Optical Pumping of Samarium Atoms in a Bichromatic Laser Field in the Presence of Velocity-Changing Collisions

Dark resonances in the ¹⁵⁴Sm -system 4f ⁶6s ²(⁷ F ₀) 4f ⁶6s6p(⁹ F ₁ ⁰) 4f ⁶ s ²(⁷ F ₁) are observed alongside the velocity selective optical pumping. The shape of the resulting spectra strongly depended on the buffer gas (He, Ar) pressure due to velocity-changing collisions (VCC): the sign of the effect could be reversed from the dark to the bright resonance. The observed spectra are interpreted within the framework of the hard-sphere collision model. The role of VCC in the formation of the dark state in the -system is discussed.     

Distinctive Features of the Absorption Spectra of Titanium and Iron Ions in α‐Al2O3:Ti,Fe Crystals

In the UV and visible radiation regions, the absorption spectra of Al₂O₃:Ti,Fe single crystals grown under oxidizing conditions by the Verneuil method are investigated. A considerable residual absorption in the regions 200–300 and 400–600 nm is revealed, which depends strongly on the conditions of growing (the growth rate and temperature drops) and which is caused by transitions in an impurityvacancy complex with charge transfer (IVC CT) O^2––Ti⁴⁺...Fe³⁺ and by conversion of the state of titanium ions Ti⁴⁺ Ti³⁺. The reversible conversion of the state of titanium ions Ti³⁺ Ti⁴⁺ on bending strain of specimens is established.     

The Effect of Increasing the Rate of Repetitions of Classical Reactions

Using quantum theory operator method, we discuss the general reversible classical reactions A ₁ + A ₁ + A _r B ₁ + B ₂ + + B _s, where r and s are arbitrary natural positive numbers. We show that if either direction of the reaction is repeated a large number of times N in a finite total times T then in the limit of very large N, keeping T constant, one remains with the initial reacting particles only. We also show that if the reaction evolves through different possible paths of evolution, each of them beginning at the same side of the reaction, proceeds through different intermediate consecutive reactions and ends at the other side, then one may realize any such path by performing in a dense manner the set of reactions along it. the same results are also numerically demonstrated for the specific reversible reaction A + B A + C. We note that similar results have been shown to hold also in the quantum regime.     

Single crystal diffraction pattern of germanium

The diffraction pattern for the (111)-reflection of germanium was measured by means of the three-crystal arrangement and compared with dynamical theory. The results obtained indicate the possibility of using germanium crystals for precise measurements in X-ray spectroscopy.

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(111) . .

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In conclusion the authors thank Ing. Hrubý for preparing the germanium single crystals and participating in the preparation of the surfaces; they are also indebted to V. Smutná, R. ída and A. Irra for the care with which they carried out various tasks and V. Horáková for carefully performing the numerical calculations.     

A Note on Anisotropic Percolation

We consider an anisotropic independent bond percolation model on , i.e. we suppose that the vertical edges of are open with probability p and closed with probability 1–p, while the horizontal edges of are open with probability p and closed with probability 1– p, with 0 < p, < 1. Let , with x₁ < x₂, and . It is natural to ask how the two point connectivity function P_p,({0 x}) behaves, and whether anisotropy in percolation probabilities implies the strict inequality P_p,({0 x})> P_p,({0 x}). In this note we give affirmative answer at least for some regions of the parameters involved.Mathematics Subject Classifications (2000). 82B20, 82B41, 82B43.     

Mössbauer study of mixed valent silicides Eu(Ir1−x Pd x )2Si2

The solid solutions Eu(Ir_1–x Pd _x )₂Si₂, which exist for 0x0.125 and 0.75x1. cristallize with the tetragonal ThCr₂Si₂-type structure. The variation of the europium valence with composition has been thoroughly studied at temperatures 4.2T293 K by¹⁵¹Eu Mössbauer resonance. For 0x0.125 the europium valence at room temperature decreases asx increases. For 0.75x1 the valence transition temperature Eu³⁺Eu²⁺ increases asx increases.     

Traces of Intertwiners for Quantum Groups and Difference Equations

In this Letter we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights ,, three scalar parameters q,,k, and spectral parameters z ₁,...,z _N , which may be regarded as q-analogs of conformal blocks of the Wess–Zumino–Witten model on an elliptic curve. It is expected that in the rank 1 case they essentially coincide with the elliptic hypergeometric functions defined by Felder and Varchenko. Our main result is that after a suitable renormalization the traces satisfy four systems of difference equations – the Macdonald–Ruijsenaars equation, the q-Knizhnik–Zamolodchikov–Bernard equation, and their dual versions. We also show that in the case when the twisting automorphism is trivial, the trace functions are symmetric under the permutation , k . Thus, our results generalize those of Etingof and Schiffmann, dealing with the case q=1, and Etingof, Varchenko, and Schiffmann, dealing with the finite-dimensional case.     

Off-shell effects inpp↔πd spin observables

We show that spin observables inppd are fairly sensitive to small changes in the off-shell N helicity amplitudes. This is illustrated at proton laboratory kinetic energies ofT _p=515 MeV andT _p=578 MeV. A reduction of the helicity-flip amplitude by 13% brings the predictions of the relativistic rescattering model much closer to experiment.     

Muon level crossing resonance in aluminium

Cross relaxation between implanted positive muons and²⁷Al nuclei in Al metal, lightly doped with Cu to impede the muon diffusion, shows weak resonances at 2.3 and 4.0 mT. Assignment of these to polarization transfervia the 1/2 3/2 and 3/2 5/2 transitions of the (J=5/2) spins leads to a quadrupole coupling constante ²qQ/h=1.8(1) MHz,i.e. an electric field gradient on Al nuclei immediately adjacent to the muon siteq=0.048(3) a.u., with a small departure from axial symmetry.     

The Crystallography of Interphase Boundaries Between Silicon Carbide and Silicon Nitride in Silicon Nitride—Silicon Carbide Particulate Composites

Interphase boundaries between 3C SiC grains and two different -Si₃N₄ morphologies in Si₃N₄–SiC composites have been studied by transmission electron microscopy. In general, boundaries between small -Si₃N₄ intragranular precipitates and surrounding SiC grains were relatively free of intergranular films, whereas boundaries between large -Si₃N₄ grains and adjacent SiC grains were invariably covered with thin intergranular films. Orientation relationships approximating to [110] 3C SiC [0001] -Si₃N₄ and (001) 3C SiC (10 0) -Si₃N₄ were found to dominate between 3C SiC grains and the intragranular -Si₃N₄ precipitates, but there was no evidence of any favoured orientation relationship between the large -Si₃N₄ grains and adjacent SiC grains. The rationale for special orientation relationships arising when there is no intergranular film present at 3C SiC–-Si₃N₄ interfaces is explored geometrically using the near-coincidence site lattice model, with the significant result that the dominant orientation relationships between 3C SiC grains and the intragranular -Si₃N₄ precipitates have low misfits relative to all other possible orientation relationships between 3C SiC and -Si₃N₄.     

Continued fractions and fermionic representations for characters of M(p,p′) minimal models

We present fermionic sum representations of the characters _{, s} ^{(p, p)} of the minimal M(p,p) models for all relatively prime integers p>p for some allowed values of r and s. Our starting point is biomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin 1/2 chain of anisotropy –=–cos((p/p)). We use the Takahashi-Suzuki method to express the allowed values of r (and s) in terms of the continued fraction decomposition of {p/p} (and p/p), where {x} stands for the fractional part of x. These values are, in fact, the dimensions of the Hermitian irreducible representations of SU _q- (2) (and SU _q+ (2)) with q–=exp(i{p/p}) (and q+=exp(i(p/p))). We also establish the duality relation M(p,p) M(p–p,p) and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Dedicated to Prof. Vladimir Rittenberg on his 60th birthday     

Laser action below threshold inversion due to coherent population trapping

The possibility of lasing without inversion on the 1079.8 nm line of a HeNe laser is investigated. It is shown that a modified double- scheme can be realized by use of the 877.9 nm line for introducing Zeeman coherence. It is shown experimentally that Zeeman coherence can enforce laser action, even if the inversion is below threshold. A different choice of the polarization of the driving beam can result in suppression of laser action above threshold. The underlying mechanisms are examined. On the 611.8 nm line, laser action below threshold inversion is obtained with the driving beam tuned to 824.9 nm (up-conversion).     

Lorentz covariance of theP(φ)2 quantum field theory without higher order estimates

We give a simple proof of Lorentz covariance for theP()₂ model without using the higher order estimates: For each Poincaré transformation {a, } and each bounded regionB of Minkowski space there exists a unitary operatorU which correctly transforms the Heisenberg picture field operator:U (f)U*=(f _(a,)),f C ₀ (B).     

Study of the Influence of the Excitation Laser Power Density on the Intermediate-Field Electric Modulation Component of the GaAs Photoreflection E 0-Signal

The influence of the excitation laser power density L on the amplitude A and characteristic time constant of the intermediate-field electric modulation component of photoreflection spectra measured in the region of the E ₀ fundamental transition of GaAs is studied. Crystalline samples with the charge carrier concentration n 10¹⁶ cm^–3 are investigated for L = 100 W/cm²–1 W/cm². A logarithmic dependence of the electric modulation signal on the excitation laser power density has been established for all examined samples. It is demonstrated that the observed change in the characteristic time constant does not have any noticeable effect on the dependence A(L).     

Dispersion of the permittivity of high-resistance semiconductors

We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length L_s of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time _M and the times of carrier capture: _c and ejection _e by an impurity center. For _cetm and (/L_s) _e/_c1 the dispersion of and is the same as for thick plates (/L_s1). For _{c m e} and (/L_s)_e/_c1 the () curve has a characteristic kink in the region 1/_e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Nonlinear Response of the Semiconductor Laser with Pump Current Modulation

The influence of tuning the lasing monochromatic radiation frequency _g within the amplification band on the nonlinear response of the semiconductor laser with harmonic modulation of pump current is investigated theoretically. It is established that the principal features of the behavior of the nonlinear amplitude-detuning characteristic (ADC) are determined by the relation between the current modulation frequency _m and the main resonance frequency of the laser _r. If _{m r}, then with increase in _g the response decreases monotonically mainly due to the decrease of its dynamic component. The exception is provided by the spectral regions where peaks on the ADC appear because of the explicitly nonlinear lasing regimes (period doubling, chaos, etc.) When _m < _r, the resonance conditions for induced oscillations are satisfied only for definite spectral intervals within the amplification band and a dip appears on the low-frequency side of the ADC. With decreasing _m, the dip boundary shifts to a more high-frequency region of the band corresponding to smaller local resonance frequencies. The peaks on the ADC corresponding to the radiation period doubling shift to the region of smaller values of _g on increase in _m.     

The character of cyclotron instability of hydromagnetic waves

The method of energy balance is used for calculating the growth rate of hydromagnetic waves ( _H in the regime of a cyclotron resonance. The HM waves are propagated at an angle to the external magnetic field. A tenuous beam of charged particles with a finite Larmor radius penetrating through a cold plasma is assumed to be responsible for the cyclotron instability process.The author is grateful to Assoc. Prof. Dr. A. Hruka CSc. for helpful discussions and remarks concerning the problem. He is also indebted to Mrs. E. Lomecká for the graphical work.     

Unitarity bounds for 4-fermion contact interactions

In this paper we consider the effect of unitarity bounds s_bs(E₁+E₂) _cms ² for the recently proposed types of nonderivative 4-fermion contact interactions. To this purpose we decompose the helicity amplitudes at c.m.s. into partial waves. The bounds are defined to hold for all reaction channels due to the same type of contact interaction. We find s_b=4/. Here is the coupling constant. The factor depends on the type of coupling and on the different cases to identify the fermions. It ranges from 1/3 to 4.     

On the maximization of the central gravitational red-shift of a schwarzschild sphere with a given surface gravitational red-shift

Following Bondi static, spherically symmetric equilibrium configurations with a core and an envelope have been considered. It has been shown that for any configurations with nonnegative pressure and density and with a surface red-shiftz _s 4.77 arbitrarily large central red-shiftsz _c are possible in the limiting case of arbitrarily large radius. The effects of imposition of further constraints in the form of a real speed of sound not exceeding the speed of light are also examined. It is seen that for a given limiting sound-to-light-speed ratio . (i) There exists a limiting surface red-shiftz _s() 1.71. (ii) A configuration withz _s >z _s() is not possible, (iii) A configuration withz _s=z _s() has a unique and finitez _c=z _c(). (iv) Forz _s<z _s() arbitrarily large central red-shifts can be obtained for configurations with arbitrarily large radii.