Sixth-order Term Research Articles

The Skyrmion Skyrmion interaction and the meson exchange model for the NN potential

The properties of nucleon-nucleon (NN) potentials derived from the Skyrme model are investigated compared to those of typical One-Boson-Exchange (OBE) models, For that purpose the NN as well as the nucleon-antinucleon (N¯N) potentials are evaluated for the isoscalar central channel, the isovector spin channel, and the isovector tensor channel. A comparison of NN and N¯N interactions allows a separation into terms with positive and negativeG-parity and therefore a detailed comparison with the properties of the OBE model. This analysis is performed using the classical Lagrangian of the Skyrme model and considering an extension of this Lagrangian by a term of sixth order, which has recently been proposed. The results indicate that the extended Lagrangian yields an interaction which is quite consistent with the OBE picture. The extended model, however, is much more sensitive to the values of the parameters and the approximations being used for the evaluation of the field for two baryons.

Static properties of nucleons in the modified Skyrme model

Static properties of nucleons are evaluated in the modified Skyrme model with a term of sixth order in momentum, but at most of second order in its component. Taking the nucleon mass, the pion decay constant, and the axial coupling constant as inputs, we could predict other quantities in good agreement with the experiments.

Geometrical and dynamical aspects of skyrmion fluctuations

Geometrical and dynamical aspects of skyrmion fluctuations are analysed and compared with baryon resonances in πN scattering. The adiabatic approximation which neglects the dynamical influence of rotation in isospace on the vibrational modes is reformulated in the isospace-fixed frame. This allows us to explicitly remove the coupling to exotic channels contained in the Skyrme model. There is indication that exclusion of the spin = isospin = 5 2 baryon improves the unsatisfactory high-energy behaviour of the πN scattering amplitudes obtained in the Skyrme model, while it seems that inclusion of a finite pion mass and a sixth-order term in the lagrangian does not lead to a systematic improvement of the results.

Charge-density-wave transitions in 1T-VSe2

An electron diffraction and imaging study of charge-density-wave phases in 1T-VSe2 is presented. Two phase transitions are found. At 110K a 3q-state is formed which at 80K transforms into an irregular pattern of 2q-domains. A Landau theory of these transitions is presented. In order to explain the 3q-2q transition sixth-order terms must be included in the free-energy expansion.

The magnetic field of saddle-shaped coils. II. Transverse components

For pt.I see ibid., vol.17, pt.1 (1984). The transverse Cartesian components By and Bz of the magnetic field of cylindrical saddle-shaped coils are evaluated in a series expansion. The terms of the series are written in the form Almnxlymzn, where the coefficients Almn are functions of the coil size and shape parameters R0, Z0, Phi 0 (R0 and 2Z0 are the radius and height of the cylinder defining the geometry of the saddle-shaped coil, Phi 0 is the angle of the arcs). The y component of the magnetic field is determined to the fourth order (l+m+n=4); the z component was evaluated including the sixth-order terms. The existence or non-existence of the second-order terms determine the limiting properties of By and Bz for r to 0. the analysis of the second-order terms as a function of the coil parameters reveals some general properties of the magnetic field at the coil centre.

On the Temperature Dependence of the Elastic Constant C66in Layered Perovskite-Type Crystals of the (CH3NH3)2MCl4-Family

The temperature dependence of the elastic constant c 66 of the (CH 3 NH 3 ) 2 MCl 4 (M=Mn, Fe, Cu, Cd) is discussed in the relationship with the successive structural phase transitions on the basis of a simple Landau-type thermodynamic potential. It has turned out that a sixth order term in the transition parameters plays an important role in determining the temperature behavior of c 66 .

A program for EPR powder spectrum simulation

A program to compute powder EPR spectra for noncoincident tensors has been written. The spin Hamiltonian used includes anisotropic g, A, D, and Q tensors, isotropic nuclear Zeeman term, fourth- and sixth-order terms in S and first-order anisotropic ligand hyperfine terms. All terms except the ligand hyperfine terms are treated exactly. Data can be saved and reused if the program runs out of time. An efficient method is used for the variation of the orientation of the magnetic field, and for locating resonance fields.

Gell-Mann-Low function and Callan-Symanzik function: the three-lepton case and symmetry under e↔μ↔τ

The Callan-Symanzik functionβ eμτ(α) and the Gell-Mann-Lowψ eμτ are calculated for the three-lepton case up to the sixth order. The symmetry properties of the «asymptotic part» of the photon proper self-energyαπ c ∞ (--k 2/m e 2 k 2/m μ 2 ,k 2/m τ 2 ,α are examined under e↔μ↔τ. This leads to constraints among the sixth-order terms of απ c ∞ which are in agreement with its explicit calculations. An expression for then-leptonβ eμτ...n(α) is also given.

A note on Le Verrier's expansion of the disturbing function

An examination of Le Verrier's seventh-order expansion of the disturbing function has revealed only one non-trivial error in Le Verrier's work. The error occurs in a sixth order term in the eccentricities.

On the Temperature Dependence of an Elastic Constant in the Layered Perovskite-Type Crystals of the (CH3NH3)2MCl4-Family

The temperature dependence of the elastic constant c 66 of the (CH 3 NH 3 ) 2 MCl 4 (M=Mn, Fe, Cu, Cd) is discussed in the relationship with the successive structural phase transitions on the basis of a simple Landau-type thermodynamic potential. It has turned out that a sixth order term in the transition parameters plays an important role in determining the temperature behavior of c 66 .

Fluctuations in anisotropic magnetic superconductors

Fluctuations of the magnetic order parameter in anisotropic magnetic superconductors are studied within a model with (a) an easy-magnetization axis, and (b) a minimum of the reciprocal susceptibility $\ensuremath{\omega}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ on a ring in the reciprocal space. Both the quartic and the sixth-order terms in the free-energy functional are included. The model is studied in $d\ensuremath{\ge}3$ dimensions, and the phase diagram is proposed. Fluctuations in real magnetic superconductors such as Er${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$ and Ho${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$ are discussed.

Heat-capacity studies near the smectic-A—smectic-C(—smectic-C*) transition in a racemic (chiral) smectic liquid crystal

High-resolution heat-capacity measurements have been carried out on the chiral and racemic versions of 2-methylbutyl-4\ensuremath{'}-$n$-pentyloxy-biphenyl-4-carboxylate (2M45OBC). Both smectic-$A$---smectic-$C$ and smectic-$A$---chiral-smectic-$C$ transitions are found to be mean-field-like with a large sixth-order term in the Landau free-energy expansion. Our results also shed light on similarities and differences between the chiral and racemic compounds.

A high resolution X-ray scattering study of the phases and phase transitions in N-(4-n-butyloxybenzylidene)-4-n-heptylaniline (40.7)

We report high resolution X-ray scattering measurements of the smectic phases and phase transitions in the material N-(4-n-butyloxy-benzylidene)-4-n-heptylaniline (40.7) (I → N → Sm A → Sm C → Sm B). For the nematic to smectic A transition we have measured the critical exponents γ = 1.45 ± 0.03, ν ∥ = 0.78 ± 0.02, and ν⊥ = 0.65 ± 0.02. The in-plane positional correlations in the smectic A phase are described by a nearly two dimensional azimuthally-averaged Lorentzian liquid lineshape with a correlation length of 15.8 A. Measurements of the molecular tilt and lattice spacing in the smectic C phase along with previously reported heat capacity and light scattering measurements indicate that the smectic A-smectic C transition is described by a mean-field Landau-Ginsburg theory with an anomalously large sixth order term. The smectic C to smectic B phase transition is first order with a coexistence region of approximately 0.5 °C. Within this region the smectic B phase may coexist with either a smectic A or a smectic C phase. Finally, in the smectic B phase the layers undergo a continuous restacking transition from an ABAB to ABCABC stacking sequence with decreasing temperature between 35 and 31°C.

A phenomenological gibbs function for BaTiO3 giving correct e field dependence of all ferroelectric phase changes

The elastic Gibbs function for BaTiO3 introduced by Buessem, Goswami and Cross1 has been modified by including the last symmetry permitted sixth order term HP12P22P32 with a coefficient H = 4.91 × 109 Vm9 C-5. The function predicts the correct high electric field behavior of the low temperature ferroelectric: ferroelectric phase changes in the single crystal and suggests an interesting change of sign of the pyroelectric effect at high field levels in the induced tetragonal ferroelectric phase.

Dependence of the Tilt Angle on External Forces for Smectic-C And Chiral Smectic-C Liquid Crystals—Measurement of the Heat Capacity of DOBAMBC

Abstract A measurement of the specific heat of DOBAMBC is presented, and it is shown that a Landau expansion of the free-energy density with a sixth-order term is adequate to describe the measurement. The coefficients in the Landau expansion are estimated from this measurement. The dependence of the tilt angle on applied electric and magnetic fields is discussed for both smectic-C and chiral (ferroelectric) smectic-C liquid crystals. Numerical estimates of the Landau coefficients are used to show that the effect of external forces on the tilt angle is negligible except when being less than approximately 0.2 K from the transition to the smectic-A phase. The effect on the smectic-C-smectic-A phase-transition temperature is also discussed. Boundary effects can also affect the tilt angle, and an expression for the penetration depth of a boundary-induced disturbance is calculated. For thin, planar samples, a coupling between the two boundaries can induce a transition to the smectic-A phase. It is demonstrated ...

The differential cross section of the reaction pp → πd for proton energies between 500 and 600 MeV

The differential cross section of the pp → πd reaction was measured for seven energies between 516 and 582 MeV with an overall absolute precision better than 2%. Pions and deuterons were detected in coincidence with scintillation detectors, using time-of-flight techniques for event identification. Experimental techniques for absolute energy calibration, normalization and measurement of relative distributions are described. Detailed corrections have been applied to the data, which have been fit with Legendre polynomials. An upper limit of 50 μb for a sixth-order term is obtained. The results are compared with those of a recent precision experiment for the inverse reaction, and with theoretical predictions.

Fluctuation-induced tricritical points

In the vicinity of a tricritical point an $n$-component spin system is shown to have continuous transitions which are driven by fluctuations (they would be first order according to Landau's theory). We show that spin anisotropies which imply crossover to lower symmetry (e.g., of $m$-component spins with $m<n$) may turn these fluctuation-driven continuous transitions first order via tricritical points. In cubic systems, which exhibit fluctuation-driven first-order transitions, the anisotropy may yield two consecutive tricritical points. We present a detailed renormalization-group analysis of these situations with emphasis on the importance of the sixth-order terms in the Ginzburg-Landau-Wilson continuous-spin Hamiltonian. A list of possible experimental realizations is also given.

PROMETHEUS. A program system for investigation of anharmonic thermal vibrations in crystals

PROMETHEUS is a Fortran IV program system for investigation of anharmonic thermal vibrations in crystals, using elastic X-ray or neutron data. Three different anharmonic temperature-factor equations can be used, one of them up to sixth-order terms. The corresponding probability densities and mean effective atomic potentials can be calculated. Programs for correction of isotropic thermal diffuse scattering and of isotropic and anisotropic extinction are included. Fast averaging of symmetrically equivalent reflections combined with extended reflection statistics is possible. Calculations of Fourier syntheses and their errors and of Patterson functions can be carried out and the corresponding contour maps can be plotted.

Smectic-A-smectic-Ctransition: Mean field or critical

We have carried out a detailed study of the smectic-$A$-smectic-$C$ transition in butyloxybenzylidene heptylaniline (40.7) using high-resolution x-ray, heat-capacity, and light scattering techniques. Although the order-parameter data are consistent with heliumlike critical behavior, the data as a whole are uniquely described by a mean-field Landau model with an anomalously large sixth-order term.

Electric-Field Induced Tricritical Points in Antiferroelctric Phase Transitions

The tricritical point in temperature-electric field phase diagrams was derived for the Landau-type free energy applicable to the antiferroelectric phase transitions. The adopted free energy written in terms of two sublattice polarizations and the applied external field of the symmetry breaking nature contains three possible fourth-order terms and a sixth-order term, thus being capable of producing various types of phase diagrams. Examples of the tricritical points in the phase diagrams are presented for several parameter values.