Anisotropy of X-ray critical scattering in 4,4-di-n-hexyl-biphenyl liquid crystal

We have carried out a high-resolution X-ray critical scattering experiment in the isotropic phase connected with the isotropic-smectic-B transition in 4,4-di-n-hexyl-biphenyl. The measurements yield the following parameter values: $\text{d = 23.92}\text{A}\text{?}$, $\text{q}{}_0\text{= 0.268}\text{A}\text{?}{}^{\mathrm{?1}}$ and the critical exponents γ = 1.51 ± 0.12, ν_∥ = 0.65 ± 0.06, ν_⊥ = 0.70 ± 0.08. At the temperature t = 10^?3 ($\text{t =}\text{T}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{?1}$) the correlation lengths are $\text{ξ}{}_{\mathrm{\parallel }}\text{= 390}\text{A}\text{?}$ and $\text{ξ}{}_{\mathrm{\perp }}\text{= 1080}\text{A}\text{?}$.     

Stochastic saturation of three-drift-wave interaction at finite parallel wavelength

The interaction of three drift waves is considered at finite parallel wavelength. The coupling to ion sound waves has a profound effect on the saturation levels. For k_|L_n～ 1. turbulent amplitudes are of the magnitude $\text{eΦ?T}{}_{\mathrm{e}}\text{～}\text{1}\text{k}{}_{\mathrm{\perp }}\text{L}{}_{\mathrm{n}}$ as predicted by usual estimates, in contrast to previous studies neglecting this effect.     

Production and decay of quark-gluon strings: inclusive distributions of hadrons in p⊥ and x

The dependence of inclusive cross sections of the production of hadrons $\text{p}\text{p}\text{→ hX}$ on p_⊥ (and also on x and √s) is calculated at high energy in the region of small p_⊥ ? 1–2 GeV. The model of production and decay of quark-gluon strings is used under the simplest assumptions about the k_⊥ dependence of the quark distributions in nucleons ～ exp(?γ₁k²_⊥) and about the form of the string fragmentation function $\text{G}\text{?}{}^{\mathrm{<mtext>h</mtext>}}\text{～}\text{exp}\text{[?γ}{}^{\mathrm{<mtext>h</mtext>}}\text{(}\text{p}{}_{\mathrm{\perp }}\text{? z}\text{k}{}_{\mathrm{\perp }}\text{)}{}^2\text{]}$ where γ₁ and γ^h are some constants. The theory reproduces all existing experimental data and yields the “seagull effect” for the dependence of 〈p_⊥〉 on x. Predictions are given for the p_⊥ dependence of the spectra of π^± mesons produced at high energies at SPS and other future colliders.     

Electromigration in tin single crystals

Atom transport in high-purity tin single crystals due to the influence of large direct currents has been measured by the “vacancy flux” technique. Cylindrical specimens were selected with c-axis oriented with 9° perpendicular or parallel to the direction of current flow. Rates of both longitudinal and transverse dimensional changes were used to calculate the anode-directed atom drift velocity. The results gave $\text{Z}{}^1{}_6\text{?}{}_6\text{= ?18±2}$ and $\text{z}{}^1{}_{\mathrm{\perp }}\text{?}{}_{\mathrm{\perp }}\text{= ?18 ±2}$, where Z¹ is the effective charge number and ?₆ = 0.89 and ?_⊥ = 0.54 are the estimated correlation factors in the parallel and perpendicular directions. These values for Z¹ are appreciably smaller than the results reported earlier for polycrystalline tin by Kuz'memko. The activation energies for $\text{Z}{}^1\text{?}$ agree within experimental error with those of self-diffusion.     

Optical absorption and ESR study of F centres in BaClF and SrClF crystals

Magnetic and optical properties of two types of F centres, calledF(F^?) and F (Cl^?), created in BaClF and SrClF tetragonal crystals are described. The experimerttal position of the absorption bands and the [g] principal values of each centre are the following at 78K. In BaClF, $\text{F(}\text{Cl}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{}}\text{=438}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=550}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.9690 ± 0.0003, g}{}_{\mathrm{\perp }}\text{=1.9798±0.0003; F(}\text{F}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{\parallel }}\text{=532}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=}\text{430}\text{nm}\text{446}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.9836 ± 0.0003, g}{}_{\mathrm{\perp }}\text{=1.9695±0.0003.}\text{In SrCIF}\text{, F(}\text{Cl}{}^{\mathrm{?}}\text{): γ}{}_{\mathrm{\parallel }}\text{=380}\text{nm}\text{, λ}{}_{\mathrm{hu}}\text{=465}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.996±0.002, g}{}_{\mathrm{\perp }}\text{=1.993±0.002; F(}\text{F}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{\parallel }}\text{=410}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=}\text{345}\text{nm}\text{363}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.997±0.001, g}{}_{\mathrm{\perp }}\text{=1.993+0.001. (∥}\text{and}\text{⊥}$ refer to the light polarization or the magnetic field direction with respect to the fourfold axis of the crystal).This attribution disagrees with that proposed by Nicklaus and Fischer, but accounts for the values of the energy levels of F(F^?) and F(C1^?) in BaClF and SrClF calculated by S. Lefrant and A.H. Harker.     

Magnetophonon oscilation of thermoelectric power in the conduction band of tellurium

At about 200K where the Hall coefficient of p-Te reverses its sign, magnetophonon oscillation of electron in the conduction band was observed for the first time in H6c and H⊥c. It was attained by measuring the second derivative of the longitudinal magneto-Seebeck coefficient (?²α₆/?H²). It is found to be explained fairly well by a simple parabolic band model even for H6c. Effective mass values of the conduction band at 200K are deduced on an interpretation; $\text{m}{}^1{}_{\mathrm{\perp }}\text{=0.160m}{}_0$ and $\text{m}{}^1{}_6\text{= 0.072m}{}_0$. Rather large contribution of electron in ?²α₆/?H² may be due to the enhanced electron diffusion in a transition region from p-type to intrinsic as reported recently in p-InSb. This interpretation is supported also by the oscillation of longitudinal magnetoresistance (?²?₆/?H²) which was observed for H6c.     

Tensor interaction in heavy-ion scattering: (I). The turning-point model

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power $\text{T}{}_{\mathrm{2q}}$ have certain relations with each other for each type of tensor interaction (T_R, T_P and T_L types). The predicted relations between the $\text{T}{}_{\mathrm{2q}}$ are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for ⁷Li and ²³Na elastic scattering from ⁵⁸Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a T_P? or T_L-type tensor interaction in polarized heavy-ion scattering. The presence of a T_P-type tensor interaction is suggested by measured $\text{T}{}_{20}\text{/}\text{T}{}_{22}$ ratios for ⁷Li+⁵⁸Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail.     

Thermal expansion of zirconium—II

The generalised Gruneisen parameters γ′ = ?? log ω/??′ and γ″ = ?? log ω/??″ have been calculated for various normal mode frequencies using the force model for Zirconium obtained on Keating's approach. There is a general agreement between the normalised frequency distribution curve of Zirconium obtained on the present model and that of Bezdek et al. The temperature dependence of the effective Gruneisen functions $\text{γ}\text{?}{}_{\mathrm{\perp }}\text{(T)}$ and $\text{γ}\text{?}{}_{\mathrm{|}}\text{(T)}$ has been calculated using the procedure of Blackman. The high temperature limits of $\text{γ}\text{?}{}_{\mathrm{\perp }}\text{(T)}$, $\text{γ}\text{?}{}_{\mathrm{|}}\text{(T)}$ and $\text{γ}\text{?}{}_{\mathrm{v}}$ are in good agreement with those obtained by Goldak et al. from an analysis of the thermal expansion data of Zirconium.     

Transport properties of a Van der Waals fluid near the critical point

The behaviour of the transport coefficients of a Van der Waals fluid is studied in the one-phase region along the critical isochore of the liquid-vapour phase transition. When $\text{?=}\text{(T?T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}\text{→0}$ the strongest singularity is found in the case of the bulk viscosity (??^?2). The divergence of the heat conductivity is shown to be weaker than $\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$. The shear viscosity tends to a finite limit. The coefficients of the asymptotic laws are explicitly given. All the results are established in the region where the Ornstein-Zernike theory applies.     

Magnetothermal effect in semiconductors in strong magnetic fields

We have derived an expression for the adiabatic differential temperature change $\text{(}\text{?T}\text{?H}\text{)}{}_{\mathrm{s}}$ of a semiconductor in the extreme quantum region. The transition to non-degeneracy is characterised by a sharp negative dip in $\text{(}\text{?T}\text{?H}\text{)}{}_{\mathrm{s}}$, which may be greatly modified by the Zeeman splitting. A numerical calculation of $\text{(}\text{?T}\text{?H}\text{)}{}_{\mathrm{s}}$ has been made for GaAs with electron concentrations of 1.2 × 10¹⁶ and 3.8 × 10¹⁶ cm^?3 at temperatures of 2,1 and 0.5 K.     

Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

Hadron production at transverse momenta from 0.5 up to 2.2 GeV/c in proton-proton collisions at 70 GeV

The cross sections for π^±, K^±, p, and $\text{p}$ production in pp collisions have been measured at transverse momenta from 0.48 up to 2.21 GeV/c at 70 GeV. The data are compared with results obtained at lower and higher proton energies and also with the quantum chromodynamics parton model (QPM) calculations. Common behaviour of the cross sections of the form $\text{g(p}{}_{\mathrm{\perp }}\text{)?(x}{}_{\mathrm{\perp }}\text{)}$ in the energy range above 200 GeV does not take place at lower energies. Qualitatively QPM fits the data and the best agreement is for π⁺/π^? and K⁺/π⁺ ratios.     

A comment on higher twist contributions to σLσT

We consider the contribution to $\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{t}}$ in deep inelastic lepton-hadron scattering from a certain class of 4-quark operators in the framework of QCD. We find for this case by explicit calculation that $\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ is of order g²(Q²), with g²(Q²) the running coupling strength of QCD, in agreement with a general result of Politzer.     

Critical slowing down of fluctuations in squaric acid (H2C4O4) at the phase transition observed by 13C spin-lattice relaxation

Spin lattice relaxation T₁ of naturally abundant ¹³C nuclei in squaric acid was measured close to the antiferroelectric-paraelectric phase transition temperature T_c = 373 K. A rapid increase in $\text{1}\text{T}{}_1$ is observed close to T_c coming from above, which follows the power law $\text{1}\text{T}{}_1\text{～ ε}{}^{\mathrm{?1.4}}$ where $\text{ε =}\text{(T ? T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}$. This behaviour is explained on the basis of the two-dimensional character of the fluctuations.     

Core-level reflectance spectroscopy of germanium by means of synchrotron radiation

Reflectance spectra due to 3d core-levels of Ge have been measured in the photon-energy region from 29 to 38 eV by means of synchrotron radiation. Second-energy-derivative spectra have newly shown pairs of doublet structures with energy separation of the Ge $\text{3d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{?}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core-level splitting. The observed doublet structures are assigned to the transitions from the $\text{3d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and $\text{3d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core-levels to the flat regions of the conduction band around the particular symmetry points of Δ₆^c and L(₃^c(L₆^c, L_4,5^c).     

Specific heat and resistivity of GdSb and HoSb above the néel temperature

The specific heat C_P is found to vary as $\text{dR}\text{dT}$ in the critical region above T_N for the antiferromagnets GdSb and HoSb. This correspondence holds despite a dramatic difference between the two systems in the strength of the divergence C_P = A?^?α, $\text{? =}\text{(T ? T}{}_{\mathrm{N}}\text{)}\text{T}{}_{\mathrm{N}}$, where for HoSb we find α = 0.83 ± 0.10 while for GdSb α = 0.20 ± 0.10.     

Hartree-fock wave functions and oscillator strengths for the helium isoelectronic sequence

Oscillator strengths for 1¹S?n¹P transitions for some members of the helium isoelectronic sequence have been calculated by utilizing the dipole length, velocity and acceleration forms of the transition matrix element with coupled H.F. wave functions. Good agreement has been obtained between the values of the oscillator strengths. The quantities $\text{(?}{}_{\mathrm{A}}\text{??}{}_{\mathrm{L}}\text{)}$ and $\text{(?}{}_{\mathrm{A}}\text{??}{}_{\mathrm{V}}\text{)}$ decrease slowly with nuclear charge Z, whereas $\text{(?}{}_{\mathrm{L}}\text{-?}{}_{\mathrm{V}}\text{)}$ first increase to a maximum value and then decreases slowly.     

Electron paramagnetic resonance of 61Ni+ in CuGaS2

EPR of ⁶¹Ni⁺ doped CuGaS₂ at 4.2 K leads to the following experimental data: $\text{g = 1.918 ± 0.006 A  < 12 × 10}{}^{-4}\text{cm}{}^{-1}\text{, g}{}_{\mathrm{\perp }}\text{= 2.328±0.006 A}{}_{\mathrm{\perp }}\text{= (65±2) × 10}{}^{-4}\text{cm}{}^{-1}$. High axial field splitting of ²T₂ state stabilizes the center against Jahn-Teller interaction. Covalency reduction factor k is 0.76.     

Self-adjointness of the minimal Schrödinger operator with potential belonging to L1, loc

Let $\text{0 ?q(x) ∈L}{}_{\mathrm{1,loc}}\text{(}\text{R}{}^{\mathrm{m}}\text{)}$,m? 1.Consider the operatorT₀ = ?Δ+q with domain consisting of all bounded measurable functions $\text{u(x), x ∈}\text{R}{}^{\mathrm{m}}$, having bounded support, for which the distribution ?Δu+qu belongs to $\text{L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The main result of the paper is essential self-adjointness of $\text{T}{}_0\text{in L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential.     

Some properties of heavy lepton families

The simplest four-quark SU(2) ? U(1) models with an anomally-free heavy lepton sector can have two charged heavy leptons and one or two neutral leprons. Such models also explain the rise in R (the ratio of hadronic to muon pair production in e⁺e^? collisions). We study some consequences of different choices of leptonic numbers for L₁ and L₂. In particular, we derive, the leptonic decay width when several final-stae leptons are massive; the cross section for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_1\text{L}{}_2$ production; the branching ratio for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_2\text{L}{}_2\text{→}\text{e}\text{3μ+}\text{missing energy}$.