A Landau theory of the Peierls-BCS transition

We introduce a Landau type theory of the Peierls instability-superconductor transition involving two complex order parameters. Under a particular inequality condition among expansion parameters, the theory predicts that the superfluid conductivity should vary as $\text{(T?T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ above the critical region and as $\text{(T}{}^1{}_{\mathrm{<mtext>c</mtext>}}\text{?T)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ below the critical region.     

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.     

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.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

Chemical diffusion in nonstoichiometric chromium sulfide,Cr2+yS3

Using the re-equilibration kinetic method the chemical diffusion coefficient in nonstoichiometric chromium sesquisulfide, Cr_2+yS₃, has been determined as a function of temperature (1073–1373 K) and sulphur vapour pressure (10?10⁴ Pa). It has been found that this coefficient is independent of sulphur pressure and can be described by the following empirical equation: $\text{D}\text{?}\text{Cr}{}_{\mathrm{2+y}}\text{S}{}_3\text{=50.86}\text{exp(-39070 cal/mole/}\text{RT)}\text{(cm}{}^2\text{s}{}^{\mathrm{?1)}}$. It has been shown that the mobility of the point defects inCr_2+yS₃ is independent of their concentration and that the self-diffusion coefficient of chromium in this sulfide has the following function of temperature and sulphur pressure: . (cm²s^?1).     

Dispersion sum rules for the amplitudes of radiative transitions in quarkonium

A dispersion approach is suggested, based on the asymptotic freedom in QCD and on analyticity, which leads to sum rules for the amplitudes of radiative transitions in quarkonium $\text{(}\text{c}\text{c}\text{,}\text{b}\text{b}\text{, …)}$ and allows one to estimate these amplitudes in a model-independent way. As an example such sum rules are derived for the ${}^3\text{P}{}_0\text{?}{}^3\text{S}{}_1$ and ${}^3\text{S}{}_1\text{?}{}^1\text{S}{}_0$ transitions. For charmonium they agree with the available data and with the predictions of nonrelativistic models.     

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     

Generalized renormalization group equation for period-doubling bifurcations

Given a mapping $\text{x → ?(λ,x)}$, whose bifurcation points accumulate at λ = Λ_∞, it is shown that the iterates $\text{(?α)}{}^{\mathrm{p\times }}\text{[?}{}^{\mathrm{2p}}\text{(Λ}{}_{\mathrm{\infty }}\text{?μ/δ}{}^{\mathrm{p}}\text{, X}{}_{\mathrm{\infty }}\text{+y/(?α)}{}^{\mathrm{p}}\text{)?X}{}_{\mathrm{\infty }}\text{]}$ converge to a function ψ(μ,y)asp→∞, where X_∞ maximizes $\text{?(Λ}{}_{\mathrm{\infty ,x}}\text{)}$. The function ψ is universal up to scaling in μ and y, and satisfies ψ(μ/δ,ψ(μ/δ,?y/α)) = ?α^?1ψ(μ,y). This result generalizes the well-known Feigenbaum universal function g(y) with g(g(?y/α)) = ?g(y/α, which is the special case for μ = 0.     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.     

Separability of an integrable case of the Henon-Heiles system

It is shown here that the Hénon-Heiles hamiltonian $\text{H =}\text{1}\text{2}\text{(}\text{x}\text{?}{}^2\text{+}\text{y}\text{?}{}^2\text{+ ω}{}_1\text{x}{}^2\text{+ ω}{}_2\text{y}{}^2\text{) + a(x}{}^2\text{y + 2y}{}^3\text{)}$ is separable in the shifted parabolic coordinates and the solution of the Hamilton-Jacobi equation is expressible in terms of hyperelliptic integrals.     

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].     

Stark effect in the torsio-rotational spectrum of propargyl mercaptan and SH bond moment determination

The Stark effect of rotational and torsio-rotational transitions of propargyl mercaptan has been analyzed. Assuming a dependence of the dipole moment components on the internal rotation angle of the type: $\text{μ}{}_{\mathrm{a}}\text{= μ}{}_{\mathrm{a}}{}^0\text{+ μ}{}_{\mathrm{a}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, $\text{μ}{}_{\mathrm{b}}\text{= μ}{}_{\mathrm{b}}{}^0\text{+ μ}{}_{\mathrm{b}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, and $\text{μ}{}_{\mathrm{c}}\text{= μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{sin}\text{α}$, the following values of the determinable quantities were obtained: $\text{μ}{}_{\mathrm{a}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.718 ± 0.003}\text{D}$, $\text{μ}{}_{\mathrm{b}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.495 ± 0.010}\text{D}$, and $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{= 0.809 ± 0.015}\text{D}$.The SH bond moment was also evaluated from $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}$ and compared with the SH bond moment of similar molecules.     

Density of states in dirty type II superconductors near Tc

We have determined the behavior of the density of states in the mixed state of superconducting alloys for T → T_c. The local density of states tends towards the BCS expression with the order parameter playing the role of the energy gap. The singularities are smeared out by the spatial average. The effective normal core radius of a vortex diverges like $\text{(1 ?}\text{T}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ for T → T_c unlike the coherence length which diverges like $\text{(1 ?}\text{T}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$.     

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.     

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.     

Two theorems on the level order in potential models

We study the potentials of the form U(r)=?r^?1+λV(r), $\text{(}\text{d}\text{d}\text{r}\text{)(}\text{r}{}^2\text{d}\text{V}\text{d}\text{r}\text{)?0}$, and show that the energy levels satisfy the inequalities $\text{E(N}{}_{\mathrm{c}}\text{, l)?E(N}{}_{\mathrm{c}}\text{, l+1)}$ to first order in λ, where N_c denotes the coulombic principal quantum number and l the angular momentum. Similarly for potentials $\text{U(r)=r}{}^2\text{+λV(r), (}\text{d}\text{d}\text{r}{}^2\text{)}{}^2\text{V(r)?0}$, we prove to first order in λ that $\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{)?}\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{+2)}$, where NH denotes the harmonic oscillator quantum number. In the latter case, we give also quantitative restrictions on the relative positions at the lth and (l+1)th states.     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

CP violation induced by penguin diagrams and the neutron electric dipole moment

In the Kobayashi-Maskawa model, penguin diagrams can induce CP violating phases in matrix elements of the type n→Λ. This produce a neutron electric dipole moment through subsequent parity violating radiative weak decay Λ→nγ. We can expect $\text{(}\text{D}{}_{\mathrm{<mtext>n</mtext>}}\text{e}\text{)?10}{}^{\mathrm{?30}}\text{cm}$, three to four orders of magnitude bigger than the mechanism based on the transition quark electric dipole moment. The reason is essentially that the GIM cancellation comes in the Penguin case from $\text{(}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{π}\text{)}\text{log}\text{m}{}^2{}_{\mathrm{<mtext>t</mtext>}}\text{m}{}^2{}_{\mathrm{<mtext>c</mtext>}}\text{abd not from}\text{π}{}^{\mathrm{?2}}\text{(m}{}^2{}_{\mathrm{<mtext>t</mtext>}}\text{?m}{}^2{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{M}{}^2{}_{\mathrm{<mtext>W</mtext>}}$ as for the transition quark electric dipole moment.     

On the sound absorption in ferrodielectrics

The damping of the sound waves in ferromagnets due to the phonon-magnon interaction is considered for the temperature $\text{θ}{}_{\mathrm{c}}\text{(}\text{μM}{}_0\text{4}\text{7θ}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>4</mtext><mtext>7</mtext>}}\text{? T ?}\text{θ}{}^2{}_{\mathrm{D}}\text{4}\text{7θ}{}_{\mathrm{c}}$ and frequency τ^?1_m-ph ? ω ? τ^?1_m ranges. This damping is found to be greater than the Landau-Rumer one due to the anharmonic interactions in the crystal. The Akhiezer's method for the calculation of the sound damping is shown to be valid for the more wide frequency range than it was regarded earlier.     

The anharmonic force field of phosphorus trifluoride from the millimeter wave spectra of vibrationally excited states

The millimeter rotational spectra of PF₃ have been recorded for all four excited fundamental vibrational states. A coriolis resonance between ν₁ and ν₃ results in anomalous distortion constants for these states and can be analyzed to yield $\text{|ζ}{}_{13}{}^{\mathrm{y}}\text{| = 0.392}$. The value of $\text{ζ}{}_{33}{}^{\mathrm{c}}$ is found to be 0.4194 which does not fit the coriolis sum rule due to anharmonic resonance. Equilibrium values for the centrifugal distortion constants are determined and have been used to find the harmonic force field. All available data is used to determine some of the anharmonic force constants.