Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Semiempirical study of perturbations of the Landé g factors of electronic-vibrational-rotational levels of hydrogen: II. i 3 g − and j 3Δ g − states of the H2, HD,and D2 molecules

The values of the Landé g factors of the i ³Π _g ⁻ , v, N and j ³Δ _g ⁻ , v, N states of the H₂, HD, and D₂ molecules have been found semiempirically for the following vibrational and rotational quantum numbers: v≤3; N≤7 for H₂; N≤5 for HD; and N≤11 for D₂. These values were obtained in terms of the nonadiabatic model, which takes into account the interaction between the 3dπ³Π_g and 3dδ³Δ_g states with the same values of v and N in the approximation of pure precession, with the use of semiempirical values of the expansion coefficients of the wave functions in the Born-Oppenheimer basis determined by us previously and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. The results obtained for the H₂ molecule are in good agreement with the data in the literature. For the i ³Π _g ⁻ and j ³Δ _g ⁻ states of the HD and D₂ molecules, the g factors were found for the first time. This made it possible to study for the first time the role of the isotopic effect in the perturbation of the dependences of the g factors of rovibrational levels on v and N for the triplet electronic states of the hydrogen molecule. It was found that the interference effects of interaction between the 3dπ³Π_g and 3dδ³Δ_g states lead both to significant differences—up to 8, 6, and 11 times for H₂, HD, and D₂, respectively (the i ³Π _g ⁻ state), 20 times for H₂ and HD, and two orders of magnitude for D₂ (the j ³Δ _g ⁻ state)—between the nonadiabatic values of the g factors and the corresponding adiabatic values for some isotopomers of the hydrogen molecule and to significant differences—up to 9 and 1.5 times for the j ³Δ _g ⁻ and i ³Π _g ⁻ states, respectively—in the nonadiabatic values of the g factors of rovibrational levels of different isotopomers of the hydrogen molecule. __________ Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 42–54. Original Russian Text Copyright ? 2004 by Astashkevich.     

A regular potential which is nowhere in L 1

A nonnegative potential V: ℝ^v→ℝ is constructed for which V ∉ L _q (G) for any nonempty open G⊂→^v, q>0, and for which nevertheless W _inf2 ^sup1 ∩ Q(V) is dense in W _inf2 ^sup1 , i.e., is a form core for −1/2Δ in L ₂.     

Magnetic dipole,electric quadrupole and magnetic octupole moments of the <Emphasis Type="Italic">Δ</Emphasis> baryons in light cone QCD sum rules

Due to the very short life time of the Δ baryons, a direct measurement on the electromagnetic moments of these systems is almost impossible in the experiment and can only be done indirectly. Although only for the magnetic dipole moments of Δ ⁺⁺ and Δ ⁺ systems there are some experimental data, the theoretical, phenomenological and lattice calculations could play crucial role. In the present work, the magnetic dipole (μ _Δ ), electric quadrupole (Q _Δ ) and magnetic octupole (O _Δ ) moments of these baryons are computed within the light cone QCD sum rules. The results are compared with the predictions of the other phenomenological approaches, lattice QCD and existing experimental data.     

Determination of electric dipole moment for the ν2 vibrational state of 15NH3 by infrared-infrared double resonances

An infrared-infrared double-resonance technique, employing the sidebands produced by electro-optic amplitude modulation of a single-frequency CO₂ laser, is used to observe the second-order Stark effect of the ν₂asR(2, 0) transition of ¹⁵NH₃. The technique enables the Stark shifts in ground and vibrationally excited states to be observed separately and yields the electric dipole moments: μ(v₂ = 1) = 1.253 ± 0.003 D, μ(v = 0) = 1.469 ± 0.004 D. The relative intensity distribution, linewidths, and line shapes of features in the double-resonance Stark spectra are also examined.     

The estimates of periodic potentials in terms of effective masses

LetG _n=(A _n ⁻ , A _n ⁺ ),n≧1, denote the gaps,M _n ^± be the effective masses and Σn=[A _n−1 ⁺ ,A _n ^- ],A ₀ ⁺ =0, be the spectral bands of the Hill operatorT=−d ²/dx ²+V(x) inL ² (R), whereV is a 1-periodic real potential fromL ²(0,1). Let the length gapL _n=|G_n|, h_n be the height of the corresponding slit on the quasimomentum domain and Δ_n=π²(2n−1)−∣Σ_n∣>0 be the band reduction. Let ,n≧1, denote the gap length for the operator . Introduce the sequencesL={L_n}, h={h_n}, l={l_n}, Δ={Δ_n},M ^±={M _n ^± } and the norms ,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖ ₁, ‖l‖₁, ‖δ‖ in terms of ‖M^±‖₂, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of i), ii) for more general potentials. The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research and INTAS.     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

A comprehensive,time-resolved SANS investigation of temperature-change-induced sponge-to-lamellar and lamellar-to-sponge phase transformations in comparison with <Superscript>2</Superscript>H -NMR results

Time-resolved small-angle neutron scattering (TR-SANS) was employed to observe temperature-induced phase transitions from the sponge (L ₃ to the lamellar ( L _α phase, and vice versa, in the water-oil (n -decane)-non-ionic surfactant ( C₁₂E₅ system using both bulk and film contrast. Samples of different bilayer volume fractions φ and solvent viscosities η were investigated applying various amplitudes of temperature jump ΔT . The findings of a previous ²H -NMR study could be confirmed, where the lamellar phase formation was determined to occur through a nucleation and growth process, while it was concluded that the L ₃ -phase develops in a mechanistically different and more rapid manner involving uncorrelated passage formation. Likewise, the kinetic trends of the nucleation and growth transition (decreased transition time with increase of φ and ΔT were witnessed once again. Additionally, NMR and SANS data that demonstrate a strong dependency of that process on solvent viscosity η are presented. Contrariwise, it is made evident via both SANS and NMR results that the L _α -to-L ₃ transition time is independent (within experimental sensitivity) of the varied parameters (φ , ΔT , η . Unusual scattering evolution in one experiment, originating from a highly ordered lamellar phase, intriguingly hints that a major rate determining factor is the disruption of long-range order. Furthermore, the bulk contrast investigations give insight into structure peak shifts/development during the transitions, while the film contrast experiments prove the bilayer thickness to be constant throughout the phase transitions and show that there is no evidence for a change in the short-range order of the bilayer structure. The latter was considered possible, due to the different topology of the L ₃ and L _α phases. Lastly, an unexpected yet consistent appearance of anisotropic scattering is detected in the L ₃ -to- L _α transitions.     

New neutrino experiments

Following incredible recent progress in understanding neutrino oscillations, many new ambitious experiments are being planned to study neutrino properties. The most important may be to find a non-zero value of θ₁₃. The most promising way to do this appears to be to measurev _μ →v _e oscillations with anE/L near Δm _atmo ² . Future neutrino experiments are great.     

Two-photon resonant four-wave mixing processes in atomic barium

By means of a N₂-laser pumped dye-laser (P _L ≈20kW, Δv _L < 10 GHZ) different two-photon resonant four-wave coupling processes in Ba vapour (n _Ba≈10¹⁶ cm⁻³) using the Ba states 6s8s ¹ S _o and 7s5d ¹ D ₂ were investigated. Coherent line radiation with conversion rates up to 10⁻³ was generated within the range of λ=190–200 nm by sumfrequency mixingv _UV=2v ₁+v ₂ of 3 laser photons and within the range of λ=250–380 nm by couplingv _UV=2v ₁±v _IR of 2 laser photons with one photonv _IR stimulated emitted in laser-induced Ba transitions. For the second coupling type the various nonlinear processes contributing to the formation of the coupling components are discussed. The power of the UV-component as function of inensity and resonance detuning of the laser as well as on the phase-mismatch was calculated on the basis of the small signal theory and compared to the experimental data.     

Time-resolved Stark effect in rapidly varying fields

The cycle-averaged ac Stark effect associated with the ^[ A _]2Σ⁺v^′=2?^[ X _]2Π1/2v^′=0 two-photon absorption of NO at intensities between 7.7 and 15.2 TW cm^-2 has been characterized in real time through a synergic combination of bichromatic laser experiments and quantum-dynamics calculations. Measurements of the fluorescence emitted by the Rydberg ^[ A _]2Σ⁺v^′=2 level as a function of time between Stark and probe components of a bichromatic field exhibit a characteristic evolution in temporal peak structure with Stark-field intensity, which is interpreted in terms of a time-dependent Floquet analysis of the laser–matter interaction. The experimental observations are consistent with a dynamic Stark shift of Δε_s(ω₁,ω₂)≤0.23 eV of the optical transition at these intensities. Received: 18 January 2002 / Revised version: 6 March 2002 / Published online: 24 April 2002     

Charge distribution studies in the fast-neutron-induced fission of <Superscript>232</Superscript>Th, <Superscript>238</Superscript>U, <Superscript>240</Superscript>Pu and <Superscript>244</Superscript>Cm

Charge distribution studies for heavy-mass fission products were carried out in the fast-neutron-induced fission of ²³²Th, ²³⁸U, ²⁴⁰Pu and ²⁴⁴Cm using radiochemical and gamma-ray spectrometric techniques. The width parameter( σ_Z/σ_A), the most probable charge/mass ( Z _P/A _P), the charge polarization (ΔZ) and the slope of charge polarization [ δ(ΔZ)/δA ^′] as a function of the fragment mass (A ^′) were deduced. The average charge dispersion parameter ( 〈σ_Z〉) and proton odd-even effect ( δ_p) were also obtained for these fissioning systems. The 〈σ_Z〉 and δ_p values in the fissioning systems ²⁴¹Pu ^* and ²⁴⁵Cm ^* were determined for the first time. The δ(ΔZ)/δA ^′ value is also determined for the first time in the fissioning systems ²³⁹U ^* , ²⁴¹Pu ^* and ²⁴⁵Cm ^* . These data along with the literature data for even-Z fissioning systems such as ²³⁰Th ^* , ²³²Th ^* , ²³³U ^* , ²³⁴U ^* , ²³⁶U ^* , ²³⁸U ^* , ²³⁹Pu ^* , ²⁴⁰Pu*, ²⁴²Pu ^* , ²⁴⁶Cm ^* , ²⁵⁰Cf ^* and ²⁵²Cf(SF) are discussed in terms of nuclear structure effect and dynamics of descent from the saddle to the scission point. The role of the excitation energy in low-energy fission is also discussed. Received: 26 July 2002 / Accepted: 3 December 2002 / Published online: 3 April 2003 RID="a" ID="a"Present address: Emeritus Scientist (CSIR) Bhabha Atomic Research Centre, Nuclear Recycle Group, WIP Building, Trombay, Mumbai-400085, India; e-mail: rhiyer@magnum. barc.ernet.in Communicated by D. Schwalm     

Study of some dipolar complexes involving long chain aliphatic alcohols

The mechanism of 1:1 dipolar complexation of some long-chain aliphatic alcohols with chlorobenzene and acetic acids in a non-polar medium is studied. The interaction dipole moment △^→μ, the excess molar polarization ΔP and apparent complex formation constantK _app are evaluated following two independent methods. It is observed from the value of △^→μ that the complex formation is mostly due to polarization interaction and is of the same type as involving lower alcohols. ΔP andK _app are, however, of different nature compared to those in lower alcohols suggesting that the unlike molecules form relatively stable linear linkage resulting in antiparallel orientation prior to forming complexes.     

Low-lying states of 6He studied via the 6Li(t,3He)6He reaction

We present the recent experimental results on the ⁶He structure studied by the ⁶Li(t, ³He)⁶He reaction at 336 MeV. Above the conspicuous peaks for ground and first excited states for ⁶He, we have observed a broad structures at E _x∼ 5 MeV, and E _x∼ 15 MeV. The angular distribution of this structure exhibits the dominance of a ΔL = 1 transition, indicating the existence of intruder dipole states at low excitation energies in ⁶He. A slight admixture of positive-parity states in this structure has been indicated as well. Received: 1 May 2001 / Accepted: 4 December 2001     

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R² ∼L and by free-energy fluctuations of order ΔF(L) ∼O(1). The low-temperature phase is characterized by an anomalous wandering exponent R²/L ∼L^ω and by free-energy fluctuations of order ΔF(L) ∼L^ω where ω∼0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature T_c. Our results concerning R²/L and ΔF(L) point towards 0.76 < T_c ≤T₂=0.79, so our conclusion is that T_c is equal or very close to the upper bound T₂ derived by Derrida and coworkers (T₂ corresponds to the temperature above which the ratio remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫T_c, the free-energy distribution is found to be Gaussian. For T ≪T_c, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ∼L^1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ∼L^ω is a near cancellation of energy and entropy contributions of order L^1/2.     

Polarization Modulation Effects in Infrared–Infrared Four-Level Double Resonance inCH3F andNH3

The elements of the Jones matrices for an optically pumped sample have been derived and used to predict four-level double resonance absorption coefficients that are functions of the velocity component of the molecules in the direction of the pump beam for different polarizations of the probe beam. When a saturating pump and weak probe are used in four-level double resonance experiments under population modulation conditions, these absorption coefficients are found to depend only on the first three statistical tensor ranks:n= 0 (population), 1 (orientation), and 2 (alignment). It is also found that for polarization modulation experiments with plane-polarized radiation, the absorption coefficient depends only on the alignment of them-state populations. Similarly, for polarization modulation with circularly polarized radiation, the absorption coefficient depends only on the orientation. The theory was used to interpret double-resonance polarization modulation experiments in¹³CH₃F and¹⁵NH₃in order to examine the effects of collisions on the initial anisotropy of the projection ofJon a space-fixedZaxis. The four-level double-resonance lineshapes were fit by least squares to absorption coefficients predicted by the theory. The collisional effects were modeled by a sum of Keilson–Storer collision kernels. The results of the fits were much improved when the value of the effective rate constant for the transfer of then= 0 tensor from the upper level of the pump to the lower level of the probe was larger than the values of the effective rate constants for the transfer of then= 1 and 2 populations. The best ratio of the rate constant forn> 0 to that forn= 0 is about 2/3 for¹³CH₃F and 1/3 for¹⁵NH₃. Additional analysis of the lineshapes showed the importance of long-range dipole–dipole interactions, elastic realignment and reorientation, and V–V mechanisms for collision-induced rotational energy transfer in¹³CH₃F and¹⁵NH₃.     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

Proton polarization in the p(e,e′p)π0 reaction and the measurement of quadrupole components in the N to Δ transition

The recoil proton polarization in the π⁰ production off the proton with longitudinally polarized electron beam has been studied as a means to measure quadrupole components in the N to Δ transition. On top of the Δ resonance a high sensitivity to a possible Coulomb quadrupole excitation is found in parallel kinematics. The ratio of S ₁₊/M ₁₊ multipole amplitudes can be determined from the ratio of the two in-scattering-plane recoil proton polarization components. Avoiding the absolute measurement of the polarizations, such a ratio allows small experimental uncertainties. Furthermore, the electron helicity independent proton polarization component enables the characterization of resonant and non-resonant pieces. Received: 3 November 1997     

The microwave spectrum of phosphabutadiyne, H---CC---CP

A detailed rotational analysis of the microwave spectrum between 26.5 and 40 GHz of phosphaethene, CH₂=PH, has been carried out. This molecule is the simplest member of a new class of unstable molecules—the phosphaalkenes. The species can be produced by pyrolysis of (CH₃)₂PH, CH₃PH₂ and also somewhat more efficiently from Si(CH₃)₃CH₂PH₂. Full first-order centrifugal distortion analyses have been carried out for both ¹²CH₂³¹PH and ¹²CH₂³¹PD yielding: A₀ = 138 503.20(21), B₀ = 16 418.105(26), and C₀ = 14 649.084(28) MHz for ¹²CH₂³¹PH. The 1₀₁-0₀₀ μ_A lines have also been detected for ¹³CH₂PH, cis-CDHPH and trans-CHDPH. These data have enabled an accurate structure determination to be carried out which indicates: r(H_cC) = 1.09 ± 0.015 Å, (H_cCP) = 124.4 ± 0.8°; r(H_tC) = 1.09 ± 0.015 Å, (H_tCP) = 118.4 ± 1.2°; r(CP) = 1.673 ± 0.002 Å, (HCH) = 117.2 ± 1.2°; r(PH) = 1.420 ± 0.006 Å, (CPH) = 97.4 ± 0.4°. The dipole moment components have been determined as μ_A = 0.731 (2), μ_B = 0.470 (3), μ = 0.869 (3) D for CH₂PH; μ_A = 0.710 (2), μ_B = 0.509 (10), μ = 0.874 (7) D for CH₂PD.