Electron-longitudinal-phonon coupling in a transition metal: Ta

Recent tunneling studies of tantalum using a proximity technique reveal stronger coupling to the longitudinal modes relative to the transverse modes than observed previously for any transition metal. This result has implications for modeling the electron-phonon coupling mechanism and for future tunneling investigations. We obtain parameter values for Ta of $\text{λ = 0.73, μ}{}_{\mathrm{ph}}{}^1\text{= 0.10}$,in agreement with optimized conventional results.     

On some recent results concerning the superconducting transition temperature

The Eliashberg gap equations relate the transition temperature T_c of an isotropic superconductor to its electron-phonon spectral function α²F(ω) and Coulomb pseudopotential parameter $\text{μ}{}^1$. Recently the Eliashberg theory has been used to derive some supposedly rigorous results bearing on the problem of attaining higher superconducting transition temperatures: Bergmann and Rainer derived an expression for the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{F(ω)}$; Allen and Dynes showed that in the asymptotic limit of very large $\text{λ(λ?10)k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{=f(μ}{}^1\text{)(λ〈ω}{}^2\text{〉)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and Leavens proved that for any isotropic superconductor k_BT_c ?0.2309A, where A is the area under its electron-phonon spectral function. In this letter we show that the result of Allen and Dynes is not compatible with the other results and is, in fact, incorrect.     

Conductivity of a quasi-one-dimensional metal at finite temperatures

The longitudinal conductivity of a quasi-one-dimensional metal is calculated for the case T?ω_D (ω_D being the limiting phonon frequency) and ω_Dl¹/v?1 where l¹ is the effective mean free path determined by impurity and phonon scattering: $\text{l}{}^1\text{= (l}{}^{\mathrm{?1}}{}_{\mathrm{ph}}\text{+ l}{}^{\mathrm{?1}}{}_{\mathrm{i}}\text{)}{}^{\mathrm{?1}}\text{, l}{}_{\mathrm{ph}}\text{= v/λT, l}{}_{\mathrm{i}}$ is the impurity mean free path. The conductivity is σ = (c₁e²/πS)l³_iv^?2ω_DλT for l_i?l_ph, σ = (c₂e²/πS)vω_D(λT)^?2 for l_i?l_ph, λ being the dimensionless electron-phonon interaction constant, c₁, c₂ ～ 1, S = a_xa_y is the (xy) area per one chain.     

Electron-phonon interaction effects on the spin susceptibility of a metal

The effective exchange interaction due to phonons, J_ph, is found to be ferromagnetic and enhanced with the Stoner exchange enhancement factor D₀ to give $\text{J}{}_{\mathrm{ph}}\text{N(?}{}_{\mathrm{F}}\text{) ? D}{}_0\text{(}\text{h}\text{?}\text{ω}{}_{\mathrm{D}}\text{??}{}_{\mathrm{F}}\text{)}$. In addition, J_ph is found to be further enhanced by phonon softening. These findings imply the fundamental importance of the phonon effects in itinerant electron magnetism.     

Spin scattering and spin-orbit coupling in metals

An identity between ε, the probability of a spin disorientation at a metal surface with the ratio of the phonon resistivity scattering time, τ_ph, to the phonon spin scattering time, τ_2ph, in the bulk metal is established. Also it is shown that, for diffuse resistivity scattering, ε at a metal-metal interface is given by the $\text{τ}{}_{\mathrm{ph}}\text{τ}{}_{\mathrm{2ph}}\text{>}$ ratio in the bulk of the higher Z metal. Finally from an approximate fit of ε and the $\text{τ}{}_{\mathrm{ph}}\text{τ}{}_{\mathrm{2ph}}$ ratios to α⁴Z⁴ it is proposed that CESR may be readily observed in titanium and molybdenum.     

Renormalization group improved predictions for quarkonium decay

A method recently suggested to resolve the ambiguity related to scheme dependence in perturbative QCD is applied to calculations of radiative corrections to quarkonium decay. Renormalization group improved predictions are given for the ratio $\text{R=Г(}{}^1\text{S}{}_0\text{→had)/Г(}{}^3\text{S}{}_1\text{→had)}$, as a function of $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$. The values obtained are substantially larger than in conventional schemes. One finds in particular that R>182 for charmonium, and R>174 for bottomium, independently of the value of the quark mass and $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$. It follows that $\text{Г(}\text{n}{}_{\mathrm{c}}\text{→}\text{had}\text{)>6.9}\text{MeV}$ and $\text{Г(}\text{n}{}_{\mathrm{b}}\text{→}\text{had}\text{)>3.6}\text{MeV}$. Values of the wave function at the origin as a function of $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$ are also extracted from the measured gluonic width of the ³S₁ state. An upper bound for $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$ is obtained under some assumptions.     

Unitary operators with discrete spectrum induced by measure preserving transformations

The purpose of this paper is to prove the following theorem.Theorem. Given a countable subset Λ on the circle K and an integer-valued function n(λ) on Λ, there exists a dynamical system with discrete spectrum (X,$\text{F}$,μ,T) such that Λ is the set of all eigenvalues of T and n(λ) is the multiplicity function of T if and only if there exist two systems of subgroups {G_i}_i∈N and $\text{{S}{}_{\mathrm{j}}\text{}}{}_{\mathrm{j\in M}}\text{(}\text{N}\text{??}{}_0\text{,}\text{M}\text{??}{}_0\text{)}$ of the circle such that Λ = G ∪ S and

$\text{n(λ)=}\text{∞}\text{for}\text{λ∈S,}\text{{i∈N; λ∈G}{}_{\mathrm{i}}\text{}}\text{for}\text{λ∈G?S,}$

where $\text{G =}\text{?}\text{i∈N}\text{G}{}_{\mathrm{i}}\text{, S =}\text{?}\text{j∈M}\text{S}{}_{\mathrm{j}}$.     

Optical properties of (TTF) (TCNQ) in the visible and infrared

Polarized optical studies of single crystals and polycrystalline compactions of the organic salt (TTF) (TCNQ) are reported. Metallic behavior is observed for light polarized parallel to the conducting axis. The plasma edge occurs at 1.4 μm with metallic reflection observed in the i.r. The plasma frequency $\text{(}\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{=}\text{1.2eV}\text{)}$ leads to an optical effective mass $\text{m}{}^1\text{=}\text{5}\text{m}{}_{\mathrm{e}}$ implying a tight-binding transfer integral of 0.1 eV in agreement with estimates obtained from other measurements. The scattering time, τ, as determined from the shape of the reflectance curve, yields a room temperature metallic conductivity of 10³(Ω-cm)^-1 in good agreement with the measured d.c. value. An estimate of the dimensionless electron-phonon coupling constant is obtained from the measured value of τ,λ_ph?1.3. The strong anisotropic absorption in the visible portion of the spectrum is attributed to interband transitions.     

A numerical estimate of deviations from the exponential decay law for the transition 2P12→1S12 in hydrogen

The deviations from the exponential decay law of the $\text{2}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states of the Dirac hydrogen atom with respect to the transition $\text{2}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→1}\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ are numerically estimated. We find |a₀(t) ? exp(?λt)|?2.5 × 10^?4 for all t, where a₀(t) is the “exact” decay amplitude and λ is a complex constant such that (2Re λ)^?1 is the “natural lifetime” of the $\text{2}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states with respect to the spontaneous transition to $\text{1}\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.     

Anomalous transient photocurrent in disordered semiconductors: Theory and experiment

Anomalous transient photocurrents are theoretically and experimentally studied in amorphous As₂Se₃. At high photogeneration rates a maximum of photocurrent I_ph(t) is formed by two asymptotes I_ph ～ t^α and $\text{I}{}_{\mathrm{ph}}\text{～ t}{}^{\mathrm{<mtext>?(1?\alpha )</mtext><mtext>2</mtext>}}$. At intermediate generation level the portion of a quasi-stationary current occurs between the two asymptotics due to monomolecular recombination, though the current decay towards the steady state is still governed by bimolecular recombination. At low generation rates the transition into steady-state is determined by monomolecular recombination alone.     

Subject index for volume 88

The emission and excitation spectra of the aromatic thioketone xanthione have been measured in Shpolskii matrices at 15 K. Under these conditions a sharp and rich vibrational structure is observed in the lowest triplet and the first and second excited singlet states. The phosphorescence excitation spectrum places the origin of the T₁ ← S₀ transition at 15 143 cm^?1, while that of the $\text{S}{}_1\text{(n, π}{}^1\text{) ← S}{}_0$ absorption is tentatively assigned to the band at 16 093 cm^?1. The phosphorescence spectrum, which shows only a weak CS stretch vibrational band, is dominated by ring vibrations. In accordance with the previous analysis of ODMR measurements, it is suggested that T₁ and T₂ states are energetically very close, thereby resulting in a lowest triplet state of heavily mixed n, $\text{π}{}^1\text{-π}$, $\text{π}{}^1$ character. No mirror-image relationship is found between the relatively strong S₂ → S₀ fluorescence and the excitation spectrum of the $\text{S}{}_2\text{(π, π}{}^1\text{) ← S}{}_0$ transition. The latter is dominated by a long, pronounced 336-cm^?1 progression.     

Precision measurement of the 2p-1s transition wavelength in muonic 13C

With the bent-crystal spectrometer at the SIN muon channel we have measured the wavelength of the 2p-1s transition in muonic ¹³C with a precision of 13 ppm. The result for the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-1}\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transition is $\text{λ(2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{) = 16.46055 ± 0.00021}\text{pm}$; it is interpreted in terms of a short-range muon-nucleon interaction not included in standard QED calculations.     

Elastic moduli and mode gammas of GaP: Their relationship to those of other isomorphic crystals and the high pressure structural-electrical transition

The transit times of ultrasonic waves associated with piezoelectrically inactive modes have been measured in sulfur-dope, n-type GaP using hydrostatic pressures up to 5 kbar. The velocities and elastic constants of most modes increase linearly with pressure but $\text{C}{}_{\mathrm{S}}\text{=}\text{1}\text{2}\text{(}\text{C}{}_{11}\text{?}\text{C}{}_{12}\text{)}$ decreases slightly. The behavior of the elastic constants and their associated mode gammas are compared to those of other III–V compounds and of Si and Ge. We suggest that the behavior of C_S is related to the occurrence of the structural-electrical transition which occurs at high pressure. A modified Born criterion for lattice stability developed by Demarest $\text{et}$$\text{al}$. is used to explain this relationship. The contribution of thermal dilatation to the temperature dependence of each elastic constant is deduced. Using it and data from the literature we find that the explicit thermal contribution to each elastic constant is significant and in the case of C₁₂ has an anomalous sign.     

The critical behaviour of spontaneous magnetization in the antiferromagnetic NiO

The spontaneous magnetization of the sublattice vs temperature in the antiferromagnetic NiO was measured by the neutron diffraction method. Temperature changes of the Bragg peaks (111), (222), (333) and (444) with the wavelengths of neutrons $\text{λ}{}_{\mathrm{I}}\text{= 4.16}\text{A}\text{?}$, $\text{λ}{}_{\mathrm{II}}\text{= 2.08}\text{A}\text{?}$, $\text{λ}{}_{\mathrm{III}}\text{= 1.39}\text{A}\text{?}$ and $\text{λ}{}_{\mathrm{IV}}\text{= 1.04}\text{A}\text{?}$, respectively were simultaneously investigated by the neutron time-of-flight spectrometer. On the basis of these measurements, the transition temperature from the antiferromagnetic into the paramagnetic phase was determined, T_N = (523 ± 1)°K. The temperature function of the (111) magnetic peak intensity has been accepted to be I ～ (T_N?T)^2β. According to the present measurements the critical point exponent is 0.33 ± ^0.02_0.04.     

Nature of the transition in nonlinear spin-S Ising models (half-integer spin)

We consider the spin-S Hamiltonian $\text{H}\text{=-JΣ}{}_{\mathrm{〈i,j〉}}\text{Q}{}_{\mathrm{S}}\text{(S}{}_{\mathrm{i}}\text{)Q}{}_{\mathrm{S}}\text{(S}{}_{\mathrm{j}}\text{)?λΣ}{}_{\mathrm{i}}\text{Q}{}_{\mathrm{S}}\text{(S}{}_{\mathrm{i}}\text{)}$ where Q_S(y) is a polynomial in y of degree 2S whose eigenvalues are ±1 and rigorously show that except for a multiplicative constant, the partition functions for all half-integer values of S are identical.     

Theory of the spin depolarisation rate of μ+ SR in pure Fe

The diffusion constant (D) and the spin depolarisation rate (λ_S) of the positive muon in the ferromagnetic b.c.c. lattices such as Fe have been calculated on the basis of the small polaron (SP) model with particular attention to the hopping and the coherent motions. They have been obtained in the forms: $\text{D=}\text{d}{}^2\text{w}{}_{\mathrm{D}}\text{6}$ and $\text{λ}{}_{\mathrm{S}}\text{=}\text{4γ}{}^2{}_{\mathrm{\mu }}\text{H}{}^2{}_{\mathrm{d}}\text{3w}{}_{\mathrm{S}}$, where d is a jump length, and H_d is a magnitude of internal dipolar field. At high temperatures, the activated-type hopping motion gives a dominant contribution to w_D, and w_S coincides with w_D. With decreasing temperature, w_D turns to be increasing owing to the coherent motion. Whereas w_S deviates from w_D, after passing the minimum, to have a maximum, and then decreases in inverse proportion to a lifetime (_B) of the SP band states. Because of the cell periodicity of the internal fields, the spin in an SP band state feels a definite magnetic field corresponding to the state, and sees various fields if scattered to other states. These scattering processes succeeding in a time shorter than (γ_μH_d)^-1 result in the motional narrowing of the spectra, with λ_{S ?} γ²_μH_d_B.     

Study of the photon spectrum in the decay KS0→π+π−γ

The branching ratio $\text{Λ(}\text{K}{}_{\mathrm{<mtext>S</mtext>}}{}^0\text{→π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{γ)}\text{Λ(}\text{K}{}_{\mathrm{<mtext>S</mtext>}}{}^0\text{→π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ has been determined to be (2.68±0.15)×10^?3 for photon energies $\text{E}{}_{\mathrm{\gamma }}{}^1$ greater than 50 MeV in the K_S⁰ rest frame. The decay K_S⁰→π⁺π^?γ is found to be dominated by the internal bremsstrahlung transition. The branching rato of a possible direct transition is found to be less than 0.06 × 10^?3 at 90% confidence level for $\text{E}{}_{\mathrm{\gamma }}{}^1\text{> 50}\text{MeV}$.     

A cubic antiferromagnet for which the ground state is known exactly

Nearest neighbour anisotropic exchange is characterized by $\text{K}{}_{\mathrm{ij}}\text{= J}{}_6\text{S}{}_{\mathrm{ix}}\text{S}{}_{\mathrm{jx}}\text{+ J}{}_{\mathrm{\perp }}\text{(S}{}_{\mathrm{iy}}\text{S}{}_{\mathrm{jy}}\text{+S}{}_{\mathrm{iz}}\text{S}{}_{\mathrm{jz}}\text{)}$ for a bond along the x-axis. For J₆ = ?J_⊥ < 0 the ground configuration of the total exchange hamiltonian is a two-sublattice antiferromagnet which is an eigenstate of the problem.