The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Measurement of the refractive index and optical absorption spectra of epitaxial bismuth substituted yttrium iron garnet films at uv to near-ir wavelengths

Refractive-index and optical-absorption spectra of Bi-substituted yttrium iron garnet films, epitaxially grown by liquid-phase epitaxy, have been measured in the spectral regime 0.26 m1.9 m by thin-film interference for 0.52 m and by ellipsometry for0.52 m. The Y_3–x–y Bi _x Pb _y Fe_5–z Pt _z O₁₂ films contain bismuth in the range Ox 1.42, lead in the range 0.01 y0.08 and platinum in the range 0.005<=z0.03. There is satisfactory coincidence between the results from ellipsometry and thin-film interference in the overlapping wavelength region. The materials investigated are the same as reported earlier from this laboratory in ter mof their magnetic and magnetooptic properties.     

Parametric relaxation of spectra

We study the change of an quasienergy spectrum upon variation of the weight of a perturbation in the Floquet operatorF=F ₀e^–iV . Employing ideas from level dynamics and random matrix-theory we show that the distribution of nearest-neighbor spacings can display effectively irreversible behavior. Small deviations from equilibrium relax in a certain collision time which scales with the numberN of levels as _collN ^–3/2.     

The quantum theory of the spontaneous magnetization of ferrimagnetics,anti-ferromagnetics and thin films with arbitrary spin at high temperatures

Using Van Vleck's modification of the Heisenberg theory of ferro-magnetism for substances with arbitrary spin per atom, a generalization of the theory is given for the case of ferrimagnetics, anti-ferromagnetics and thin films with an arbitrary number of sub-lattices and with arbitrary spin per atom. The exchange part of the energy operator is formulated by means of rotated spin operators. The theory contains the quantum-mechanical generalization of non-quantum theories given by Néel and later generalized by Yafet and Kittel. It also contains the theory of thin films proposed recently by the author. The magnetization laws are completely analogous to the relations derived from the theory of molecular fields. The constants of the molecular fields are interpreted by means of exchange integrals. For the special case of spin S=1/2the theory agrees with the results of the work of Vlasov and Imuchametov for ferrimagnetics and anti-ferromagnetics and with the author's for thin films.

---

,

, , , . . - , . , . , . . S=1/2 .

     

Band-gap structure of the spectrum of periodic Maxwell operators

We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR ³, is considered. The medium is assumed to consist of two components: the background, where (x) = _b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = _a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = _b / _a are chosen in such a way thatL ^–2, and quantities ^-1-3/2 and ² are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(^3/2)^-1 of the set {² L ^-2 k ²:kZ³}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

Stimulated IR- and vacuum-UV emission following two-photon-excitation of molecular hydrogen using an ArF laser

Hydrogen molecules are excited by two 193 nm-photons [X¹ _g ⁺ E,F¹ _g ⁺ ;Q₀₂(1)] generated with a commerical oscillator-amplifier ArF laser. Stimulated emission is subsequently observed in the IR (=752.4 nm to 836.6 nm;E, FB) and in the VUV (=134.0 nm to 160.9 nm;BX) with a VUV conversion efficiency of 0.2%. The rotational fine-structure, the saturation behaviour, pump depletion as well as SRS-onset on and off two-photon resonance are investigated.     

Estimate of foil thickness by stereomicroscopy technique

The determination of foil thickness by stereomicroscopy technique is discussed. The calculation of the foil thickness is performed in a general position of the foil in an electron microscope for a general choice of the marker position. In this case the crystallographic orientation of the foil normal has to be known. But there exists a special case (markers lie in the diffraction plane) where it is not necessary to know the orientation of the foil normal. The relative error in determining the foil thickness is about 10%.List of symbols B direction in the foil parallel with the primary beam in the first micrograph - d vector describing a common straight line of and ₁ ( ₁) - F direction in the foil parallel with the primary beam in the second micrograph - g diffraction vector - M magnification - n foil normal - o vector defined byn ×B - p ₁ first coordinate ofX in the first micrograph - p ₂ first coordinate ofX in the second micrograph - p _1i ,P _2i quantitiesP ₁,P ₂ corresponding to thei-th markers on the top surface - t _B foil thickness measured in theB direction - auxiliary quantity - corresponding to thei-th markers on the top surface - t _d foil thickness measured in thed direction - t _F foil thickness in general - t _n foil thickness measured in then direction - X ₁ point in _B characterizing one of the markers - X ₂ point in _T characterizing one of the markers - X _2i X ₂ corresponding to thei-th markers on the top surface - X _g magnitude ofX _g - X _gi magnitude ofX _gi - X magnitude ofX - X vector connecting pointX ₁ withX ₂ (X X ₂–X ₁ - X _g component ofX perpendicular to the plane ₁ - X _gi X _gi corresponding to thei-th markers on the top surface - X component ofX lying in the plane ₁ - z distance between _{1 T} and the end point ofX divided by cos Greek symbols angle between ₁ and _{1 B} - angle betweeng and _T - ₁, ₂ reflection planes - plane containingn andg - m measure error - p difference betweenp ₂ andp ₁ (p=p ₂–p ₁) - P accuracy of length measurement - (t _B )_max maximum error oft _B - maximum error of - accuracy of angle measurement - angle characterizing the deviation from the foil position when symmetrical tilting is achieved - angle of tilt betweenB andF (between stereomicrographs) - _T plane describing approximately the top surface of the foil - _b plane describing approximately the bottom surface of the foil - screen plane - angle between ₁ andX - plane containingn andB - angle of tilting from starting (after inserting the foil into the microscope) to working position (position during image observation) Special symbol intersection of two planes (common straight line)     

Light absorption in laser-heated cavities

The absorption of laser light in 0.25–1 mm diameter gold cavities, irradiated for the purpose of generating high-temperature blackbody radiation with intense laser radiation of either =0.44 m or =1.3 m wavelength, was investigated. For =0.44 m radiation the absorption exceeded 0.9 for all conditions, but dropped to only 0.3 for the smallest cavities irradiated at =1.3 m. Entrance hole and cavity filling with plasma seems important for the understanding of the observations.     

A prepared pattern with wavelength selection in directional solidification

As crystal growth is a vital link in the long chain of processes leading to state-of-the-art technological devices, a great deal is known about patterns formed at the solid-liquid interface of a growing crystal. However, some basic questions are still unanswered concerning macroscopic features exhibited by a moving solid-liquid interface. Even for the first instability, the cellular instability, a unique steady-state wavelength does not emerge from theory. Furthermore, while wavelength selection is observed in many different materials, its origin is still to be discovered. By breaking continuous rotational symmetry of the flat solid-liquid interface about the pulling direction v, we prepared a cellular pattern with a well-defined wavelength by front propagation into the unstable uniform state. The material is succinonitrile and the rectangular interface geometry is formed by loading it into a flat capillary. The capillaries are chosen to provide a sample thicknessy ₀ = 100n , and width 10y ₀ and 20y ₀. We use a high-resolution directional solidification apparatus and grow the crystal from grain-boundary-free seed crystals. Surprisingly, the shape of the groove next to the uniform state is initially well-described by nearly self-similar Gaussians. This suggests that the initial perturbation of the interface is localized to a region /2 around a groove. A pattern with a well-defined wavelength is established when the half-width of the Gaussians ₀16m is small compared to 80m so there is little overlap between a groove and its predecessor or successor. When overlap is significant, the pattern is time-dependent. These results suggest that wavelength selection in this prepared pattern is a consequence of front propagation of a localized perturbation.     

Temperature dependence of the spinS=1/2 fluctuation rate and the low-spin versus high-spin transition in native chloroperoxidase

We analyzed two preparations of native, low-spin ferric chloroperoxides as a function of temperature with the following results. (i) The spin lattice transition rateW(T) is relative slow, following a power lawW=0.035 (T/K)^4.98 (rad/s) for one of the samples. (ii) The quadrupole splitting is strongly temperature dependent, dropping from ¦E _Q¦ 2.94 mm/s at 100 K to 2 mm/s at 250 K. (iii) Starting at 190 K, the low-spin heme iron in frozen adqueous solution converts reversibly to a high-spin form, reaching 40% high-spin at 250 K. The two forms appear to be in thermal equilibrium, (iv) Optical data indicate that in a 70% glycerol glass, the conversion starts at lower temperature and reaches 50% highspin at 190 K.Supported in part by GM 49513 and GM 16406.     

Tunable UV radiation at short wavelengths (188–240 nm) generated by sum-frequency mixing in lithium borate

Sum-frequency mixing (₃=₁+₂) of UV laser radiation (₁=266 nm and 213 nm) and tunable coherent infrared light (₂=1.2–2.6 m) in lithium borate (LBO) generates radiation at short wavelengths (₃=188–242 nm). The UV radiation at ₁ is produced by the fourth and fifth harmonic of a pulsed Nd-YAG laser. The infrared light is generated with an optical parametric oscillator of beta barium borate. The phase-matching angle is measured as function of ₃ and compared with calculated values. For UV laser radiation at shorter wavelengths (173 nm₁213 nm) the calculations predict an extension of the tuning range of the sum-frequency generated at ₃ to wavelengths as short as the LBO transmission cutoff at 160 nm.     

Photometric and fluorimetric study of the acid-base behavior of 2,2′-diquinolyl and 2,2′,2″-terpyridyl

A photometric and fluorimetric study of the acid-base behavior of 2,2-diquinolyl and 2,2,2-terpyridyl was performed. In sulfuric acid medium, the doubly charged 2,2-diquinolynium ion undergoes the first dissociation atH ₀=0.20±0.09, as determined by fluorimetry (_ex=336 nm, _em=424 nm). Photometric titration is less accurate because of the overlapping of the absorption spectra. The second dissociation constant of 2,2-diquinolyl was determined by fluorimetric titration (_ex=336 nm, _em=420 nm), obtaining a value of 3.67±0.03. The triply charged 2,2,2-terpyridyl molecule was found to undergo the first dissociation atH ₀=–7.17±0.04, as determined by fluorimetric titration (_ex=316 nm, _em=350 nm), in aqueous sulfuric acid medium. Photometric titration (=335 nm) was performed in the presence of 6.5% ethanol because of the low solubility of the compound in water. In this ethanolicwater medium, a value of the dissociation constant atH ₀=–7.39±0.03 was calculated. The second dissociation constant was determined to be 2.81±0.12 by photometric titration at 285 nm, and values of 4.03±0.26 and 4.16±0.20 were found for the third dissociation constant by photometric titrations at 320 and 295 nm, in 10% ethanol, in close agreement with previously reported values. The fluorimetric titration profile obtained by exciting at 274 nm and measuring the fluorescence emission at 350 nm, in the zone betweenH ₀=–3 and pH=10, is complicated by the several equilibria involved.     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

Diode-pumped Tm: YAG solid-state lasers with indirect and direct manifold pumping

We study the continuous-wave (cw) characteristics of both two-manifold and three-manifold Tm: YAG laser pumped at _p 1.8 µm or _p = 0.785 µm and lasing at ₁ = 2.02 µm. The three-manifold rate equations are adiabatically reduced to their two-manifold form. For each pumping scheme, the steady-state rate equations are combined with the cw differential equations for the forward- and reverse-lasing fields and the pump-depletion differential equation. These three coupled cw differential equations are solved analytically. This gives the linear flux-conservation law between the input pump and the laser output, the minimum crystal length, and optimal output couplings. We show that the major difference between these two pumping schemes is due to the different pump effective absorption cross sections and not the two-for-one cross relaxation. Our example shows that the minimum intensity threshold and optimal crystal length are smaller for pumping at _tp = 0.785 µm than pumping at _p 1.8 µm.     

Analysis of the order parameter for uniform nearest particle system

The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space . The rigorous upper bound ^(mf) = ( – 1)/ for the order parameter ₂, is given by the correlation identity and the FKG inequality. Then an improvement of this bound ^(mf) is shown in a similar fashion; C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value _c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense.     

The lasing mechanism of nuclear-pumped IR lasers at krypton and argon atomic transitions

For studying the lasing mechanism of nuclear-pumped IR lasers at krypton and argon atomic transitions, the kinetics of the plasma process is considered and computations are made for the energy and threshold characteristics of He-Kr (=2.52 m) and He-Ar (=1.79 m) lasers excited by uranium fission fragments. The calculated optimal pressures, mixture compositions, laser output powers and threshold characteristics agree satisfactorily with the experimental ones.