Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Measurement of the surface density of states by field ionization

It is shown that recent measurements of field ion energy distributions from clean tungsten surfaces probe the density of metal states in the vicinity of the surface. We find j(ω) = (2π/kh)Σ_m| ∫ d³rψ_m(r)γ_z|²δ(ω??_m), where j(ω) is the ion current a ω, ψ_mand ?_m are electronic metal eigenfunctions and eigenvalues in the presence of the external electric field used in field ionization and γ(z) is a function which is large near the noble gas atom. An explicit expression for γ(z) is given in the text. It is estimated that tungsten metal states with values of k₆ at least as large as 0.5 Å^?1 make an appreciable contribution to j(ω) where k₆ is the electron momentum parallel to the surface.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.     

Scaled Limit and Rate of Convergence for the Largest Eigenvalue from the Generalized Cauchy Random Matrix Ensemble

In this paper, we are interested in the asymptotic properties for the largest eigenvalue of the Hermitian random matrix ensemble, called the Generalized Cauchy ensemble GCyE, whose eigenvalues PDF is given by

Theory for the nonlinear optical response at noble-metal surfaces with nonequilibrium electrons

We present a theory for the electron-temperature dependence T _el of optical second harmonic generation (SHG). Such an analysis is required to study the dynamics of metallic systems with many hot electrons not at equilibrium with the lattice. Using a tight-binding theory for the nonlinear susceptibility χ ⁽²⁾(ω,T _e1) and the Fresnel coefficients we present results for the SHG intensity I ⁽²⁾(ω,T _e1) and its dependence on T _el for Cu. Note, χ ⁽²⁾(ω,T _e1) rather than the Fresnel coefficients determines essentially this temperature dependence. Most interestingly we find frequency ranges where I ⁽²⁾(ω,T _e1) increases for small light intensities, while it decreases for large light intensities. Our theory yields also that SHG probes effects due to hot electrons more sensitively than linear optics. The results of our calculations are compared with recent experiments on Cu and Au.     

Experimentelle Untersuchungen am Elektroneneinfang des Mangan 54 und Zink 65

The electron capture decay of Mn 54 and Zn 65 was investigated using Na I(Tl)-detectors. Spectroscopic-coincidence techniques were employed to examine theK-electron capture rates of Mn 54 and Zn 65, the branching ratio and positron rate of Zn 65. The experimental results are:P _k ω _k (Mn)=0.2492±0.0017,P _k ω _k (Zn)=0.3927±0.0026,EC ^* /EC ⁰(Zn)=53.2±1.0/46.8±1.0,γ/β ⁺=35.1±1.7,K ⁰/β ⁺=27.7±1.5. Thus electron capture to the excited state of Cu 65 occurs to the extent of 52.4±1.0% while electron capture and positron decay to the ground state were found to be associated with 46.1±1.0% and 1.49±0.05% of the disintegrations. These data partly disagree significantly from measurements of other authors. Using the fluorescence yieldsω _k (Cr)=0.279 andω _k (Cu)=0.4425, deduced from other measurements, values ofL+M/K of electron capture to the excited state could be derived:L+M/K(Mn 54)=0.120±0.015 andL+M/K(Zn 65)=0.127±0.015. These ratios agree with the calculations ofBahcall. The half-lives of Mn 54 and Zn 65 have been determined to beT _1/2(Mn 54)=312±5d,T _1/2(Zn 65)=243±4d The energy of the Zn 65-γ-rays was measured with a Ge(Li)-counter:E ^γ=1115.5±0.5 keV.     

Reinvestigation of the decay scheme of the short-lived isomeric states in112In

The two short-lived isomeric states in¹¹²In have been reinvestigated by means of the¹¹²Cd(d, 2n) and¹⁰⁹Ag (α, n) reactions. Measurements of delayed X- andγ-ray, lifetime and TDPAD spectra have been performed. A 6.32(3) keVγ-ray has been identified in the isomeric decay and anM1 multipolarity has been assigned to it on the basis of the measured internal conversion coefficients:α _L =196(39) andα _tot=231(35). TheE1+M2(δ =+0.24(4)) andE2 multipolarities have been determined for the 263 and 188 keV transitions deexciting the 8^?(T _1/2=2.82(2) μs) and 7⁺ (T _1/2=0.93(2) μs) isomeric states, respectively. A revised isomeric decay scheme is presented.     

On asymptotic behaviour of four spin correlation functions in a linear chain of spins

Second and fourth moments of the four spin frequency correlation functions S^Z_i(t) S^Z_i+1 (t) S^Z_j+1 〉_k,ω and 〈S^x_i(t) S^z_i+1 (t) S^x_jS^z_j+1 〉_kω have been calculated in the high temperature limit for an arbitrary spin with an isotropic Heisenberg Hamiltonian.     

Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ?) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ₀ · exp(? (T ₀/T)^1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2. An expression for the thermopower in the hopping regime is derived and evaluated.     

Reconstruction of singularities for solutions of Schrödinger's equation

We determine the behavior in time of singularities of solutions to some Schrödinger equations onR ⁿ . We assume the Hamiltonians are of the formH ₀+V, where \(H_0 = 1/2\Delta + 1/2 \sum\limits_{k = 1}^n { \omega _k^2 x_k^2 } \) , and whereV is bounded and smooth with decaying derivatives. When all ω _k =0, the kernelk(t,x,y) of exp (?itH) is smooth inx for every fixed (t,y). When all ω₁ are equal but non-zero, the initial singularity “reconstructs” at times \(t = \frac{{m\pi }}{{\omega _1 }}\) and positionsx=(?1) ^m y, just as ifV=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes \(\{ x|x_{js} = ( - 1)^l js_{y_{js} } \} \) , when ω _j t/π=l _j forj=j ₁,...,j _r .     

Lift order problems for ordinary differential equations on manifolds

Fork≥0, let ττ_k:T ^k+1(M)=T(T ^k(M))→T ^k(M) denote the (k+1)th iterated tangent bundle in relation to a base manifoldT ⁰(M)=M. LetV represent a possibly nonstationary vector field overT ^k(M), and letQ be a subset/submanifold inT ^k(M). Sufficient conditions (and, whenV is completely integrable inQ, necessary and sufficient conditions) are established to ensure that all solutionsg toy′=V(t, y) lying entirely inQ have the formG=f ^[k], wheref ^[k] is thekth-order differential lift of a curvef lying inM. The relevance of the issue for higher order dynamical systems (especially in mechanics) is discussed. Higher order involutions and complete vector field lifts are examined from the viewpoint of the differential equations they present. Collateral results on the general solvability of initial value problems are obtained and numerous examples are discussed in detail. To the memory of my teacher and friend M. Kuga (1928–1990).     

Gyromagnetic ratios of the 4+ and 6+ rotational states of184W

The nuclear Larmor precession has been observed for the 2⁺, 4⁺ and 6⁺ rotational states of¹⁸⁴W in the hyperfine field of WFe by application of the TDPAC and the IPAC techniques. A carrier free radioactive source of^184m Re alloyed with high purity iron was used for all three measurements. From the Larmor precession observed in the 2⁺ state by TDPACω _L = 944(15) MHz and the knowng-factor the hyperfine fieldB _{300 K} ^hf (WFe)=?69.6(27)T was derived. The deviation from the result of a spin echo experiment with¹⁸³WFe extrapolated to room temperature may be caused by the Bohr-Weisskopf effect (hyperfine anomaly). IPAC measurements with the same sample polarized in an external magnetic field of 1.6T gave for the 4⁺ and 6⁺ rotational states: ω _L τ(4⁺)=0.0609(22) andω _L τ(6⁺)=0.00735(102). By use of experimentalB(E2)-values theg _R -factors were derived asg _R (4⁺)=+0.276(26) andg _R (6⁺)=+0.281(45). The directional correlation of the 537?384 keVγ-γ cascade has been analysed in terms of anE1/M2/E3 mixture for theK-forbidden 537keV transition. We obtained the mixing ratiosδ(M2/E1)=±0.086(16),δ(E3/E1)=?0.028(5) with the sign convention of Krane and Steffen.     

Optical pumping of short lived Β-radioactive isotopes and the magnetic moment of37K

²¹Na (T _1/2=23 sec) and³⁷K(T _1/2=1.25 sec) have been produced in gas targets by (d, n) reactions and polarized by means of optical pumping or spin exchange scattering with optically pumped⁸⁷Rb. An asymmetry up to 3% in theΒ-decay of the polarized nuclei was found, which served to detect rf transitions between hfs levels of the atomic ground states of²¹Na and³⁷K.δF=0 andδF=1 resonances have been recorded, yielding spin, hfs separation and magnetic moment, especiallyI(³⁷K)=3/2,δW(³⁷K)=240.266 (3) Mc/sec andΜ _I(³⁷K)=0.02033(6) nm (diamagnetically corrected). For²¹Na earlier rf-spectroscopic data have been confirmed.     

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〉。     

The effect of the B-site size on the structural,magnetic and electrical properties of La0.7Ca0.3MnO3−δ compounds

The perovskite-type ceramic La_0.7Ca_0.3MnO_3−δ was prepared by the solid-state reaction with 0.00?δ?0.15. X-ray diffraction, electrical and magnetic measurements were performed to examine the effect of the B-site size on the properties of these materials. We have found that the structure is orthorhombic for 0.00?δ?0.075 and becomes rhombohedral for 0.10?δ?0.15. The measurements of the magnetization as a function of the temperature, M(T), shows a ferromagnetic-paramagnetic transition at the Curie temperature T_C for δ=0.00. When increasing δ, these curves report the presence of two types of transitions. The first one is from the ferromagnetic to the antiferromagnetic state, indicating the existence of a charge-ordering state (T_CO). The second antiferromagnetic-paramagnetic transition occurs at the Neel temperature T_N. The temperature dependence of the resistivity ρ(T), indicates a metallic behaviour at low temperature (T<T_p) and a semiconductor behaviour at high temperature (T>T_p) for δ=0.00. For 0.05?δ?0.10, the ρ(T) curves shows a semiconductor behaviour revealing the disappearance of the metallic state which reappear at low temperature for δ=0.125 and 0.150.     

Electrical and electromechanical properties of lead-potassium-yttrium-niobate ceramics—piezoelectric applications

Tungsten bronze (TB)-type oxide ceramic Pb_0.74K_0.13Y_0.13Nb₂O₆ (PKYN) has been synthesized by the standard solid state reaction method. Single phase formation, orthorhombic crystal structure was confirmed by X-ray diffraction (XRD). The substitution of Y³⁺ in Pb_0.74K_0.52Nb₂O₆ (PKN) decreased the unit cell volume and T_C=260 °C. PKYN exhibited the remnant polarization, P_r=8.5 μC/cm², and coercive field, E_c=28.71 kV/cm. Electrical spectroscopy studies were carried out over the temperature (35-595 °C) and frequency (45 Hz-5 MHz) ranges, and the charge carrier phenomenon, grain-grain boundary contribution and non-Debye-type relaxation were analyzed. The relaxation species are immobile charges in low temperature and oxygen vacancies at higher temperature. The theoretical values computed using the relations, ε′=ε_∞+sin(n(T)π/2)(a(T)/ε₀)(ω^n(T)−1); σ(ω)=σ_dc+Aωⁿ are fitted with the experimental one. The n and A parameters suggested that the charge carrier's couple with the soft mode and become mobile at T_C. The activation enthalpy, H_m=0.38 eV, has been estimated from the hopping frequency relation ω_p=ω_e exp(−H_m/k_BT). The piezoelectric constants K_t=35.4%, d₃₃=69×10⁻¹² C/N, d₃₁=−32×10⁻³ mV/N, S₁₁^E=17.8 pm²/N, etc., achieved in PKYN indicate the material is interesting for transducer applications. The activation energies from different formalisms confirmed the ionic-type conduction.     

关于一级近似Tc级数解的收敛问题

本文通过一个实例说明:μ^*=0时,一级近似T_c级数解的收敛半径既不是由z_ph=-∫₀^(ω_ph)dωg(ω)dω·ω²/(ω_ph²-ω²),也不是由z_ph=∫₀^(ω_ph)dωg(ω)dω·ω^{2< 关键词：}