Correlation of mode grüneisen parameter with the ratio of phonon frequencies in binary cubic compounds

A correlation formula between the mode Grüneisen parameter γ_j and the frequency ratio of LO and TO phonons is semiempirically derived and compared with the experimental values for a large number of cubic binary and few ternary compounds. This relationship is represented by a linear function of $\text{x}{}^2\text{(x=}\text{ω}{}_{\mathrm{<mtext>LO</mtext>}}\text{ω}{}_{\mathrm{<mtext>TO</mtext>}}\text{)}$.     

Overtone bands of 14N16O and determination of molecular constants

The wavenumbers of the rotation-vibration lines of ¹⁴N¹⁶O are reported for the (2-0) and (3-0) bands. The full set of spectroscopic constants for the three bands (1-0), (2-0), and (3-0) has been determined with the method developed by Albritton, Schmeltekopf, and Zare for merging the results of separate least-squares fits. The vibrational constants ω_e, ω_ex_e, ω_ey_e, and the vibrational dependence of the rotational constants have been deduced. The apparent spin-orbit constant $\text{A}\text{?}{}_{\mathrm{<mtext>v</mtext>}}$ and its centrifugal correction $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext>}}$ (including the spin-rotation constant) have a vibrational dependence of the following form: $\text{A}\text{?}{}_{\mathrm{v}}\text{=}\text{A}\text{?}{}_{\mathrm{e}}\text{? α}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{) + γ}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{)}{}^2$ and $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>v</mtext>}}\text{=}\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>e</mtext>}}\text{? β}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{) + δ}{}_{\mathrm{A}}\text{(v +}\text{built+1}\text{2}\text{)}{}^2$; the values of the constants in these two equations have been determined.     

Devil's attractors and chaos of a driven impact oscillator

The motion of a driven elastic impact oscillator: $\text{x}\text{?}\text{+ 0.4}\text{x}\text{?}\text{+ x =}\text{cos}\text{(ωt)}$, x > 0 and $\text{x}\text{?}\text{(t}{}^{\mathrm{+}}\text{) = -}\text{x}\text{?}\text{(t}{}^{\mathrm{?}}\text{)}$ at x = 0, is studied for ω ≈ 2?4. The oscillator exhibits Feigenbaum's bifurcations (computed δ ≈ 4.70), the Feigenbaum and intermittent transitions to chaos, crises in chaos and a strong hysteresis region for ω ≈ 3.18–3.20 where the impact/period ratios of a group of attractors show the Devil's staircase behaviour with locking values between $\text{3}\text{5}$ and $\text{3}\text{4}$.     

A search for integrable two-dimensional hamiltonian systems with polynomial potential

We report the results of a search for all integrable hamiltonian systems of type $\text{H = (}\text{1}\text{2}\text{)p}{}_{\mathrm{x}}{}^2\text{+ (}\text{1}\text{2}\text{)p}{}_{\mathrm{y}}{}^2\text{+ V(x,y)}$, where V is a polynomial in x and y of degree 5 or less and the second invariant is a polynomial in p_x and p_y of order 4 or less. Both classical and quantum integrability are discussed.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Vector-axial vector interference terms in inelastic neutrino reactions extrapolated from single-pion photoproduction

By use of the generalized scaling sum rules the vector-axial vector interference terms in the scaling limit of the inelastic neutrino reactions are calculated from the absorptive parts of the single-pion photoproduction amplitudes at zero momentum transfer. The photoproduction amplitudes are evaluated by use of the results of multipole analysis. With the optimum values for the two parameters of the generalized scaling as determined in previous works, we have obtained F₃^νN(ω) which leads to good agreement with experiment in the ration of $\text{σ}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}\text{/σ}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}$. However, the zeroth moment in $\text{x( = 1/ω), ∫}{}_0{}^1\text{d}\text{x(F}{}_3{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{+ F}{}_3{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{)}$ turns out to be smaller than half of the value predicted in the fractionally charged quark model.     

Bi-solitons for a class of non-linear equations with quadratic non-linearity. I

We consider the class of non-integrable, non-linear equations,

$\text{L}{}_{\mathrm{q}}\text{K=K}{}^2\text{, L}{}_{\mathrm{q}}\text{=? +}\text{∑}\text{1?i+j?q}\text{aij?}{}^{\mathrm{i}}{}_{\mathrm{x}}{}^{\mathrm{i}}\text{?}{}^{\mathrm{j}}{}_{\mathrm{t}}{}^{\mathrm{j}}\text{, ?≠0,}$

in 1+1 dimensions. We seek rational solutions K(ω₁,ω₂), which we call bi-solitons, with exponential type variables ω_i = exp(γ_ix + ρ_it). In this paper, we restrict to q = 2 and 3, and investigate the general q case in the following paper. We find that these bi-solitons exist when the operator L_q (with ± ?) can be factorized as the product of smaller order differential operators. Besides the trivial factorized bi-solitons, we show that there exist non-trivial ones whenever K may be written as Σ^lmaxx ω^l₂F_l(Z = ω₁ + ω₂). In order to understand the origin of the factorization property, to any polynomial K = Σω^l₂F_l(Z) we associate a linear transformation such that L_qK has only the power ω^l₂ of K². For q = 2 and 3, we find that there exist particular polynomials of this type restraining L_q to be a product of smallr order operators. For the full non-linear equations we verify that all the bi-solitons can be obtained from these particular polynomials.     

Statistical flow-oscillator modeling of vortex-shedding

The very important engineering problem of modeling the fluid-structure interaction occurring during the shedding of vortices has defied, and will probably continue to defy, a closed form exact solution for the foreseeable future. Therefore, an attempt must be made to extract relevant information about the process in order to be able to have a basic understanding of it for the purpose of analysis. A useful method involves the flow-oscillator concepts of Hartlen and Currie [1] redefined here for stochastic processes. The fluid-structure system is assumed to be governed by the cross-coupled equations

$\text{x}\text{?}\text{(t)+2ξω}{}_{\mathrm{n}}\text{x}\text{?}\text{(t)+ω}{}^2{}_{\mathrm{n}}\text{=C}{}_{\mathrm{e}}\text{(t)pV}{}^2{}_0\text{(t)DL/2m (i)}$

$\text{C}\text{?}{}_{\mathrm{e}}\text{(t)+{α ? βC}{}^2{}_{\mathrm{e}}\text{(t)+γC}{}^4{}_{\mathrm{e}}\text{(t)}}\text{C}\text{?}{}_{\mathrm{e}}\text{(t)+ω}{}^2{}_0\text{C}{}_{\mathrm{e}}\text{(t)=b}\text{x}\text{?}\text{(t), (ii)}$

where these equations govern the structure and fluid oscillators, respectively. The fluid damping is non-linear. These equations are taken as stochastic differential equations because of the many unpredictable, random effects that determine the loading and response. The lift coefficient C_$\text{l}$(t) is assumed to be a zero mean, narrow band process and the velocity V₀, composed of a uniform, constant velocity current plus oscillating wave, a broad band process. The analysis is based on solving equation (i) for x(t) by using Duhamel's integral and substituting its derivative $\text{x}\text{?}\text{(t)}$ into equation (ii). This equation is then used to derive the Fokker-Planck equation for the process C_$\text{l}$(t). To obtain the Fokker-Planck equation, slowly varying variables are replaced by their long-time averages [2] and then the method of stochastic averaging is employed [3, 4]. The moment equation for the lift-oscillator process is derived from the Fokker-Planck equation and, as equation (ii) is non-linear, one finds the moment equation to be in terms of higher order moments. A truncation scheme [5] is used to derive the moment generating function. It is possible then to generate the first and second order statistics of the lift coefficient and the structure response in terms of the empirical parameters of fluid damping. This work was carried out in conjunction with an analysis of ocean wave-current forces with application to offshore fixed structures [6].     

Moments of two-time spin-pair correlation functions for a one-dimensional anisotropic Heisenberg model at infinite temperature

The first ten moments of the infinite-temperature space and frequency dependent two-spin correlation functions, $\text{?}{}^{\mathrm{x}}{}_{\mathrm{r}}\text{(ω)}$ and $\text{?}{}^{\mathrm{z}}{}_{\mathrm{r}}\text{(ω)}$ are obtained for the one-dimensional anisotropic Heisenberg model for r = 0 and r = 1. These are compared with those previously known.     

The A′(3Π2) state of ICl

Although $\text{A′(}{}^3\text{Π}{}_2\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$ is forbidden in near case c molecules the A′ ← X transition can be efficiently accomplished by the three-step sequence $\text{A′(}{}^3\text{Π}{}_2\text{) ← D′(2) ← A(}{}^3\text{Π}{}_1\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$. Transitions to a range of levels of A′, v_A′ = 2–38, have been recorded by this means, using J-selective polarization-labeling spectroscopy. Principal constants of the A′ state of I³⁵Cl are T_e = 12682.05, ω_e = 224.57, ω_eχ_e = 1.882, ω_ey_e = ?0.0107, B_e = 0.08653, and α_e = 0.000675 cm^?1. The A′ state is therefore similar in its physical characteristics to two other (relatively) deep states, $\text{A(}{}^3\text{Π}{}_1\text{)}$ and $\text{B(}{}^3\text{Π}{}_0\text{+)}$, of the 2431 configuration.     

Quantum theory of longitudinal dielectric response properties of a two-dimensional plasma in a magnetic field

An analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a two-dimensional thermal Green's function for electron propagation in a magnetic field developed in closed form. The longitudinal-electrostatic plasmon dispersion relation is discussed in the low wavenumber regime with nonlocal corrections, and Bernstein mode structure is studied for arbitrary wavenumber. All regimes of magnetic field strength and statistics are investigated. The class of integrals treated here should have broad applicability in other two-dimensional and finite slab plasma studies.The two-dimensional static shielding law in a magnetic field is analyzed for low wavenumber, and for large distances we find $\text{V(}\text{r}\text{) ～}\text{Q}\text{k}{}_0{}^2\text{r}{}^3$. The inverse screening length $\text{k}{}_0\text{=}\text{2πe}{}^2\text{??}\text{?ξ}$ (? = density, ξ = chemical potential) is evaluated in all regimes of magnetic field strength and all statistical regimes. k₀ exhibits violent DHVA oscillatory behavior in the degenerate zero-temperature case at higher field strengths, and the shielding is complete when $\text{ξ = r′}\text{l}\text{z.shtsls;}\text{ω}$, but there is no shielding when $\text{ξ ≠ r′}\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}$. A careful analysis confirms that there is no shielding at large distances in the degenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> ξ}$. Since shielding does persist in the nondegenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> KT}$, there should be a pronounced change in physical properties that depend on shielding if the system is driven through a high field statistical transition. (It should be noted that the static shielding law of semiclassical and classical models has no dependence on magnetic field in two dimensions, as in three dimensions.) Finally, we find that the zero field two-dimensional Freidel-Kohn “wiggle” static shielding phenomenon is destroyed by the dispersal of the zero field continuum of electron states into the discrete set of Landau-quantized orbitals due to the imposition of the magnetic field.     

Long time expansion of two-dimensional correlation functions

We show that the long time behaviour of the velocity correlation function in a two-dimensional classical system with pairwise repulsive potentials can be represented by a series expansion of the form

$\text{〈υ}{}_{\mathrm{1x}}\text{υ}{}_{\mathrm{1x}}\text{(t)〉 = d}{}_0\text{t}{}^{\mathrm{?1}}\text{+ d}{}_1\text{t}{}^{\mathrm{?1}}\text{log}\text{t/t}{}_0\text{+ d}{}_2\text{t}{}^{\mathrm{?1}}\text{(}\text{log}\text{t/t}{}_0\text{)}{}^2\text{+ …}$

, where t₀ is mean free time between collisions. To lowest order in the density an exact expression has been obtained for d₁ employing the kinetic theory ofsystems with hard-core interactions. The significance of the series is discussed at low and intermediate densities.     

Theory of the decay process of metastable state

The short-time and long-time behavior of the distribution function P(x, t) are investigated in the laser model by using the generating function $\text{G(α,}\text{β}\text{;t) = σ(α-y(t)) Π}{}^{\mathrm{\infty }}{}_{\mathrm{n=2}}\text{σ(β}{}_{\mathrm{n}}\text{- M}{}_{\mathrm{n}}\text{(t)),}\text{where}\text{y(t)  ?xP(x, t)}\text{d}\text{x}\text{and}\text{M}{}_{\mathrm{n}}\text{(t)  ?(x - y(t))}{}^{\mathrm{n}}\text{P(x,t)}\text{d}\text{x}$.     

Mixed electrical conduction in Ce1−xCaxO2−x

The solid electrolyte Ce_1?xCa_xO_2-?x with the fluorite-type structure (Ca-doped CeO₂) is a mixed conductor. Conduction occurs predominantly by migration of O^2? ions via oxygen vacancies or by electrons, depending on the departure from stoichiometry. The ionic transference number σ_i/σ_i + σ_e was determined as a function of dopant concentration (0.07?x?0.15), temperature (400–800°C), and oxygen pressure by emf measurements with oxygen concentration cells. It is described by

The entropy term S¹(x) changes from 38.7k for x = 0.07 to 31.7k for x = 0.15; the enthalpy term, 5.42 eV, is independent of x and in excellent accord with semi-empirical calculations.     

The emission spectrum of SeO in the far ultraviolet

The emission spectrum of SeO in the far ultraviolet first observed by Haranath (1) at low dispersion has been photographed in the region 2480-1930 Å under medium resolution and a reanalysis of the vibrational structure of the bands has been presented. Beginning at the longer wavelength end, the spectrum has been analyzed into five band systems which are designated as $\text{c(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)-b(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$, x₂-x₁, y₂-y₁, $\text{C(}{}^3\text{Π}\text{)-X}{}^3\text{Σ}{}^{\mathrm{?}}$, and $\text{D(}{}^3\text{Σ}{}^{\mathrm{?}}\text{)-X}{}^3\text{Σ}{}^{\mathrm{?}}$. The lower state of the c-b system is found to be the upper state of the $\text{b(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)-X}{}^3\text{Σ}{}^{\mathrm{?}}$ system observed recently by us (2). The derived constants in cm^?1 for SeO are as follows (the constants of the b state are those derived from Ref. 2).

     

17.

Charge density wave commensurability in 2H-TaS₂ and Ag_xTaS₂     

G.A. Scholz  O. Singh  R.F. Frindt  A.E. Curzon 《Solid State Communications》1982,44(10):1455-1459

The charge density wave transition in 2H-TaS₂near 75 K has been observed to be incommensurate, using electron diffraction, with $\text{q}{}^1\text{= (}\text{0.338}\text{±}\text{0.002}\text{)a}{}^1{}_0$ along the 〈10.0〉 directions which, within the experimental uncertainty, remains temperature independent to about 14 K. Incommensurate charge density formation is also observed in Ag_xTaS₂ samples for $\text{x?}\text{0.26}$ with an increase in q¹ to $\text{(}\text{0.347}\text{±}\text{0.002}\text{)a}{}^1{}_0$ when x?0.26. Within the experimental error q¹ appears to be temperature independent to 25 K.     

18.

Singular perturbation potentials     

Evans M. Harrell 《Annals of Physics》1977,105(2):379-406

This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrödinger operators of the form ?Δ + A + λV, defined on the Hilbert space L²(Rⁿ), where $\text{Δ = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{n}}\text{?}{}^2\text{?X}{}_{\mathrm{i}}{}^2$, A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, $\text{?d}{}^2\text{dx}{}^2\text{+ x}{}^2\text{+}\text{l(l + 1)}\text{x}{}^2\text{+ λ|x|}{}^{\mathrm{?\alpha }}$, where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrödinger perturbative correction, (u₀, Vu₀), where u₀ is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.     

19.

Polariton modes at the interface between two conducting or dielectric media     

P. Halevi 《Surface science》1978,76(1):64-90

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

20.

Electron exchange between Fe²⁺ and Fe³⁺ ions on octahedral sites in spinels studied by means of paramagnetic Mössbauer spectra and susceptibility measurements     

F.K. Lotgering  A.M.Van Diepen 《Journal of Physics and Chemistry of Solids》1977,38(6):565-572

Mössbauer spectra were obtained of the paramagnetic spinels $\text{Zn}{}^{\mathrm{2+}}\text{|}\text{Zn}{}^{\mathrm{2+}}{}_{\mathrm{<mtext>(1?x)</mtext><mtext>2</mtext>}}\text{Ti}{}^{\mathrm{4+}}{}_{\mathrm{<mtext>(1+x)</mtext><mtext>2</mtext>}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>(1?</mtext><mtext>x)</mtext>}}\text{Fe}{}^{\mathrm{2+}}{}_{\mathrm{x}}\text{|}\text{O}{}_4$ and susceptibilities were measured. The strong difference between the paramagnetic Fe²⁺ and Fe³⁺ spectrum, due to the different quadrupole splitting, is used for the distinction between the two species. At 300 K a superposition of the Fe³⁺ and the Fe²⁺ spectra is found for most of the iron and, in addition, some continuous absorption. The latter is strongest for equal Fe³⁺ and Fe²⁺ concentration $\text{(x =}\text{1}\text{2}\text{)}$ while it disappears towards the end members (Fe³⁺ only or Fe²⁺ only) as well as with decreasing temperature (between 78 and 200 K). From this it is concluded that it arises from thermally activated electron exchange, the frequency of which passes a “critical” value of ～10⁸ sec^?1 for increasing temperature. Paramagnetic susceptibilities are found to obey a Curie-Weiss law down to low temperatures. From the dependence of the asymptotic Curie temperature on the composition the magnetic interaction parameters J₁₁ = ?1.4 K, J₂₂ = ?3.3 K and J₁₂ = + 1.6 K for the Fe³⁺Fe³⁺, Fe²⁺Fe²⁺ and Fe³⁺Fe²⁺ interactions are derived. The experimental results are discussed in terms of a hopping model with an activation energy q ～- 0.12eV and a non-equivalence of the octahedral sites expressed by a varying potential energy difference U₀ between neighbouring sites. The continuous absorption at 300 K for $\text{x =}\text{1}\text{2}$ is attributed to about 17% of the iron on sites with U₀ running from 0 to ??0.06 eV. The ferromagnetic Fe³⁺, Fe²⁺ interaction (J₁₂) is attributed to electron transfer from localized Fe²⁺ ions to Fe³⁺ neighbours via a transfer integral b of the order of 0.05 eV. The magnitudes of J₁₂ and b are tentatively explained.     

State	$\text{T}{}_{\mathrm{e}}$	$\text{ω}{}_{\mathrm{e}}$	$\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}$	λ
$\text{y}{}_2$	$\text{y}{}_1\text{+ 47830}$	974	6.0
$\text{y}{}_1$	$\text{y}{}_1$	906	21.0
$\text{x}{}_2$	$\text{x}{}_1\text{+ 46009}$	993	2.0
$\text{x}{}_1$	$\text{x}{}_1$	877	8.0
$\text{c(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$	53080	954	13.0
$\text{D(}{}^3\text{Σ}{}^{\mathrm{?}}\text{)}\text{F}{}_2$	51422	955	9.3
F1	51356	955	8.5	～36
$\text{C(}{}^3\text{Π}\text{)}$	50873	1034	9.3
$\text{b(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$	9570.7	834.9	5.5

Charge density wave commensurability in 2H-TaS2 and AgxTaS2

The charge density wave transition in 2H-TaS₂near 75 K has been observed to be incommensurate, using electron diffraction, with $\text{q}{}^1\text{= (}\text{0.338}\text{±}\text{0.002}\text{)a}{}^1{}_0$ along the 〈10.0〉 directions which, within the experimental uncertainty, remains temperature independent to about 14 K. Incommensurate charge density formation is also observed in Ag_xTaS₂ samples for $\text{x?}\text{0.26}$ with an increase in q¹ to $\text{(}\text{0.347}\text{±}\text{0.002}\text{)a}{}^1{}_0$ when x?0.26. Within the experimental error q¹ appears to be temperature independent to 25 K.     

Singular perturbation potentials

This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrödinger operators of the form ?Δ + A + λV, defined on the Hilbert space L²(Rⁿ), where $\text{Δ = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{n}}\text{?}{}^2\text{?X}{}_{\mathrm{i}}{}^2$, A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, $\text{?d}{}^2\text{dx}{}^2\text{+ x}{}^2\text{+}\text{l(l + 1)}\text{x}{}^2\text{+ λ|x|}{}^{\mathrm{?\alpha }}$, where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrödinger perturbative correction, (u₀, Vu₀), where u₀ is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

Electron exchange between Fe2+ and Fe3+ ions on octahedral sites in spinels studied by means of paramagnetic Mössbauer spectra and susceptibility measurements

Mössbauer spectra were obtained of the paramagnetic spinels $\text{Zn}{}^{\mathrm{2+}}\text{|}\text{Zn}{}^{\mathrm{2+}}{}_{\mathrm{<mtext>(1?x)</mtext><mtext>2</mtext>}}\text{Ti}{}^{\mathrm{4+}}{}_{\mathrm{<mtext>(1+x)</mtext><mtext>2</mtext>}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>(1?</mtext><mtext>x)</mtext>}}\text{Fe}{}^{\mathrm{2+}}{}_{\mathrm{x}}\text{|}\text{O}{}_4$ and susceptibilities were measured. The strong difference between the paramagnetic Fe²⁺ and Fe³⁺ spectrum, due to the different quadrupole splitting, is used for the distinction between the two species. At 300 K a superposition of the Fe³⁺ and the Fe²⁺ spectra is found for most of the iron and, in addition, some continuous absorption. The latter is strongest for equal Fe³⁺ and Fe²⁺ concentration $\text{(x =}\text{1}\text{2}\text{)}$ while it disappears towards the end members (Fe³⁺ only or Fe²⁺ only) as well as with decreasing temperature (between 78 and 200 K). From this it is concluded that it arises from thermally activated electron exchange, the frequency of which passes a “critical” value of ～10⁸ sec^?1 for increasing temperature. Paramagnetic susceptibilities are found to obey a Curie-Weiss law down to low temperatures. From the dependence of the asymptotic Curie temperature on the composition the magnetic interaction parameters J₁₁ = ?1.4 K, J₂₂ = ?3.3 K and J₁₂ = + 1.6 K for the Fe³⁺Fe³⁺, Fe²⁺Fe²⁺ and Fe³⁺Fe²⁺ interactions are derived. The experimental results are discussed in terms of a hopping model with an activation energy q ～- 0.12eV and a non-equivalence of the octahedral sites expressed by a varying potential energy difference U₀ between neighbouring sites. The continuous absorption at 300 K for $\text{x =}\text{1}\text{2}$ is attributed to about 17% of the iron on sites with U₀ running from 0 to ??0.06 eV. The ferromagnetic Fe³⁺, Fe²⁺ interaction (J₁₂) is attributed to electron transfer from localized Fe²⁺ ions to Fe³⁺ neighbours via a transfer integral b of the order of 0.05 eV. The magnitudes of J₁₂ and b are tentatively explained.