Multiphonon relaxation in fluoride and ternary sulfide laser crystals with neodymium ions

It is shown that, in ternary sulfide crystal matrices, in contrast to fluoride matrices with similar phonon spectra, the multiphonon relaxation rate as a function of the number p _eff of “effective phonons” (the energy gap ΔE _min between the J′ and J levels of the Nd³⁺ ion) has a steep slope, which does not decrease with increasing p _eff. This indicates that, compared to fluoride crystals, the multiphonon relaxation rate of mid-IR transitions (in the range 4–5 μm) in ternary sulfide matrices sharply decreases, by three to four orders of magnitude.     

The analysis of the densities of <Emphasis Type="Italic">s</Emphasis>-wave neutron resonances separated with respect to spin

The density ratio of s-wave neutron resonances z=ρ(J₁)/ρ(J₂) was analyzed on the basis of the experimental data for 22 atomic nuclei and the Gilbert-Cameron formula for ρ(J). Here, J₁=I_x—1/2 and J₂=I_x+1/2, where I_x denotes the spin of the target nucleus in the ground state. Our aim was to verify whether the factor η(I_x), as a multiplier, can be applied in the expression describing ρ(J₁), with the assumption that ρ(J₂) values remain unchanged, or whether the factor 1η(I_x) can be applied, as a multiplier with ρ(J₂), while the ρ(J₁) values remain unchanged. The final conclusions, e.g., the confirmation or the negation of the fact that it may be necessary to apply the η(I_x) factor, depend on the values of “real” errors Δz of the z variable, which can be calculated if the optimal values of Δρ(J₁) and Δρ(J₂) are known.     

Effect of the orbital structure and symmetry of electronic states on nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing: Dibenzofuran

The nonradiative S-T intersystem crossing S ₁(ππ*) ? T ₁(ππ*) in dibenzofuran (DB(O)) molecules has been theoretically investigated within the model of vibronically induced spin-orbit (VISO) coupling of electronic states, where the vibronic perturbation takes into account all out-of-plane vibrational modes of a molecule. It is established that the S-T intersystem crossing S ₁(¹ A ₁) ? T ₁(³ B ₂) involves also the intermediate (T _m )T ₂(³ A ₁) and T ₃(³ B ₂) triplet states. The calculated rate constant K _ST = (4.5–4.7) × 10⁷s^?1 of the nonradiative transition is in agreement with the known experimental data. The manifestation of approximate (belonging to the D _2h group) symmetry of singlet and triplet molecular states in VISO couplings has been studied. An effect of the heavy (oxygen) atom of a DB(O) molecule on K _ST is established.     

The effective Hamiltonian for copper oxides

The concentration dependence of the exchange integral for the subsystem of spin moments of copper ions J(h) = J ? J ₁ × h ? J ₂ × h ² has been calculated for the Emery model within the effective Hamiltonian obtained with due regard to intersite interactions and oxygen configurations with different numbers of holes. It is shown that allowance for the oxygen single-hole states occurring upon doping leads to additional contributions to J(h), whose intensities depend on the intersite correlations of the nearest environment of exchange-coupled copper ions.     

Alzheimer random walk

Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy’s Weibull distribution \(b{\left( {\tfrac{a}{b}} \right)^{\tfrac{{a + 1}}{b}}}{\left[ {\Gamma \left( {\tfrac{{a + 1}}{b}} \right)} \right]^{ - 1}}{x^a}\exp \left( { - \tfrac{a}{b}{x^b}} \right)\) where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as ~p ^{? α} with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) ? ν(0) ] / [ ν(1) ? ν(0) ] = p ^β with β = 0.388 when p ? 0.1 and β = 0.0822 when p ? 0.1.     

Der Einfluß von Plasmawellen auf das Reflexionsvermögen von Metallen (I)

The wellknown derivation ofFresnel's formula for the reflection coefficient of a metal surface in the case of an oblique incident wave polarized parallel to the plane of incidence includes a mistake concerning the boundary conditions and neglecting the possibility of optical excitation of plasma waves. The right formula for this case is derived in the following paper byForstmann. The discussion of an approximate formula obtained by a simplified method leads in the case of vanishing reflectivity forΩ>Ω _p to a real Brewster-angleα _B . ForΩ<Ω _p there exists another solution with a complex Brewster-angle, representing a surface wave in form of a Zenneck-wave. For large wave numbers and for light velocity ? electron velocity the dispersion formula for these surface waves is nearly identical with that obtained byRitchie andWagner, while for small wave numbers there is a great difference between these two formulas. In the middle region the frequenceΩ is nearlyΩ _p /√2.     

Behavior of the excitation cross sections of the perturbed series of the xenon atom

Behavior of the excitation cross sections of the perturbed 6s[3/2]_n°?np[1/2]₀ spectral series of the xenon atom is experimentally studied. By using the methods of extended electron beam and optical spectroscopy, the cross sections are measured and the optical excitation functions are recorded for the transitions of this series with n=6–13. A deviation of the dependence Q=f(n) from a power-law function is revealed, as well as changes in the form of optical excitation functions and in the nature of the branching caused by perturbation of the 7p[1/2]₀ level by levels of the 5p ⁵(² P _1/2°)6p configuration.     

The Condition of Applicability for the Extended Boundary Conditions Method for Small Multilayer Particles

We have examined an analog to the extended boundary conditions method (EBCM) with the standard spherical basis, which is popular in light scattering theory, with respect to its applicability to the solution of an electrostatic problem that arises for multilayer scatterers the sizes of which are smaller compared to the wavelength of the incident radiation. It has been found that, in the case of two or more layers, to determine the polarizability and other optical characteristics of particles in the far-field zone, the parameters of the surfaces of layers should obey the condition max{σ₁^(j)} < min{σ₂^(j)}. In this case, appearing infinite systems of linear equations for expansion coefficients of unknown fields have a unique solution, which can be found by the reduction method. For nonspheroidal particles, this condition is related to the convergence radii of expansions of regular and irregular fields outside and inside of the particle, including its shells—R₁^(j) = σ₁^(j) and R₂^(j) = σ₂^(j). In other words, a spherical shell should exist in which expansions of all regular and irregular fields converge simultaneously. This condition is a natural generalization of the result for homogeneous particles, for which such a condition is imposed only on expansions of the “scattered” and internal fields—R₁ < R₂. For spheroidal multilayer particles, which should be singled out into a separate class, the EBCM applicability condition is written as max{σ₁⁽¹⁾, σ₁⁽²⁾, …, σ₁^(J?1), σ₁^(J)} < min{σ₂⁽¹⁾, σ₂⁽²⁾, …, σ₂^(J?1)} and parameters σ₂^(j) of the surfaces of shells are not related to corresponding convergence radii R₂^j of irregular fields. Numerical calculations for two-layer spheroids and pseudospheroids have confirmed completely theoretical inferences. Apart from the EBCM algorithm, an approximate formula has been proposed for the calculation of the polarizability of two-layer particles, in which the polarizability of a two-layer particle is interpreted as a linear combination of the polarizabilities of homogeneous particles that consist of the materials of the shell and core proportionally to their volumes. The range of applicability of this formula is wider than that for the EBCM, and the calculation error is smaller than 1%.     

Analytic properties of the effective dielectric constant of a two-dimensional Rayleigh model

Analytic properties of the dimensionless static effective dielectric constant f(p, h) of a two-dimensional Rayleigh model (p is the concentration and h is the ratio of the dielectric constants of components) are considered as a function of the complex variable h. It is shown that the only singularities of the function f(p, h) are first-order poles for real h = h _n < 0 (n = 1, 2, ...) with the condensation point h = ?1, which form an infinite discrete (countable) set. The positions of the first ten poles of the function f(p, h) and the residues at these points are calculated and represented graphically versus the concentration. Based on the results obtained, a pole-type approximate formula is proposed that describes the behavior of the function f(p, h) over a wide range of p and complex h.     

Untersuchungen über die Energieabhängigkeit von Kernreaktionen mit Neutronen im Energiebereich zwischen 12 und 19 MeV

Continuing earlier investigations we studied the energy dependence of the cross sections of the following nuclear reactions produced by neutrons in the energy range from 12 to 19 MeV: P³¹(n, 2n)P³², P³¹(n,α)Al²⁸, Cu⁶⁵(n, 2n)Cu⁶⁴, Cu⁶⁵(n, p)Ni⁶⁵, Zn⁶⁴(n, 2n)Zn⁶³, Zn⁶⁴(n, p)Cu⁶⁴, V⁵¹(n, p)Ti⁵¹, Br⁷⁹(n, α)As⁷⁶, O¹⁶(n, α)C¹³. The results were compared with cross sections calculated according to the statistical theory, considering the competition ofγ-ray emission and particle (predominantly neutron) emission from the excited residual nucleus.     

ABC effect and resonance d*(2380)

A new state in the two-baryon system with mass 2380 MeV and width 80 MeV has been detected in the experiments at the Juelich Cooler Synchrotron (COSY). The new particle denoted now d*(2380) has quantum numbers I(J ^p ) = 0(3⁺). The total cross sections for the d and ⁴He fusion reactions show similar to each other resonance-like energy dependence. The resonance-like structure is sensed in the double-pionic fusion channels and polarized np scattering.     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.     

Depolarizing collisions in ytterbium vapor: Isotropic and anisotropic relaxation

Isotropic depolarizing collisions are studied using a stimulated photon echo with a specific polarization of the excitation radiation pulses in a mixture of ytterbium with krypton for the J = 1 ? J = 0 transition of ¹⁷⁴Yb. The difference between the relaxation rates of orientation and alignment γ _b ⁽²⁾ ? γ _b ⁽¹⁾ of the ³ P ₁(6s6p) ¹⁷⁴Yb level is measured as a function of the krypton pressure. The collision photon echo at the J = 1 ? J = 0 transition induced by the anisotropic relaxation is studied for the Yb + Xe mixture. The power of the collision echo increases from zero with the addition of a buffer gas to ytterbium, reaches an optimal level, and decreases with an increase in the buffer gas pressure. The polarization of this collision-induced echo differs from the polarization of the conventional echo. The experimental results are in qualitative agreement with theoretical predictions.     

Modified multicomponent band pass optical reflection filters at oblique incidence

Reflection and transmission characteristics of a modified long-wavelength cutoff filter using a three-component system with an angular dependence are studied. In this case, a layer of high refractive index is sandwiched between edge layers of equivalent refractive index with the base structure [G(0.5AB0.5A)]^N; then, an optimized structure of the form [(0.5AB0.5A)^N?X (0.5AB0.5A)^X (0.5AB0.5A)^N?X] is taken and its spectral properties are studied. In the case of a short-wavelength three-component cutoff filter, a layer of low refractive index is sandwiched between two edge layers of high equivalent refractive index with a base structure [G(0.5BA0.5D)]^N and its spectral characteristics are studied. Then, the structure is optimized [(0.5BA0.5B)^{N? X}(0.5BA0.5B)^X(0.5BA0.5B)^N?tX] and spectral characteristics of this structure are also studied. Spectral properties of band pass optical reflection filters of the type [G(XY)A] whose components are the proposed long-wavelength cutoff [(0.5AB0.5B)^{N? X}(0.5AB0.5A)^X(0.5BA0.5B)^N?X] and short-wavelength cutoff [(0.5BA0.5B)^N?X(0.5BA0.5B)^X(0.5BA0.5B)^N?X] filter structures are studied with angular dependences. No increase in the bandwidth with the least oscillatory components at the edges can be precisely formed by known classes of a two-component system at normal incidence. It is shown that the use of reflection and transmission filters with oblique bands yields an ideal polarizer. Angular dependences of the filter and the transmission and reflection band shapes on the parameters of a high-reflectance multilayer coating, such as the thickness, refractive indices, and the number of layers, are analyzed in detail.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Measurement of the nuclear magnetic dipole moment of Au197 and hyperfine structure measurements in the ground states of Au197, Ag107, Ag109 and K39

Using an atomic beam magnetic resonance apparatus the nuclear magnetic dipole momentμ _I of the stable isotope Au¹⁹⁷ was measured directly with the doublet method. The result isμ _I(Au¹⁹⁷)=0.143491 (9)μ _n, uncorrected for atomic diamagnetism. Further hyperfine structure measurements were performed in the ground states of K³⁹, Ag¹⁰⁷, Ag¹⁰⁹ and Au¹⁹⁷ with the following results:Δv(K³⁹)=461.719723 (38) MHzΔv(Ag¹⁰⁷)=1712.512111 (18) MHzΔv(Ag¹⁰⁹)=1976.932075 (17) MHzΔv(Au¹⁹⁷)=6099.320184 (13) MHzg _J(Ag¹⁰⁷)/g _J(K39)=1.0000260 (20)g _J(Au¹⁹⁷)/g _J(K39)=1.0005076 (20).     

Low-temperature contribution to the resonant tunneling conductance of a disordered N–I–N junction

A formula for the contribution ΔG ^res(T) to the resonant tunneling conductance of the N–I–N junction (where N is a normal metal and I is an insulator) with a weak (low impurity concentrations) structural disorder in the I layer from the low-temperature “smearing” electron Fermi surfaces in its N shores is obtained. It is shown that the temperature dependence ΔG ^res(T) in such a “dirty” junction qualitatively differs from the corresponding dependence ΔG ₀(T) in a “pure” (without resonant impurities in the I layer) junction: ΔG ^res(T) < 0, d(ΔG ^res)/dT < 0; ΔG ₀(T) > 0, d(ΔG ₀)/dT > 0, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered I layer.     

Many-electron character of Rydberg series converging to the ionization thresholds of the 4<Emphasis Type="Italic">p</Emphasis><Superscript>4</Superscript>5<Emphasis Type="Italic">s</Emphasis> states of KrII

The photoionization cross sections of the 4p shell and the 4s main level and 4p ⁴(³ P) 5s ⁴ P _{5/2, 3/2} satellite subvalence levels of KrII have been calculated in the 4s-near-threshold range of excitation energies from 28.48 to 28.70 eV. The calculation takes into account the core relaxation by the methods of the theory of non-orthogonal orbitals, the interaction between resonant states through autoionization channels by solving the complex secular equation, and the interaction between the channels of the continuous spectrum in all orders of the perturbation theory by the K-matrix method. Good quantitative agreement between the energy-integrated theoretical and experimental photoionization cross sections for the satellite levels has been obtained for the first time. It is shown that only simultaneous consideration of the above-mentioned effects leads to such agreement. The resonant structure of the photoionization cross sections in this excitation energy range is related to the autoionization decay of the 4p ⁴5s(⁴ P _1/2)np and 4p ⁴5s(² P _3/2)np Rydberg series. The specificity of this process is that both series manifest themselves not independently but owing to their strong electrostatic interaction with the prominent 4p ⁴(¹ D)5s ² D _5/2 6p _3/2 resonance, which lies in this excitation energy range.