Analysis of the 2770-Å emission system in I2

A weak emission spectrum of I₂ near 2770 Å is reanalyzed and found to to minate on the A(1u³Π) state. The assigned bands span v″ levels 5–19 and v′ levels 0–8. The new assignment is corroborated by isotope shifts, band profile simulations, and Franck-Condon calculations. The excited state is an ion-pair state, probably the 1g state which tends toward $\text{I}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{I}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_1\text{)}$. In combination with other results for the A state, the analysis yields the following spectroscopic constants: T″_e = 10 907 cm^?1, $\text{D}$″_e = 1640 cm^?1, ω″_e = 95 cm^?1, $\text{R″}{}_{\mathrm{e}}\text{= 3.06}\text{A}\text{?}$; T′_e = 47 559.1 cm^?1, ω′_e = 106.60 cm^?1, $\text{R′}{}_{\mathrm{e}}\text{= 3.53}\text{A}\text{?}$.     

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.     

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.     

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].     

Surface hydroxylation at a Zn(0001)O surface

We report the investigation of the hydroxylation of a Zn(0001)O surface by water vapour using both valence and core level spectroscopies. Hydroxylation is induced by pre-exposure of the Zn(0001) surface to oxygen and occurs in the temperature range 80–200 K. Dehydroxylation is observed above 250K in two steps: $\text{OH}{}^{\mathrm{?}}\text{(a)→o}{}^{\mathrm{?}}\text{(a)+}\text{1}\text{2}\text{H}{}_2\text{(g)}$ followed by O^?(a) → O^2?(b).     

Transition magnetic moments of hadrons and sidewise dispersion relations

Systems of linear relations for the magnetic moments of the nucleon and transition moments μ_ωπγ, μ_?πγ and ${}^{\mathrm{\mu }}\text{N}{}^1{}_{1470}\text{N}\text{γ}$ are obtained on the basis of sidewise dispersion relations in the one-pion approximation. In such an approach the magnetic moments of the transition ω(?)→ πγ and $\text{N}{}^1{}_{1470}\text{→Nγ}$ are expressed in terms of the anomalous magnetic moments of the nucleon and the strong interaction coupling constants.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Multiplicities in lepton-hadron processes

The average multiplicity in deep inelastic electro- and neutrinoproduction at large ω(ω～s/Q² + 1) is related in Feynman's version of the parton model to the average multiplicities in high-energy electron-positron annihilation and hadron-hadron scattering. The relation is: , where C_e⁺e^? and C_h are, respectively, the coefficients of ln(s/M_1⊥²) in the multiplicities from e⁺-e^? and P-P in to hadrons, and M_1⊥ is an average transverse mass.     

Photoemission loss spectra of metals with emergence parallel to the surface

A theory is presented for the energy loss spectra of photoelectrons emitted from atoms located outside a metal sample at a distance z₀ from the surface. These electrons travelling along trajectories parallel to the surface, loss energy mostly by surface plasmon excitation, the losses by bulk plasmon or pair excitations being negligible. The intensity of losses by surface plasmon excitations is found to be proportional to the logarithm of the length l of the trip of the photoelectrons along the surface, a length which extends from the emitting atom to the surface edge. But this intensity does not depend on the distance z₀ as long as z₀/l small. Considering only the high energy photoemission where the initial energy ?₀ of the electrons is much larger than the surface plasmon energy ω_s, we find that these l-dependent losses only occur when the angle of emergence is smaller than $\text{(ω}{}_{\mathrm{s}}\text{/?}{}_0\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and peak strongly when this angle is smaller than ω_s/2?₀. An experiment with appropriate parameters is proposed to verify the principal results of our theory. Further investigation will yield interesting information on the surface plasmon structure, e.g. the dispersion rule.     

Observation of muon pairs in neutrino interactions at Serpukhov 70 GeV accelarator

A search for dimuons produced in a spark chamber experiment in neutrino and antineutrino beams of the Serpukhov accelerator is reported. The clear dimuon signal has been observed in vN interactions. R_v = N(2ω)/N(1ω)? (6.2 ± 1.7) × 10^?3 in the energy interval 7.5 ÷ 30 GeV. From antineutrino data we conclude that in the same energy range $\text{R}{}_{\mathrm{<mtext>v</mtext>}}\text{? 1.1. × 10}{}^{\mathrm{?2}}\text{(90\% C.L.)}$.     

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.     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

Critical spin relaxation in GdCl3

In the critical region of the insulating, uniaxial ferromagnet GdCl₃ the real part of the uniform susceptibility χ(q = 0, ω; T) has been measured by means of a frequency counting method in the ranges $\text{1.7 MHz ?}\text{ω}\text{2π}\text{? 720 MHz, 0.003 ? (}\text{T}\text{T}{}_{\mathrm{c}}\text{? 1 ≡ ?) ? 0.5}$. Parallel to the easy direction at all temperatures, χ′(ω) has a lorentzian shape, its amplitude being equal to the static susceptibility, χ_T. The half-widths τ^?1 exhibit s critical slowing down: above ?_c = 0.03 they are proportional to χ^?1_T, while at ?_c a change-over to $\text{τ}{}^{\mathrm{?1}}\text{∝ χ}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{T}}$ occurs, the origin of which is uncertain.     

Central peak in polaronic crystals

A possibility of the central peak appearance in crystals with low concentration of small-radius polarons is pointed out. The intensity of the central peak increases sharply with the softening of the phonon mode $\text{(ω}{}_{\mathrm{<mtext>K</mtext><mtext>0</mtext>}}\text{→ 0)}$ in the vicinity of the structural phase transition . The peak width γ₀ is determined by the probability W of the polaron hopping between the sites γ₀ = K₀²a²W.     

On the electronic spectrum of the Mo2 molecule observed after flash photolysis of Mo(CO)6

Absorption and emission spectra of Mo₂ were investigated using flash photolysis of the Mo(CO)₆ molecule. Tentative vibrational and rotational analyses of the ⁹⁸Mo₂ spectra were performed. For the ground state, ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ type was proposed with ω_e = 477.1 cm^?1, $\text{r}{}_{\mathrm{e}}\text{= 1.929}\text{A}\text{?}$, and D₀(Mo₂) = 95 ± 15 kcal mole^?1. The results were compared with theoretical calculations for Mo₂ and experimental results for Cr₂ obtained previously. It seems reasonable that the transition metal diatomic molecules of this type have a high bond order.     

The ã3A2 ← X̃1A1 absorption spectrum of thioformaldehyde: A vibrational and rotational analysis

The results of a vibrational and rotational analysis of the banded $\text{a}\text{?}{}^3\text{A}{}_2\text{←}\text{X}\text{?}{}^1\text{A}{}_1$ transition in $\text{CH}{}_2\text{S}\text{CD}{}_2\text{S}$ are presented. Only three of the six vibrational modes are active in the spectrum with $\text{ν′}{}_2\text{=}\text{1320}\text{1012}$, $\text{ν′}{}_3\text{=}\text{859}\text{798}$, and $\text{2ν′}{}_4\text{=}\text{711}\text{516}\text{cm}{}^{\mathrm{?1}}$. The spin forbidden transition gains intensity primarily by a mixing of the ${}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$ and ${}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. This is confirmed by a rotational analysis of the 0₀⁰ band of both isotopes. The rotational analysis shows that the coupling in the $\text{a}\text{?}{}^3\text{A}{}_2$ state is near Hund's case b and that the spin constants are nearly 10 times greater than those observed for CH₂O. A $\text{CNDO}\text{2}$ calculation shows that this difference is due to the greater spin orbit coupling of S in CH₂S and to the smaller energy differences between the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{b}\text{?}{}^3\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{X}\text{?}{}^1\text{A}{}_1$, and the $\text{a}\text{?}{}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. The r₀ structure calculated from the rotational constants is $\text{r}{}_{\mathrm{<mtext>CS</mtext>}}\text{= 1.683}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>CH</mtext>}}\text{= 1.082}\text{A}\text{?}$, β_HCH = 119.6°, and α (out of plane) = 16.0°. A simultaneous fit of the vibrational levels in ν′₄ of CH₂S and CD₂S to a double minimum potential function yielded a barrier to molecular inversion of 13 cm^?1 and an equilibrium out-of-plane angle of 15°.     

The ultraviolet absorption spectrum of thioformaldehyde

The spectra of H₂CS and D₂CS were surveyed over the wavelength region from 230 to 180 nm and four distinct absorptions were identified. These are assigned to transitions from the $\text{X}\text{?}{}^1\text{A}{}_1$ ground state to the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π, π}{}^1\text{)}$, $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$, $\text{D}\text{?}{}^1\text{A}{}_1\text{(n, 3p}{}_{\mathrm{y}}\text{)}$, and $\text{E}\text{?}{}^1\text{B}{}_2\text{(n, 3p}{}_{\mathrm{z}}\text{)}$ electronic states. A vibrational and rotational analysis of the second system was undertaken. The results indicate that the molecule is planar in the $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$ state and that while the CH and CS bond lengths remain near their ground-state values, the HCH angle increases substantially.     

Excited vibrational state microwave spectra,structure, and force-field of trifluorosilane

The J = 2?1 microwave spectrum of six isotopic species of HSiF₃ has been observed and assigned in excited states of five of the six fundamental vibrations. The assignment is based on relative intensities, double resonance experiments, and trial anharmonic force constant calculations. Analysis of the spectra leads to experimental values for five of the $\text{α}{}_{\mathrm{r}}{}^{\mathrm{B}}$ constants, all three l-doubling constants q_t, one Fermi resonance constant φ₂₃₃, and one zeta constant $\text{ζ}{}_{\mathrm{6,\; 6}}{}^{\mathrm{(z)}}$.The harmonic force field has been refined to all the available data on vibration wavenumbers, centrifugal distortion constants, and zeta constants. The cubic anharmonic force field has been refined to the data on $\text{α}{}_{\mathrm{r}}{}^{\mathrm{B}}$ and q_t constants, using two models: a valence force model with two cubic force constants for SiH and SiF stretching, and a more sophisticated model. With the help of these calculations, the following equilibrium structure has been determined: $\text{r}{}_{\mathrm{e}}\text{(}\text{SiH}\text{) = 1.4468(±5)}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(}\text{SiF}\text{) = 1.5624(±1)}\text{A}\text{?}$, ∠HSiF = 110.64(±3)°,     

Classical integrable finite-dimensional systems related to Lie algebras

During the last few years many dynamical systems have been identified, that are completely integrable or even such to allow an explicit solution of the equations of motion. Some of these systems have the form of classical one-dimensional many-body problems with pair interactions; others are more general. All of them are related to Lie algebras, and in all known cases the property of integrability results from the presence of higher (hidden) symmetries. This review presents from a general and universal viewpoint the results obtained in this field during the last few years. Besides it contains some new results both of physical and mathematical interest.The main focus is on the one-dimensional models of n particles interacting pairwise via potentials V(q) = g²ν(q) of the following 5 types: $\text{ν}{}_{\mathrm{<mtext>I</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{, ν}{}_{\mathrm{<mtext>II</mtext>}}\text{(q)=a}{}^{\mathrm{?2}}\text{sinh}{}^2\text{(aq), ν}{}_{\mathrm{<mtext>III</mtext>}}\text{(q)=a}{}^2\text{/}\text{sin}\text{2(aq), ν}{}_{\mathrm{<mtext>IV</mtext>}}\text{=a}{}^2\text{P}\text{(aq), , ν}{}_{\mathrm{<mtext>V</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{+ω}{}^2\text{q}{}^2$. Here $\text{P}$(q) is the Weierstrass function, so that the first 3 cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbor potential, g_j²exp[-a(q_j?q_j+1)], is moreover considered. Various generalizations of these models, naturally suggested by their association with Lie algebras, are also treated.     

Activation energy of field emission flicker noise power due to adsorbed potassium on tungsten

The temperature dependence of the field emission flicker noise spectral density functions has been investigated for potassium adsorbed on tungsten (112) planes by a probe hole technique. By integration of the spectral density functions $\text{W(?) = B}{}_{\mathrm{i}}\text{?}{}^{\mathrm{?ge}}\text{i}$ the noise power $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ for different frequency intervals Δ? is obtained. From the exponential temperature dependence of $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ noise power “activation energies” q_Δ? are determined. Plots of these energies versus coverage show a similar “oscillating” behaviour as recently found for $\text{W(?}{}_{\mathrm{j}}\text{)}$ or which indicates phase transitions of the adsorbed potassium submonolayers. The noise activation energies are discussed in terms of existing models and a comparison is made between the experimental q values and surface diffusion energies E_d as determined by conventional methods.