Optical measurements of the superconducting gap in MgB 2

Far-infrared reflectivity studies on the polycrystalline intermetallic compound MgB₂ with a superconducting transition temperature T _c = 39 K were performed at temperatures 20 K to 300 K. We observe a significant raise of the superconducting-to-normal state reflectivity ratio below 70 cm ^-1 , with a maximum at about 25-30 cm ^-1 , which gives a lower estimate of the superconducting gap of 2Δ(0) ≈ 3-4 meV. Received 7 March 2001 and Received in final form 18 April 2001     

Cold rubidium molecule formation through photoassociation: A spectroscopic study of the 0 g - long-range state of 87 Rb 2

We report the detailed analysis of translationally cold rubidium molecule formation through photoassociation. Cold molecules are formed after spontaneous decay of photoexcited molecules from a laser cooled atomic sample, and are detected by selective mass spectroscopy after two-photon ionization into Rb ₂ ⁺ ions. A spectroscopic study of the 0 _g ^- (5 S + 5 P _3/2 ) pure long-range state of ⁸⁷Rb₂ is performed by detecting the ion yield as a function of the photoassociation laser frequency; the spectral data are theoretically analyzed within the semiclassical RKR approach. Molecular ionization is resonantly enhanced through either the 2 ³ Π _g or the 2 ³ Σ ⁺ _g intermediate molecular states. Some vibrational levels of the latter electronic state are observed and assigned here for the first time. Finally, cold molecules formation rates are calculated and compared to the experimentally measured ones, and the vibrational distribution of the formed molecules in the a ³ Σ ⁺ _u ground triplet state is discussed. Received 18 January 2001 and Received in final form 10 April 2001     

Absolute absorber quantification in turbid media at small source–detector separations

The aim of our studies was to develop a method to determine the absorption coefficient of a turbid medium in a reflection geometry with small source–detector separations. Therefore, the time-integrated microscopic Beer–Lambert law (MBL) was modified in order to obtain the absolute absorption coefficient from mean time of flight and dc-intensity measurements. The new technique was evaluated using turbid phantoms having varying scattering (μ_s ^′ between 0.2 and 2.2 mm^-1) and absorbing properties (μ_a between 0.04 and 0.14 mm^-1), comparable to many biological tissues at various source–detector separations between 3 and 11 mm. The measurements were performed at a wavelength of 1064 nm. We found that this new method was able to determine the absolute absorption coefficient of the selected phantoms with a standard error of less than 0.005 mm^-1 over the range of optical properties investigated. Received: 23 November 2001 / Revised version: 28 February 2002 / Published online: 14 May 2002     

Ab initio calculation of excited state dipole polarizability - Application to the first 1, 3 Σ + g,u states of Li 2

Firstly, imaginary frequency-dependent dipole polarizabilities of Li in its ² S ground state and the first ² P excited state are calculated from a time-dependent gauge-invariant method using effective core pseudo-potentials and the multi-configuration one-electron wave function. C₆ dispersion coefficients of the 2 s + 2 s and 2 s + 2 p dissociations are deduced and also compared with all-electron values. Then, static polarizabilities of Li₂ in its ground and first excited ^{1, 3} Σ ⁺ _g,u states are obtained at interatomic distance corresponding to the energy minimum of each state. Received 10 May 2001 and Received in final form 14 September 2001     

Oscillator strength of the strongly “forbidden” Pb 6 p 2 3 P 0 ?6 p 2 3 P 1 transition at 1278.9 nm

The “forbidden” Pb 6p^{2 3}P ₀ ↦6 p ^{2 3}P₁ line at 1278.9 nm is measured by diode laser absorption in a resistively heated hot-pipe filled with a lead vapour and argon as buffer gas. The measurements performed at a temperature of 1170 K and a lead number density of 2.4×10 ¹⁵ cm^-3 yield the oscillator strength f _F = (4.5±1.1)×10 ^-7 which corresponds to a radiative transition probability A _F = (6.1±1.5) s^-1. Within the error bars, the result is in agreement with theoretical data published by different authors. Received 11 October 2000 and Received in final form 5 January 2001     

Hopping conductivity and activated transport in InxGa1-xAs quantum wells

We present measurements of the diagonal R_xx and off-diagonal R_xy magnetoresistance under quantum Hall conditions on several high electron mobility transistors (HEMT) based on In_xGa_1-xAs quantum wells. From the magnetoresistance tensor we obtain the longitudinal conductivity σ _xx . We study the transport mechanisms near the σ _xx minima at temperatures ranging between 2 K and 35 K; activated transport is the dominant mechanism for temperatures above 7 K while variable range hopping conductivity is significant for lower temperatures. We show that electron-electron correlations should be taken into account to explain the conductivity vs temperature behaviour below 5 K. Finally, we study the behaviour of the localization length as a function of Landau level filling and obtain a critical exponent γ = 3.45±0.15. Received 6 June 2001 and Received in final form 16 October 2001     

Transparent conducting antimony-doped tin oxide films deposited on flexible substrates by r.f. magnetron-sputtering

Transparent conducting antimony-doped tin oxide (SnO₂:Sb) films were deposited on organic substrates by r.f. magnetron-sputtering. Polycrystalline films with a resistivity of ≈ 6.5×10^-3 Ω cm, a carrier concentration of≈ 1.2×10²⁰ cm^-3 and a Hall mobility of ≈ 9.7 cm² v^-1 s^-1 were obtained. The average transmittance of these films reached 85% in the wavelength range of the visible spectrum. Received: 20 April 2001 / Accepted: 23 July 2001 / Published online: 17 October 2001     

Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation

We consider front solutions of the Swift–Hohenberg equation ∂ _t u= -(1+ ∂ _x ²)² u + ɛ² u -u ³. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non-linear stability of these solutions. It turns out that this problem is closely related to the question of stability of the trivial solution for the model problem ∂ _t u(x,t) = ∂ _x ² u (x,t)+(1+tanh(x-ct))u(x,t)+u(x,t) ^p with p>3. In particular, we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front. Received: 23 February 2001 / Accepted: 27 August 2001     

Electron transport properties of MgB<Subscript>2</Subscript> in the normal state

We report measurements of the resistivity, ρ, and the Seebeck coefficient, S , of a MgB₂ sintered sample, and compare S with theoretical calculations based on precise electronic structure calculations. ρ is fitted well by a generalized Bloch-Grüneisen equation with a Debye temperature Θ _R of 1050 K. S is given by the sum of a diffusive and a phonon drag term and the behavior in the temperature region T _c < T < 0.1Θ _R follows the relationship AT+BT³. The phonon drag term indicates a strong electron-phonon interaction. The diffusive term, compared with calculations, suggests that σ bands give the main contribution to the Seebeck effect. Received 16 November 2001 and Received in final form 21 December 2001     

500-Hz two-photon Ramsey fringes with a SF6 beam: towards a new frequency standard in the 30-THz spectral region

A two-photon Ramsey-fringe experiment with a supersonic beam of SF₆ has been performed with an interzone distance of up to 50 cm. Using a He-seeded beam with 50% of SF₆, the two-photon transition P(4)E⁰ in the 2ν₃ band reveals its magnetic hyperfine structure and the periodicity of the fringes is 500 Hz. The strength of the central fringe of the main hyperfine component corresponds to a flux of 10¹⁰–10¹¹useful molecules/s, which is very promising for a new frequency standard in the 30-THz spectral region. Received: 27 April 2001 / Revised version: 18 June 2001 / Published online: 18 July 2001     

The flexoelectric effect in nematic liquid crystals: A statistical- mechanical approach

The flexoelectric coefficients e₁ and e₃ for polar liquid crystals, such as 4-n-pentyl- 4^′-cyanobiphenyl, are investigated theoretically by means of an integral equation approach, which takes into account translational, orientational correlations as well as their coupling. e₁ and e₃ are evaluated from microscopic expressions derived on the basis of a density-functional method. Received 27 April 2001 and Received in final form 27 August 2001     

Widely usable interpolation formulae for hyperfine splittings in the 127I2 spectrum

Based on new systematic high precision measurements of hyperfine splittings in different rovibrational bands of ¹²⁷I₂ in the near infrared spectral range between 778 nm and 816 nm, and the data in the range from 660 nm to 514 nm available from literature, the quantum number dependence of the different hyperfine interaction parameters was reinvestigated. As detailed as possible parameters were re-fitted from the reported hyperfine splittings in literature, considering that the interaction parameters should vary smoothly with the vibrational and rotational quantum numbers, and follow appropriate physical models. This type of consistency has not been sufficiently taken into account by other authors. To our knowledge it is now possible for the first time to separate the hfs contributions of the two electronic states B ³ and X ¹ Σ ⁺ _g for optical transitions in a very large wavelength range. New interpolation formulae could be derived for both states, describing the quantum number dependences of the nuclear electric quadrupole, of the nuclear spin-rotation and also of the nuclear spin-spin interactions. Using these new interpolation formulae the hyperfine splittings for the components with the quantum number condition F - J = 0 can be calculated with an uncertainty of ≤30 kHz for transitions in the wavelength range between 514 nm and 820 nm. Received 17 July 2001 and Received in final form 17 October 2001     

Magnetic resonance on LiCuVO 4

EPR and ⁷Li NMR measurements were performed in the distorted inverse spinel V(LiCu)O₄ down to 1.5 K. Anisotropy effects on magnetic resonance spectra due to the Jahn-Teller distortion of the oxygen octahedra surrounding the copper ions are discussed. The estimation of the spin-spin interactions deduced from the EPR-relaxation rate Δ H reveals a situation comparable to the prototypical one-dimensional S = 1/2 Heisenberg antiferromagnet CuGeO₃. Approaching three-dimensional antiferromagnetic order ( T _N ≈ 2 K) from above, both magnetic relaxation rates, Δ H _EPR and ⁷ (1/ T ₁ ), respectively, exhibit nearly the same critical divergence reminding to the onset of three-dimensional order in two-dimensional layered systems. Received 22 January 2001 and Received in final form 6 May 2001     

Electron phonon interactions and superconductivity in α ′ -TTF[Pd(dmit)2]2

A simple model is developed to understand superconductivity in α ^′ -TTF[Pd(dmit)₂]₂. We include electron-intra molecular and intermolecular phonon interactions as the mechanism of superconductivity. Intramolecular vibrations included are the eight symmetric A_g modes of the Pd(dmit)₂ molecule. Intermolecular vibrations included are the longitudinal acoustic and transverse acoustic (LA and TA) modes of the Pd(dmit)₂ column. All the electron-phonon coupling constants are calculated from first principles. We find that largest el-intramolecular vibration coupling is to the A_g mode with the highest frequency (1449 cm^-1). The el-intermolecular coupling to the LA mode is found to be larger than the total el-intramolecular couplings. We also find el-(TA)phonon coupling to be at least an order of magnitude smaller than el-(LA)phonon coupling. Estimate of superconducting transition temperature is comparable to experimental result. We also provide a detailed discussion, employing the results of recent numerical calculations on two-chain Hubbard model and the specific material parameters, on the relative importance of el-ph and Coulomb-origin mechanisms of superconductivity in α ^′ -TTF[Pd(dmit)₂]₂ and TTF[Ni(dmit) ₂ ] ₂ . Received 29 March 2001 and Received in final form 7 August 2001     

Superconductivity of Rb 3 C 60 : breakdown of the Migdal-Eliashberg theory

In this paper, through an exhaustive analysis within the Migdal-Eliashberg theory, we show the incompatibility of experimental data of Rb₃C₆₀ with the basic assumptions of the standard theory of superconductivity. For different models of the electron-phonon spectral function α ² F (Ω) we solve numerically the Eliashberg equations to find which values of the electron-phonon coupling λ, of the logarithmic phonon frequency and of the Coulomb pseudopotential μ ^* reproduce the experimental data of Rb₃C₆₀. We find that the solutions are essentially independent of the particular shape of α ² F (Ω) and that, to explain the experimental data of Rb₃C₆₀, one has to resort to extremely large couplings: λ = 3.0±0.8. This results differs from the usual partial analyses reported up to now and we claim that this value exceeds the maximum allowed λ compatible with the crystal lattice stability. Moreover, we show quantitatively that the obtained values of λ and strongly violate Migdal's theorem and consequently are incompatible with the Migdal-Eliashberg theory. One has therefore to consider the generalization of the theory of superconductivity in the nonadiabatic regime to account for the experimental properties of fullerides. Received 30 March 2001     

Wavelength-modulation spectroscopy using a frequency-doubled current-modulated diode laser

We have studied atomic absorption in an argon discharge by wavelength-modulation spectroscopy with a frequency-doubled diode laser. The tunable wavelength-modulated radiation at 430 nm was generated by frequency doubling a current-modulated 860-nm diode laser in a KNbO₃ crystal. 2f-, 4f- and 6f-harmonic spectra as a function of diode laser modulation depth were measured on a Doppler-broadened sample of excited argon atoms produced in a capacitively coupled plasma chamber. Characterisation of the harmonic signals was accomplished. Minimum detectable absorbances of 7.7×10^-5 and 1.9×10^-4 based on a 3σ criterion (σ being the standard deviation of the noise) were estimated for 2f- and 4f-harmonic detection of the frequency-doubled radiation with a time constant of 0.1 s. The concentrations of argon in the 1s₄ state were found to be in the range of 3×10⁸ to 1.2×10¹¹ cm^-3 for the experimental conditions studied. Received: 25 February 2002 / Revised version: 4 April 2002 / Published online: 14 May 2002     

Hole doping by Li substitution and antiferromagnetism in YBa Cu O studied by neutron powder diffraction measurements

The magnetic structure of tetragonal insulating YBa₂Cu_3-xLi_xO_y has been studied as a function of x and y. The Néel temperature and the mean ordered magnetic moment on the Cu2 sites were determined by neutron powder diffraction measurements. The decrease of these two parameters as compared to YBa₂Cu₃O₆ is much stronger for lithium than for zinc substitution. The difference is quantitatively explained by the presence of holes created in the CuO₂ planes. These holes arise from the substitution of plane Cu²⁺ by Li⁺. We suggest an explanation why such holes are not seen for the same substitution of plane Cu²⁺ by Li⁺ in orthorhombic superconducting YBa₂Cu_3-xLi_xO _{7 - δ} . Received 31 October 2001 and Received in final form 6 March 2002 Published online 25 June 2002     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

Determination of the helium-4 mass in a Penning trap

The determination of the rotational quadrupole alignment of diatomic molecules via REMPI detection is investigated. In this process a high focal intensity usually increases the detection probability. At high intensities the AC Stark effect may cause a splitting of the normally degenerate m_J sublevels of a rotational state J beyond the spectral width of the exciting radiation. This leads to a selective detection of only certain m_J states with the consequence that deduced alignment factors can be misleading. From the theoretical considerations line profiles are explicitly calculated for dynamic polarizabilities which represent the B ¹Σ⁺ _u←X ¹Σ⁺ _g transition of H₂, in order to fit an experimental (3+1) REMPI spectrum and to predict (1+1') line shapes as a function of laser intensity. It is further shown that the deduced quadrupole alignment factor A ₀ ⁽²⁾ is significantly changed by the second order AC Stark effect when the intensities are chosen high enough to observe asymmetric broadened line profiles. Different combinations of relative linear polarizations of the exciting and ionizing laser beams are discussed. Received 1st August 2000 and Received in final form 2 May 2001