An ESCA investigation of some thiocyanato complexes

A series of simple thiocyanato complex ions have been investigated as their tetraphenylphosphonium and potassium salts. The binding energies of N, C and S were determined as well as those of the metals. From the first-mentioned data effective charge-values were estimated for the atoms of the ligands. For this purpose linear relations E_b = kq + E_b0 were used that had been previously established within a scheme having C_1s (phenyl) as the internal standard.From the data thus obtained the effective charge on the metal atoms was estimated. For elements where we have sufficient data the same type of linear relation seems to he followed. Tentatively valid examples are E_b(Ni) = 6.74q_Ni + 848.3 eV and E_b(Pd) = 4.45q_Pd + 333.9 eV.In this interpretation the atoms of the metals are considered to be positively charged and surrounded by the negative charge of the electrons occupying the s band.It is further suggested for complexes with pronounced π backbonding (Pt(SCN)₄^2?, Pd(SCN)₄^2? and Hg(SCN)₄^2?) that the C 1s binding energy measured for the carbon atom of the SCN^? ligand is composed of the ionisation energy from the 1s level and an additional term corresponding to the intraligand π → π* transition.     

An ESCA investigation of some dithiooxalato complexes

A series of dithiooxalato complex ions have been investigated as their tetraphenyl-phosphonium and potassium salts. Core-electron binding energies (E_b) of S, C, and O were determined, as well as those of the metals. From the first-mentioned data, effective charge values (q) were estimated for the atoms of the ligands. For this purpose linear relations (E_b = k · q + E_bO) were used that had been previously derived within a scheme using C ls (phenyl) as the internal standard. From the data thus obtained the effective charge on the metal atoms could be estimated. The data is used to test if analogous linear relations also hold for the heavy elements; for example, we have found E_b(Pt) = 3.17 · q_pt + 71.1 eV.     

An ESCA investigation of some copper complexes

A series of copper complexes have been investigated by ESCA. All complexes were salts of the tetraphenylphosphonium ion. The binding energies of all the atoms in the complexes were determined. From the binding energies of the ligand atoms we estimated the effective charges on these atoms. For this purpose we used linear relations of the formE_b = kq + E_bO which had been established previously within our scheme of C 1s (phenyl) as internal standard. From the data thus obtained, the effective charge on the copper atom was estimated. A linear relation between binding energy and the effective charge on the copper atom was found, i.e.,E_b(Cu) = 1.52q_Cu + 932.2ESCA spectra were recorded for the complexes bis(1,3-diphenyl-1,3-propanediono) copper (II) and bis(3-phenyl-2,4-pentanediono) copper (II). By a combination of the XPS binding energies and IR intensities of the ν_CH vibrations of the phenyl groups in the complexes with empirical relations between these entities and the effective charges of the atoms and groups, a fairly complete mapping of the charge distributions of these complexes has been achieved.     

Charge exchange and excitation cross sections at collisions of alpha particles with be-like impurity oxygen ions in a plasma

The charge exchange and excitation cross sections at collisions of alphas with O⁴⁺(1s ²2s ²) impurity atoms in a hot plasma for striking energies E _c varying from 20 keV to 2 MeV are determined for the first time. The cross sections are calculated using the method of close-coupling equations with 13 singlet four-electron quasi-molecular states taken as a basis. The partial cross sections of charge transfer to the 1s, 2s, and 2p states of a He⁺ ion and for O⁴⁺(1s ²2s ²) → O⁴⁺(1s ²2lnl’) (n = 2, 3) electronic excitation of an oxygen ion are found. The maximal value of the charge exchange total cross section roughly equals 2.2 × 10^?16 cm² at E _c ≈ 0.7 MeV. The excitation total cross section has a maximum of ≈ 7.7 × 10^?16 cm² at E _c ≈ 80 keV for single-electron excitation and ≈6.5 × 10^?16 cm² at E _c ≈ 0.7 MeV for two-electron excitation.     

Isometric immersions of pseudo-Riemannian space forms

In this paper we study local isometric immersions f:M_sⁿ(K)→N_s+q²ⁿ⁻¹(c) of a time-like n-submanifold M_sⁿ(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form N_s+q²ⁿ⁻¹(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold M_sⁿ(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in N_n−1²ⁿ⁻¹(c) and N₁²ⁿ⁻¹(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.     

The far-infrared spectrum of tetrahydrothiophene: The bend/twist vibrations and associated barriers

The far-infrared spectrum of tetrahydrothiophene is reinvestigated with a resolution of 0.12 cm^?1 in the region of 50–350 cm^?1. In addition to the bend transitions (ν_b) below 120 cm^?1 reported previously, a number of sequences revealed by the improved resolution are observed for the first time and assigned to transitions of 2ν_b, of the twist (ν_t), and of difference combinations (ν_t - ν_b). Simple one-dimensional modeling of the twist sequence, which is derived from a self-consistent bend-twist energy level diagram, with a quadratic-quartic Hamiltonian suggests a barrier to planarity on the order of 4250 cm^?1. A two-dimensional potential function in the dimensionless coordinates is found to be V(q_b, q_t) = ?249.6q_b² + 4.48q_b⁴ ? 215.5q_t² + 2.73q_t⁴ + 7.00q_b²q_t².     

On stochastic spatial patterns and neuronal polarity

To investigate the statistical behavior in the sizes of finite clusters for percolation, cluster size distribution n _s (p) for site and bond percolations at different lattices and dimensions was simulated using a modified algorithm. An equation to approximate the finite cluster size distribution n _s (p) was obtained and expressed as: log?(n _s (p)) = as ? b log?s + c. Based on the analysis of simulation data, we found that the equation is valid for p from 0 to 1 on site and for the bond percolation of two-dimensional (2D) and three-dimensional (3D) lattices. Furthermore, the relationship between the coefficients of the equation and the occupied ratio p was studied using the finite-size scaling method. When \(x = D(p - p_c )L^{y_t }\) , p < p _c , and D was a nonuniversal metric factor. a was found to be related only to p, and the a-x curves of different lattices were nearly overlapped; b was related to the dimensions and p, and the scaled data of the b of all lattices with the same dimension tended to fall on the same curves. Unlike a and b, c apparently had a quadratic relation with x in 2D lattices and linear relation with x in 3D lattices. The results of this paper could significantly reduce the amount of tasks required to obtain numerical data of on the cluster size distribution for p from 0 to p _c .     

Flicker noise of hot electrons in silicon at T = 78 K

From flicker-noise and current-voltage measurements performed on an n⁺nn⁺ silicon planar device at T = 78 K we calculated Hooge's parameter α as a function of the electric field strength, E₀. We found that α(E₀) = α(0)/[1 + (E₀/E_c)²]. E_c is a critical field where the drift velocity equals the sound velocity, indicating the connection of the observed effect with acoustical phonon scattering.     

Extrapolation from positive to negative energy of the Woods-Saxon parametrization of the n-208Pb mean field

The real part V(r); E) of the nucleon-nucleus mean field is assumed to have a Woods-Saxon shape, and accordingly to be fully specified by three quantities: the potential depth U_v(E), radius R_V(E) and diffuseness a_v(E). At a given nucleon energy E these parameters can be determined from three different radial moments [r^q]_v = (4π/A) ∝V(r; E)r^q dr. This is useful because a dispersion relation approach has recently been developed for extrapolating [r^q]_V(E) from positive to negative energy, using as inputs the radial moments of the real and imaginary parts of empirical optical-model potentials V(r; E) + iW(r; E). In the present work, the values of U_v(E), R_v(E) and a_v(E) are calculated in the case of neutrons in ²⁰⁸Pb in the energy domain −20 < E < 40 MeV from the values of [r^q]_V(E) for q = 0.8, 2 and 4. It is found that both U_V(E) and R_v(E) have a characteristic energy dependence. The energy dependence of the diffuseness a_a(E) is less reliably predicted by the method. The radius R_V(E) increases when E decreases from 40 to 5 MeV. This behaviour is in agreement with empirical evidence. In the energy domain −10 MeV < E < 0, R_V(E) is predicted to decrease with decreasing energy. The energy dependence of the root mean square radius is similar to that of R_V(E). The potential depth U_v slightly increases when E decreases from 40 to 15 MeV and slightly decreases between 10 and 5 MeV; it is consequently approximately constant in the energy domain 5 < E < 20 MeV, in keeping with empirical evidence. The depth U_v increases linearly with decreasing E in the domain −10 MeV < E < 0. These features are shown to persist when one modifies the detailed input of the calculation, namely the empirical values of [r^q]_v(E) for E > 0 and the parametrization [r_q]_w(E) of the energy dependence of the radial moments of the imaginary part of the empirical optical-model potentials. In the energy domain −10 MeV < E < 0, the calculated V(r; E) yields good agreement with the experimental single-particle energies; the model thus accurately predicts the shell-model potential (E < 0) from the extrapolation of the optical-model potential (E > 0). In the dispersion relation approach, the real part V(r; E) is the sum of a Hartree-Fock type contribution V_HF(r; E) and of a dispersive contribution ΔV(r; E). The latter is due to the excitation of the ²⁰⁸Pb core. The dispersion relation approach enables the calculation of the radial moment [r^q]_ΔV(E) from the parametrization [r^q]_w(E): several schematic models are considered which yield algebraic expressions for [r^q]_ΔV(E). The radial moments [r^q]_HF(E) are approximated by linear functions of E. When in addition, it is assumed that V_HF(r; E) has a Woods-Saxon radial shape, the energy dependence of its potential parameters (U_HF, R_HF, a_HF) can be calculated. Furthermore, the values of ΔV(r; E) can then be derived. It turns out that ΔV(r; E) is peaked at the nuclear surface near the Fermi energy and acquires a Woods-Saxon type shape when the energy increases, in keeping with previous qualitative estimates. It is responsible for the peculiar energy dependence of R_V(E) in the vicinity of the Fermi energy.     

Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16³ × 32 × 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling α _s,g1(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling α _s,g1(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling α _s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q ²) with c ≃ 2.8 GeV² on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling α _s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling α _s,g1(q) in the infrared region increases monotonically as q→ 0. Above 2 GeV, the quark-gluon coupling α _s,g1(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at     

Glauber Dynamics for the Mean-Field Potts Model

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q??3 states and show that it undergoes a critical slowdown at an inverse-temperature ?? _s (q) strictly lower than the critical ?? _c (q) for uniqueness of the thermodynamic limit. The dynamical critical ?? _s (q) is the spinodal point marking the onset of metastability. We prove that when ??<?? _s (q) the mixing time is asymptotically C(??,q)nlogn and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order n. At ??=?? _s (q) the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order n ^4/3. For ??>?? _s (q) the mixing time is exponentially large in n. Furthermore, as ?????? _s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O(n ^?2/3) around ?? _s . These results form the first complete analysis of mixing around the critical dynamical temperature??including the critical power law??for a model with a first order phase transition.     

Measurement of π−p → π0n at large momentum transfer

New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/c, extending in momentum transfer up to ?t = 1.8 (GeV/c)², are reported and compared with an optical impact parameter model, together with previous data for the reaction π^?p → ηn at the same energy. The imaginary part of the pole trajectory b₀(s) is determined from the slope of the tangent to the maxima of $\text{(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{d}\text{σ}\text{d}\text{t}$. The linear increase of Im b₀(s) with log s, which has been observed at low energies, continues up to 40 GeV/c.     

Collective excitations in the 1-D-ferromagnet CsFeCl3 with singlet ground state

By means of inalastic neutron scattering we have determined the dispersion relation of the magnetic excitations in CsFeCl₃ at different temperatures.The dispersion in c-direction, along the Fe-chains is typically ferromagnetic and in the hexagonal plane antiferromagnetic. Due to the lack of an applicable theory the data were parametrized by the simple heuristic formula:?ω = [2J[1 - cos πq_c] [A + 2J(1 - cos π)q_c)] + [C + J' (1.5 + γ(q))]²]^{$\text{1}\text{2}$}The gap was found to be C = 0.148 THz, the easy plane anisotropy A = 0.308 THz, the ferromagnetic interaction J = 0.148 THz and the antiferromagnetic interaction J' = -0.04 THz. At 1.25 K all excitations had a width smaller than the instrumental resolution ΔE = 0.025 THz. These results can be interpreted as follows: CsFeCl₃ is a singlet ground state system with strong ferromagnetic interaction J along the crystallographic c-axis and weak antiferromagnetic interaction J' in the plane perpendicular to c.In addition we have measured the influence of a magnetic field along the hexagonal c-axis. The splitting found agrees with the assumed level scheme yielding g = 2.5 for the first excited level.     

Inclusive cross sections in the central region and the supercritical pomeron

Using the double-Regge formalism and a supercritical pomeron with α_P(0)=1+Δ, we analyse the energy dependence of inclusive cross sections for negatively charged particles (c⁻) and K_s⁰ at CM rapidity y=0 in the CERN PS-Sp̄pS collider energy range. The values of Δ(c⁻)=0.170±0.008 and Δ(K_s⁰)=0.167±0.024 are found to be very close to each other and compatible with estimates of Δ derived from the total cross sections.     

Millimeter-wave spectrum of the C4v molecule IOF5: l-type doubling of the kl = −1 transitions in the v11(E) = 1 state spectrum

Measurements of the rotational spectrum of the C_4v molecule IOF₅ are reported for the excited vibrational state v₁₁(E) = 1 for the transitions J13 ← 12, 14 ← 13, 16 ← 15, and 17 ← 16 (55–72 GHz) including the observation of the kl = −1 (q⁻), l-doubling effect. Detailed assignments of the E-state spectrum are presented based on the overlapping quadrupole structure. These data are analyzed together with earlier results for the excited vibrational state v₆(B₁) = 1 to give information concerning the ν₆(B₁)-ν₁₁(E) Coriolis interaction and the (Δl, Δk) = (2, 2) (q⁺) and (2, −2) (q⁻)l-resonance interactions. It is found that q₁₁⁻ = −2.57(10) MHz, |q₁₁⁺| = 0.094(20) MHz, Δ = ν₆ − ν₁₁ = 45.2(7) cm⁻, ζ_11,11^z = +0.18(1) and |ζ_6,11^y| = 0.73(4).     

Stability of bipolarons in the presence of a magnetic field

The stability of large Fröhlich bipolarons in the presence of a static magnetic field is investigated with the path integral formalism. We find that the application of a magnetic field (characterized by the cyclotron frequence ω _c) favors bipolaron formation: (i) the critical electronphonon coupling parameter α _c (above which the bipolaron is stable) decreases with increasing ω _c and (ii) the critical Coulomb repulsion strength U _c (below which the bipolaron is stable) increases with increasing ω _c. The binding energy and the corresponding variational parameters are calculated as a function of α, U and ω _c. Analytical results are obtained in various limiting cases. In the limit of strong electron-phonon coupling (α ? 1) we obtain for ω _c ? 1 that E _estim ? E _estim(ω _c = 0) + c(u)ω _c/α ⁴ with c(u) an explicitly calculated constant, dependent on the ratio u = U/α where U is the strength of the Coulomb repulsion. This relation applies both in 2D and in 3D, but with a different expression for c(u). For ω _c ? α ²? 1 we find in 3D E _estim ? ω _c - α ² A(u) ln²(ω _c/α ²), (also with an explicit analytical expression for A(u)) whereas in 2D E _estim ^2D ? ω _c - α√ω _cπ(u-2-√2)/2. The validity region of the Feynman-Jensen inequality for the present problem, bipolarons in a magnetic field, remains to be examined.     

Infrared-microwave double resonance of 12CH3OH with a CO2 laser

The Stark effect of the 2₂ ← 2₁(E₁), 2₁ ← 3₀(E₁) microwave transitions in the ground state and the 2₂ ← 2₁(E₁) microwave transition in the first excited CO stretching vibrational state are measured by means of infrared-microwave double resonance with the ^qQ₁(2)E₁ infrared transition as the pump transition in the range of 1000 to 2300 V/cm. The dipole moments μ_a and μ_b as well as the off-diagonal rotational constant D_ab are determined for both the ground and the excited states. The frequency of the ^qQ₁(2)E₁ infrared transition is found to be lower by 128 ± 2 MHz than that of the P(34) CO₂ laser.     

Electrical charging of non-conductors in a photoelectron spectrometer; effect of X-ray source voltage

The electrical charging on samples of gadolinium trifluoride, sodium fluoride and fused silica, has been investigated as a function of the voltage in the X-ray source of a photoelectron spectrometer. The results can be expressed in the form,E_c = d + c(V – V₀) + a(1 - e^{?b(V – V₀)}) an equation which expresses the linear dependence of the intensity of the photoelectrons on X-ray intensity and the dependence of the low energy electrons as that corresponding to the equivalent electrical circuit consisting of an emf, a capacitor, and a resistor. With gadolinium trifluoride and sodium fluoride, both of which have a relatively high photoconversion, the electrical potential is positive for all voltages. With fused silica, which has a relatively low photoemission, the electrical potential is negative for the lower voltages. Relative to an assumed value of 83.8 eV for the binding energy for Au(4f_{$\text{7}\text{2}$}) of gold deposited on NaF and GdF₃, the charge corrected values for F(1s) and the Gd(4f_{$\text{sol7}\text{2}$}) orbital binding energies are determined to be 684.57 ± .07 and 10.1 eV, respectively.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

Inelastic neutron scattering study of spin waves in MnO

The dispersion relation E(q) for spin waves in MnO has been measured at 4.2°K by neutron inelastic scattering. The isotropic exchange integrals as well as the anisotropy constants have been determined by fitting the Hamiltonian to the data. It is found that the exchange striction plays main role in the anomaly in the magnetic interactions in MnO and the biquadratic exchange interaction j₁(S₁·S₂)² is almost absent (j₁/J₁ ? 0.002).