

We generalize to any order q, the methods developed in a companion paper for q = 2,3 for finding bi-solitons, solutions of the class of non-integrable non-linear equations L_qK = K²; L_q = ? + Σ_i+j≤qa_ij?_xⁱ?_lⁱ, ? ≠ 0 in 1 + 1 dimensions. We call bi-solitons K(ω₁,ω₂) of the exponential type variables ω_i = exp(γ_ix + ρ_it), i = 1,2 and deal only with the so-called “non trivial” solutions which may be written as a finite sum K = Σ^lmax₀ω¹₂F_i(Z)_, F₁ rational function of Z = ω₁Z = ω₁ + ω₁. To any such polynomial K, we associate a linear transformation such that L_qK has only the power ω¹₂ of K² and we find that there are particular polynomialswhere the above restriction provide a factorization of the linear operator L_q in the product of smaller order differential operators. After this linear phase, we show in a second step that these forms yield solutions for the full non linear equation which can be derived in an intrinsic manner. Examples in the monomial and binomial cases are given.     

Z-production in deep inelastice P-scattering

We discussZ ⁰-production in the processe ^? +P → e ^? +Z ⁰ +X in the context of the standard modelSU (3) _C ×SU (2) _L ×U (1) of the strong and electroweak interactions. Besides results for the total cross section and the differential cross section as a function of the parameters of the outgoing electron, we present results for the energy spectrum and the angular distribution of the producedZ ⁰, for energies available at HERA in the near future. We find that the energy and angular distributions forZ ⁰-production are strongly peaked, which will permit a clear identification of the producedZ ⁰.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Rotating frames in special relativity

A uniformly rotating frame is defined as the rest frame of a particle revolving with constant velocityω in a circle about theZ-axis of an inertial frame Σ⁰. Under the conditionz=Z,r=R, theoretical constraints are established for the solution of the transformation problem Σ⁰→Σ^ω r,Σ^ω r being the cylindrical subframe of Σ^ω. The unique solution of the problem in cylindrical coordinates is isomorphic to the special Lorentz transformationL _x, withβ=v/c replaced byβ _r=ωr/c. Hence the intrinsic geometry on the surface of a rotating cylinder is Euclidean. Though there exists no complete intrinsic geometry on the surface of a rotating disk, the geodesics on it are straight lines while the circumference of a concentric circle isK _r2πr as predicted by Einstein.     

Effect of kink-rounding barriers on step edge fluctuations

The effect that an additional energy barrier E_kr for step adatoms moving around kinks has on equilibrium step edge fluctuations is explored using scaling arguments and kinetic Monte Carlo simulations. When mass transport is through step edge diffusion, the time correlation function of the step fluctuations behaves as C(t)=A(T)t^1/4. At low temperatures the prefactor A(T) shows Arrhenius behavior with an activation energy (E_det+3?)/4 if E_kr<? and (E_det+E_kr+2?)/4 if E_kr>?, where ? is the kink energy and E_det is the barrier for detachment of a step adatom from a kink. We point out that the assumption of an Einstein relation for step edge diffusion has lead to an incorrect interpretation of step fluctuation experiments, and explain why such a relation does not hold. The theory is applied to experimental results on Pt(1 1 1) and Cu(1 0 0).     

Impedance and dielectric studies of ferroelectric SrBi2Nb2O9 ceramics

This paper reports the dielectric and impedance characteristics of ferroelectric SrBi₂Nb₂O₉ (SBN) ceramics in the 100 Hz-1 MHz frequency range at various temperatures (300-823 K). A strong low frequency dielectric dispersion (LFDD) associated with an impedance relaxation has been found to exist in these ceramics in the temperature range 573-823 K. The Z″ of the AC complex impedance showed two distinct slopes in the frequency range 100 Hz-1 MHz suggesting the existence of two dispersion mechanisms. This non-ideal behavior has been explained on the basis of the expression, Z*=R₀/(1+(iω/ω₁)^m+(iω/ω₂)ⁿ) [J. Phys. Chem. Solids 53 (1992) 1] where ω₁ and ω₂ characterize the lattice response and the charge carrier behavior, respectively. The exponents m and n were obtained from the curve fitting. The exponent n was found to exhibit a minimum at the Curie temperature, T_c (723 K) whereas the m was temperature independent.     

The barrier for compound-nucleus formation in the nearly symmetric systems86Kr+123Sb→209Fr and124Sn +94Zr→218Th

Evaporation residues from the fusion of the nearly symmetric systems⁸⁶Kr+¹²³Sb and¹²⁴Sn+⁹⁴Zr have been detected. The compound nucleus²¹⁸Th could be produced with an excitation energy as low as 21 MeV. The barriers for the formation of a compound nucleus were deduced from the evaporation residue cross sections. There is no evidence for an additional amount of energy needed to fuse these systems, if compared with the extrapolation of fusion barrier systematics or with results of fusion model calculations not including friction phenomena. One of the systems reaches a value ofZ ₁·Z ₂=2,000, about the highest value where evaporation residues have ever been observed.     

New acceleration mechanism of electrons by an electromagnetic wave in a weakly magnetized plasma

Acceleration of electrons by an electromagnetic wave has been observed in a weakly magnetized (ω_ce/ω₀ ? 10^?2) inhomogeneous plasma. This acceleration is interpreted as a V_p × B₀ acceleration, which is a new concept for heating or accelerating electrons very efficiently to high energy.     

Laser photoluminescence spectra of the M+S2− species in solid argon at 12K

Matrix reactions of alkali metal atoms with S₂Cl₂ and photolyzed H₂S samples have been examined by laser excitation at 457.9 nm. The strong photoluminescence spectrum from 12 300 to 18 300 cm^?1 exhibited vibrational spacings near 550 cm^?1. Observation of the same ZPL spectrum with two different precursors identified the carrier as Na⁺S₂^?. The vibrational numbering was made possible by the Na⁺³²S³⁴S^? species in natural abundance and from a 33% ³⁴S-enriched sample of S₂Cl₂. The spectroscopic constants ν₀₀ = 19 990 ± 10 cm^?, ω₀″ = 586 ± 2 cm^?1 and ω₀x₀″ = 2.8 ± 0.2 cm^?1 are in excellent agreement with those reported for S₂^? in alkali halide crystals at low temperature.     

Measurement of elastic ω photoproduction at HERA ZEUS Collaboration

The reaction γp →ωp(ω → π⁺π^?π⁰ and π⁰ → γ γ) has been studied in ep interactions using the ZEUS detector at photon-proton centre-of-mass energies between 70 and 90GeV and ∣t∣ < 0.6GeV², where t is the squared four momentum transferred at the proton vertex. The elastic ω photoproduction cross section has been measured to be σ_{γp → ωp} = 1.21 ±0.12 ±0.23 μb. The differential cross section dσ_γp→ωp/d¦t¦ has an exponential shape e^?b∣t∣ with a slope b =10.0 ± 1.2 ± 1.3 GeV^?2. The angular distributions of the decay pions are consistent with s-channel helicity conservation. When compared to low energy data, the features of ω photoproduction as measured at HERA energies are in agreement with those of a soft diffractive process. Previous measurements of the ρ⁰ and ? photoproduction cross sections at HERA show a similar behaviour.     

The harmonic oscillator energy level spacing for neutrons and protons in nuclei

Approximate expressions of?ω for neutrons and protons separately, as functions of the neutron numberN and the proton numberZ respectively, are derived. The dependence ?ω_n(?ω_p) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of?ω show “discontinuities in the slope” at the closed shells throughout the periodic table. The difference ?ω_n — {ie17-01} is also discussed.     

Noises- and delay-enhanced stability in a bistable dynamical system describing chemical reaction

The energy spectrum of a graphene sheet subject to a single barrier potential having a time periodic oscillating height and subject to a magnetic field is analyzed. The corresponding transmission is studied as function of the incident energy and potential parameters. Quantum interference within the oscillating barrier has an important effect on quasiparticles tunneling. In particular the time-periodic electrostatic potential generates additional sidebands at energies ? + l?ω (l = 0, ±1,...) in the transmission probability originating from the photon absorption or emission within the oscillating barrier. Due to numerical difficulties in truncating the resulting coupled channel equations we limited ourselves to low quantum channels, i.e. l = 0, ± 1.     

The twistM λ,T=0 giant modes in spherical nuclei

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)=?ω _F \(\left[ {\frac{{(2\lambda + 3)(\lambda - 1)}}{5}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) andB(M λ) = γ_λ Z² A ^(2λ-4)/3 μ² fm^(2λ-2)respectively. The comparison with data for the 2^? resonance and predictions for higher multipoles are presented.     

Filamentation and modulational instabilities of laser radiation in magnetoactive piezoelectric semiconductors

Following the fluid model for the nonlinear response of electrons, a theoretical investigation has been made on the filamentation and modulational instabilities of high power laser radiation in magnetoactive piezoelectric semiconductors. The ponderomotive force on electrons is responsible for the parametric amplification of the low frequency electrostatic perturbation which may cause the filamentation or modulational instability of the incident laser beam depending upon the direction of propagation of the perturbation. For typical parameters in n-InSb: ?_L = 16 at 77°K, ω_p = 10¹³radsec^?1, v₀ = 10¹¹radsec^?1,K² = 10^?3, ω_c = 10¹²radsec^?1,k = 5 × 10²cm^?1, and when the power density of the 10.6 microm CO₂ laser is 2.37 MW cm^?2 ($\text{|?}{}_{\mathrm{0x}}\text{C| = 10}{}^{\mathrm{?3}}$), the growth rate of the filamentation instability is ~ 10⁴ rad sec^?1 and the growth rate of the modulational instability is ~ 10³ rad sec^?1. It is observed that the external static magnetic field decreases the growth rate of the filamentation instability, whereas it has insignificant effect on the modulational instability of laser beams in piezoelectric semiconductors.     

Pion production at large transverse momentum

A constituent interchange model is used to give a natural explanation of the observed energy dependence of ISR data for π° production at 90°. It is predicted that at large fixed p_T and sufficiently high energy the cross section will become constant, with a p_T dependence of (p_T²)^?2.5. It is also tentatively suggested that the e⁺e^? annihilation structure function $\text{ν}\text{W}{}_2$ should behave like ω^?1.5 near ω = 0.     

Study of the electromagnetic transition form-factor in ω→π0μ+μ− decay

Sixty events of the rare eletromagnetic decay ω→π⁰μ⁺μ^? have been detected. The branching ratio for this decay been obtained to be BR(ω→π⁰μ⁺μ^?) = (9.6 ± 2.3) × 10^?5. The effective mass spectrum for muon pairs has been measured and the electromagnetic transition form-factor for the vertex ωπ⁰, F_ω(m_μμ²;m_π²0) = (1 ? m_μμ²/Λ²)^?1, has been determined, Λ = (0.65 ± 0.03) GeV/c². The results are compared with the vector-meson dominance model.     

Rotational properties of the odd-Z transfermium nucleus 255Lr by a particle-number-conserving method in the cranked shell model

Experimentally observed ground state band based on the 1/2-[521] Nilsson state and the first exited band based on the 7/2-[514]Nilsson state of the odd-Z nucleus ~(255)Lr are studied by the cranked shell model(CSM) with the paring correlations treated by the particle-number-conserving(PNC) method. This is the first time the detailed theoretical investigations are performed on these rotational bands. Both experimental kinematic and dynamic moments of inertia(J~(1)and J~(2)) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia J~(1) with the experimental ones extracted from different spin assignments, the spin 17/2~-→13/2~- is assigned to the lowest-lying 196.6(5) ke V transition of the 1/2~-[521] band, and 15/2~-→11/2~- to the 189(1) ke V transition of the 7/2~-[514] band, respectively. The proton N = 7 major shell is included in the calculations. The intruder of the high- j low-? 1 j_((15)/2)(1/2~-[770]) orbital at the high spin leads to band-crossings at ω≈0.20( ω≈0.25) Me V for the 7/2~-[514] α =-1/2(α = +1/2) band, and at ω≈0.175 Me V for the1/2~-[521] α =-1/2 band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.