The sensitivity of the transition temperature to changes in α2 F(ω)

The transition temperature of a superconductor depends on α² F(ω), the spectral function of the effective interaction due to phonon exchange. We discuss how strongly the transition temperature is influenced by different frequency parts of α² F(ω). For this purpose the functional derivative δT _c /δα² F(ω) is calculated. It is shown that all frequency regions of α² F(ω) yield a positive contribution toT _c and that the most effective range covers frequencies, slightly above 2πT _c . The functional derivative is calculated numerically for several superconductors from their measured α² F(ω)-spectra. Finally, we discuss the change in transition temperature due to the softening of α² F(ω) which has been observed in amorphous superconductors.     

Equivalence of optimized conventional and proximity electron tunneling (PET) for niobium

A comparison is made of effective phonon spectra α²F(ω) obtained by a fully corrected proximity electron tunneling spectroscopy (PETS) on recrystallized foils of Nb with new results from “conventional” junctions of the form Ag-Al₂O₃-Nb. The latter show the largest strong coupling phonon structure ever observed for Nb and lead directly to an α²F(ω) in good agreement with PETS. This comparison suggests the equivalence of the two techniques if clean and highly ordered NS proximity structures are employed.     

Thermodynamics of superconducting Nb3Sn

Shen's experimental data on α²(ω)F(ω) and μ¹ in superconducting Nb₃Sn is used to calculate its thermodynamic properties. It is found to exhibit the same size strong coupling corrections to BSC as does Pb. Comparison with experimental data shows satisfactory agreement.     

On the inversion of tunneling characteristics in superconductors with spin fluctuations

We have calculated the current-voltage characteristics of a superconductor with spin fluctuations explicitly included in the kernels of the Eliashberg equation along with the electron-phonon spectral density α²(ω)F(ω). These characteristics are then inverted using the method outlined by Galkin et al. to get an effective electron-phonon spectral density assuming no paramagnons are present in the Eliashberg equations during the inversion procedure. The effective electron-phonon spectral density found in this way is, to an excellent approximation, a scaling factor of $\text{1}\text{(1+λ}{}_{\mathrm{sf}}\text{)}$ times the original α²(ω)F(ω), with λ_sf the paramagnon mass renormalization.     

奇点zph与超导临界温度级数

基于对复变函数F_α(y)=∫₀^(ω_ph-α)(ω²y)/(ω²y+1)g(ω)dω解析性质的分析,本文认为:在决定的收敛半径以外,吴杭生等提出的T_c级数解的部分和作为近似T_c公式仍可用于1/λ的适当范围。但它可能达到的精度依赖于谱形,一般来说是有限的。 关键词：     

Mössbauer effect of119Sn in amorphous superconducting metals

Mössbauer spectra for¹¹⁹Sn in crystalline and disordered Sn, as well as in crystalline and liquid-like amorphous Sn_1-x Cu _x (X=0.10?0.18), have been measured at 2.6 K≦T≦108 K. The Debye-Waller-Factor (DWF) obtained from the spectra is identical for the crystalline and for the disordered phase. The DWF of the amorphous phase is smaller than the DWF of the crystalline phase athigh temperatures, but it shows a stronger temperature dependence than the DWF of the crystalline phase and reaches the latter one at about 4 K. From this low-temperature result we conclude that the differences of the Eliashberg functionα ²(ω)F(ω) and of the superconducting transition temperatureT _c in these two phases cannot be related to changes in the phonon spectrumF(ω), but must result from changes of the interaction parameterα ² (ω). A comparison between DWF,α ² F, and specific heat data is performed. From the values for the isomeric shift of the Mössbauer line we can show that the hybridisation and covalency of the electronic bonds present in the crystalline and in the disordered phases are destroyed in the amorphous phase. Both, the DWF and the isomer shift demonstrate that the electronic properties of crystalline and amorphous Sn(Cu) differ appreciably. The electronic and superconducting properties of amorphous Sn(Cu) are similar to the properties of the high pressure phase of tin.     

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.     

Electron-phonon interaction in NbB2: a comparison with MgB2

We present a comparison of electron-phonon interaction in NbB₂ and MgB₂, calculated using full-potential, density-functional-based methods in P6/mmm crystal structure. Our results, described in terms of (i) electronic structure, (ii) phonon density of states F(ω), (iii) Eliashberg function α²F(ω), and (iv) the solutions of the isotropic Eliashberg gap equation, clearly show significant differences in the electron-phonon interaction in NbB₂ and MgB₂. We find that the average electron-phonon coupling constant λ is equal to 0.59 for MgB₂ and 0.43 for NbB₂, leading to superconducting transition temperatures T_c at around 22 K for MgB₂ and 3 K for NbB₂.     

超导临界温度理论(Ⅰ)

本文求出了Eliashberg方程在T=T_c时的解,得到了下面的临界温度级数表示式:T_c=α₀(μ^*)(λ〈ω²〉)^1/2{1+1/λα₁(μ^*)〈ω⁴>/〈ω²>²+1/λ²(α₂₁(μ^*)〈ω⁶>/〈ω²>³+α₂₂(μ^*)〈ω⁴>²/〈ω²>⁴) +1/λ³(α₃₁(μ^*)〈ω⁸>/〈ω²>⁴+α₃₂(μ^*)(〈ω⁴>〈ω⁶>)/〈ω²>⁵)+α₃₃(μ^*)〈ω⁴>³/〈ω²>⁶+…},其中α₀(μ^*),α₁(μ^*)等仅是μ^*的函数。新的T_c公式表明了,T_c不仅依赖于λ、μ^*和〈ω²〉,而且依赖于有效声子谱α²F(ω)的各级矩〈ω²ⁿ〉。     

Electron-phonon interaction near a normal metal-superconductor boundary

Electron tunneling has been used to study the electron-phonon interaction in PbCd proximity effect samples by injecting electrons into Pb side. For Pb thicknesses ranging from 950 to 330 Å, the phonon structure occurs at the same energy as bulk Pb and the magnitude of the structure scales as T_c². The shape of the phonon spectral function, α²F(ω), remains essentially unchanged even though T_c has been depressed by 35%.     

Form factors,threshold relations,and large angle elastic scattering of pions

The form factor F(q²) of the pion in a simple core model is investigated, together with the deep inelastic electroproduction structure function, F₂(ω). A relation between these two, analagous to the Drell-Yan-West relation for nucleons, is derived and it is found that F₂ is related to either the form factor or the square of the form factor depending on how rapidly F(q²) ultimately falls with momentum transfer. The unitarity equation and its implications for this kind of threshold relation are discussed. The simple core model is also applied to elastic large angle ππ scattering.     

Crossing relations for deep-inelastic and annihilation processes

We calculate in a model field theory [φ³]_σ the structure functions $\text{F}\text{?}\text{(ω), F(ω)}$ for the processes e⁺+e^?→h+X and e^?+h→e^?+X in the next to leading logarithm approximation. We find that $\text{F}\text{(ω) and F(ω)}$ satisfy the analytic continuation relation but not the Gribov-Lipatov reciprocity relation.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

On the properties of the extended ground rotational bands in actinide even-even nuclei

The energies of the yrast levels extending up to I = 28 in even-even actinide nuclei were analyzed in terms of an angular velocity expansion E_rot(I) = ∑_i=1ⁿα_iω_I²ⁱ with n = 2?7 to test the application of this expansion to high spin. A strong ω²-dependence is observed for the Variable Moment of Inertia model (VMI) with two parameters α_i(ω²), particularly at the higher spins. There is a marked difference in the ω²-dependence, of these parameters between the N = 142 and other nuclei studied in this region to indicate structure effects are present at the higher spin.     

ωNN vertex function and the γπππ anomaly

We show that the empirical ωNN form factor (cut-off 1400–C1500 MeV) can be understood as arising from a combination of a quark model form factor (typical cut-off 700–C800 MeV) and an anomalous form factor ～ q ² arising from the 3π-intermediate state. The anomaly contributes to the Dirac form factor F ₁(q ²) with F ₁(0) = 0, (and sizable), and to the Pauli form factor F ₂(q ²) with F ₂(0) ≠ 0. The resulting tensor coupling F2(0) is sensitive to the cut-off of the pion momenta in the two-loop integrals and turns out to be small for values around 1 GeV. The quark model ωNN tensor coupling F ²(0) vanishes for point-like quarks. The anomaly, however, contributes a non-vanishing tensor coupling which can be seen to effectively enhance the vector coupling in NN models which do not include a tensor coupling.     

Threshold properties of electroproduction and annihilation

The threshold relation for deep-inelastic electroproduction that was suggested by Drell and Yan and by West is not a general property of softened field theories. However, for individual Feynman graphs of certain perturbation-expansion models it is valid in the form of an inequality. This is shown for every graph in φ³ theory, and for certain simple graphs when fields and particles with spin are considered, provided that the fields to which the electromagnetic current couples have the same spin as the target particle. The structure functions F₂(ω) and $\text{F}{}_2\text{(ω)}$ for electroproduction and electron-positron annihilation are both expected to behave like |ω ? 1 |^p at ω = 1, with the same power p for each but not necessarily the same coefficient. The behaviour of $\text{F}{}_2\text{(ω)}$ at ω = 0 is investigated and is found to result in finite multiplicity in the annihilation process at infinite energy.     

Implications of the quark-gluon light cone current algebra on neutrino scattering

The explicit canonical structure of the light cone restriction of the commutator of the weak current with its divergence is considered in the interacting quark-gluon model quantized in the finite momentum frame. The implications on neutrino scattering are analyzed. W₄ and W₅ are predicted to scale nontrivially as ν⁻²F₄(ω) and ν⁻²F₅(ω), which provides a simple test of light cone current algebra feasible in the near future. The Σ-term for weak currents is deduced from a casual representation near the light cone, and a correction is also made in the W₅-sum rule obtained by naive infinite momentum techniques.     

An analysis of the new pion form factor data

A form factor F(t) for the pion is constructed which is compatible with analyticity and the data in the space-like and time-like region. For the mean square pion radius 〈r²〉 = (0.46_?0.08^+0.06) fm² is obtained. Typical errors of the extrapolated F(t) are given (e.g. F(t =?8 GeV²/c²) = 0.07_?0.10^+0.04). Assuming F(t) ≈ β/(?t)^α at the end of the space-like data region we obtain β = 0.31, α = 0.81 for t in GeV²/c² together with the error contours of (α, β). No conclusive answer on the existence of zeroes of F(t) can be given.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

The influence of inelastic πω channel on pion form factor at s<(mω + mπ)2

It is shown that F_π(s) can be calculated in a model independent way if one knows the phase δ₁ and the inelasticity η of the p-wave ππ scattering and also F_π and the form factor of the γ¹ → π°ω transition for s> (m_ω + m_π)². The correction on F_π(s) for s< (m_ω + m_π)² due to the πω state with a strong ?′(1250) allows to explain the discrepancy between ?-dominance predictions and the experimental data.