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It is shown that a previous calculation of the escape factor G for moderate values of the optical depth yields to large values. [ABSTRACT FROM AUTHOR]

In continuation of a previous paper we investigate the interaction of one or several cavity modes described by standing waves with a set of atoms each with two optically active levels and a homogeneously broadened line. The modes may or may not be at resonance with the atomic transition. The pumping is again introduced explicitly. A deeper motivation of its mathematical formulation is given in the Appendix, together with the description of another pumping mechanism. If the time-dependent response of the atomic system is small, the following results are obtained: Above threshold several modes can exist due to the different spatial inversion of the atomic inversion. The amplitudes fluctuate around values obeying algebraic equations which are for moderate pumping power equivalent to those of a previous paper by Haken and Sauermann. The phases may, however, undergo an undamped diffusion process, giving rise to a linewidth, which, if properly normalized, is that of single mode operation. The linewidth is determined explicitly for several physical situations. Finally, the complex degree of mutual coherence of two modes from the same laser is compared with that of two different lasers. [ABSTRACT FROM AUTHOR]

The temperature dependence of the thermal resistivity of alkali metals lithium, sodium, potassium, rubidium and caesium is determined within the free electron approximation by using Krebs's model for the phonon dispersion relations. The normal and Umklapp contributions are obtained separately from an improved method following the procedure of an earlier paper. The results of calculations are compared with available experimental information. The theoretical and experimental resistivity curves are found to be of similar nature, but they show considerable disagreement at low and high temperatures. [ABSTRACT FROM AUTHOR]

A short derivation of the Random Phase Approximation of angular momentum waves in solid Ortho-H is presented. Methods and results of papers on the same topic are compared. [ABSTRACT FROM AUTHOR]

The mean lives ofMg levels have been studied using the Doppler-shift attenuation method in theMg( d, pγ) reaction at E=6 MeV. Except for the E=6873 keV level, all levels between 2 MeV excitation energy and the neutron binding energy could be investigated, yielding 11 mean lives and 30 limits thereof. A large number of multipole transition rates could be deduced and several parity assignments be made. The relevance of the data with respect to the rotational model is discussed. A serious breakdown of the K-selection rule, which has been proposed earlier for some high-spin states, is confirmed. [ABSTRACT FROM AUTHOR]

We extend our previous quantum mechanical nonlinear treatment of laser noise to the following problem: We consider a set of atoms each with three levels, which support laser action of one or several modes. The laser action can take place either between the upper or the lower two levels. The atomic line is assumed to be homogeneously broadened. The broadening can be caused by the decay into the nonlasing modes, by the pumping process, lattice vibrations and other, non specified sources. The fluctuations of the atomic variables (or operators) are taken into account in a quantum mechanically consistent way using results of previous papers by Haken and Weidlich as well as Schmid and Risken. The laser modes are coupled to the thermal resonator noise using Senitzky's method. In the first part of the present paper, we treat quite generally multimode laser action. It is shown, that each light mode chooses a specific collective atomic 'mode' to interact with. We introduce a set of suitable collective atomic 'modes', which leads to a simplification of the equations of motion for the Heisenberg operators of the light field and the atomic operators. From the new equations we can eliminate all atomic operators. We are then left with a set of coupled nonlinear, integro-differential equations for the light field operators alone. These equations, which are completely exact and valid both for running and standing waves, represent a considerable simplification of the original problem. In the second part of this paper, these equations are specialized to single mode operation, which is studied above laser threshold. In the vicinity of the threshold the laser equation can be simplified to an operator-equation, whose classical analogue is vander-Pol's equation with a noisy driving force. With increasing inversion, the full equation must be treated, however. Using the method of our previous paper, we decompose the light amplitude into a phase-factor and a real amplitude, which is expanded around its stable value. We determine the Fourier-transform of the intensity correlation function and the total intensity of the fluctuating part of the amplitude. Somewhat above threshold this intensity drops down with the inverse of the photon output power, P, while the inherent relaxation frequency increases with P. The noise intensity stems in this region from the off-diagonal elements of the noise operators and not from the diagonal elements, which are responsible for the shot noise. This result is insofar remarkable, as a rate equation treatment would include only the latter ones. Under certain conditions the intensity fluctuations can show resonances with increasing output power, P. At high inversion the vacuum fluctuations of the light field are dominant, while the other noise sources give rise to contributions which vanish with the inverse of the output power. As a by-product our treatment yields the following formula for the linewidth (half width at half power) which is caused by phase fluctuations: κ is the cavity half-width, γ the atomic half-width for the transition (3→2). N and N are the steady state occupation numbers of the atoms, n is the number of thermal quanta. This formula is valid for running and standing waves (with finite wavelength) and a two, three or four level system. It contains previous results of the present author, as well as those of Lamb, Sauermann and Lax, either as special cases, or generalizes the range of applicability, as discussed in the text. [ABSTRACT FROM AUTHOR]

We consider a N-level system of one electron being subject to a heatbath or fluctuating forces as well as to classical or quantum mechanical driving forces. We assume that the equation of the density matrix averaged over the heatbath is already determined with all damping constants and transition probabilities. By this procedure the electron transition operators a (t) a (t) loose, however, their property to form an algebraic ring with the relation a a a a= δ a a (1) (in the one-particle subspace). We reintroduce now fluctuating forces (which have disappeared by the averaging) into the density matrix equation and require that (1) holds if it is averaged over the heatbath. We show, that this requirement determines uniquely all second order correlation functions of the fluctuating forces, which are assumed to be Markoffian. An explicit formula is given, by which these correlation functions can be calculated by a simple sum over averaged density matrix elements multiplied with the coefficients of the averaged density matrix equation. Usually, the fluctuating forces stem from many, statistically independent subsystems of the heatbath, so that they are to a very good approximation Gaussian. In this case our treatment fixes also all higher correlation functions. Equivalent results are found in a simultaneous paper by Risken and Schmid, who use a different method. If we specialize to a 2-level system the results agree with those of Sauermann. As will be shown in a forthcoming paper these results lend themselves in a straight-forward way to determine the laser linewidth and amplitude fluctuations of atoms with several levels. [ABSTRACT FROM AUTHOR]

Using the same model as in the previous paper a prediction for the polarization of the recoil protons is given in case of polarized photons. The determination of E and E from measurements is discussed. Furthermore the influence of the ππ-interaction on polarization is considered. In the case of π-production the polarization of the recoil neutrons is investigated and the dependence of the cross section on the polarization state of the target protons is discussed. [ABSTRACT FROM AUTHOR]

In this paper a contribution to the nonlinear theory of laser noise is given. The lasing field is treated as a classical random variable, the noise is introduced by the concept of fluctuating dipoles. In order to obtain correlation functions the method of distribution functions is employed. The distribution functions are calculated by the Fokker-Planck equation. [ABSTRACT FROM AUTHOR]

In the present paper we start an investigation of the generation of second order vorticity (streaming) in an electric conducting, viscous and compressible fluid embedded in an external magnetic field. The equations used are those pertaining to the one-fluid model. First, fairly general equations for the generation of fluid vorticity as well as magnetic vorticity are derived. By using the method of successive approximations, the systems of equations of first and second order are developed. By the use of dimensional analysis the importance in the vorticity generation of the different generating terms is briefly investigated. Next the linear equations for two-dimensional problems are solved in the case of fluid motion above a flexible plate, vibrating in an external magnetic field. [ABSTRACT FROM AUTHOR]

In an earlier paper it was proposed to regard the Second Law of Thermodynamics, in the form of the Principle of Carathéodory, primarily as an essential link in an argument leading directly to the existence of a certain order amongst the states of any adiabatically enclosed system, and to the consequent definition of a continuous empirical entropy function. The previous line of reasoning was unfortunately afflicted with certain errors which require rectification. In the present paper, the first of two, this is achieved in the first place by falling back upon the existence of a continuous and differentiable energy function. This means that the full content of the First Law of Thermodynamics has been invoked. However, in order to go some way towards a clear separation between the contents of the First and Second Laws, it is then shown that the results already obtained may also be deduced by essentially similar arguments if one replaces the First Law by rather weaker assumptions. [ABSTRACT FROM AUTHOR]

In this paper it is shown that the set of kernels introduced previously by Gerlach, Gromes and Petzold can be enlarged considerably. The paper concludes with a remark on the theory of massless particles. [ABSTRACT FROM AUTHOR]

The paper gives an account of numerical results for l=0 and l=1 multipole amplitudes of pion photoproduction. They have been obtained by solving integral equations which originate from fixed-angle dispersion relations that have been deduced in an earlier paper. In this Part I outlined are some difficulties usually encountered in course of solving the problem of pion photoproduction by dispersion techniques, and proposed is an approach which introduces arbitrary parameters - cutoffs in the integral equation for transition amplitudes. Numerical results show some implications of this philosophy on the rôle played by the terms representing physical singularities and terms representing left-hand singularities controlled by one-particle (Born) contributions. [ABSTRACT FROM AUTHOR]

In the present paper frequency shifts and other characteristic properties of the Stokes modes in a solid Raman-active sample are investigated theoretically. The Raman process is described by nonlinear Heisenberg equations for running waves, which is convenient in order to satisfy the momentum conservation condition. The Stokes shifted electromagnetic waves are assumed to be reflected at the endfaces of the crystal to establish standing waves (modes), whereas the vibrational waves are treated as running waves because of their large damping. The calculations are done for (a) one mode in the 1. Stokes line, (b) one mode in the 1. and one mode in the 2. Stokes line and (c) two modes in the 1. Stokes line. Case (c) can be established only if the two modes are placed symmetrically with respect to the center of the line. In all three cases homogeneously broadened lines are assumed. The frequency shifts in (a) and (c) are power-independent. Only in (b) the shift of the 1. Stokes mode depends on the incident laser flux. Nonlinear pulling and power-dependent pushing of arbitrarily situated modes in the 1. Stokes line occur if additonal modes oscillate simultaneously in the higher order lines. Detailed calculations of these interesting cases are given in a forthcoming paper. [ABSTRACT FROM AUTHOR]

In this paper the effect of biquadratic exchange on Curie temperature has been discussed on the basis of double-time temperature-dependent Green-function formalism with the utilization of Callen decoupling scheme. Calculation has been done for a spin-1 bcc Heisenberg ferromagnet by the method of Flax and Raich and it has been observed that the variation of Curie temperature with the biquadratic exchange parameter α obeys a law prescribed by the previous authors. [ABSTRACT FROM AUTHOR]

We present a quantum mechanical nonlinear treatment of the phase and amplitude flucutations of gas lasers, i.e. lasers with moving atoms, and of solid state lasers with an inhomogeneously broadened line. The atoms may possess an arbitrary number of levels. As in our preceding papers the noise due to the pump, incoherent decay, lattice vibrations or atomic collisions, as well as due to the thermal and zero point fluctuations of the cavity is completely taken into account. The linewidth (due to phase diffusion), and the intensity fluctuations (due to amplitude noise) are essentially expressed by the threshold inversion, the unsaturated inversion and the saturated population numbers of the two atomic levels, which support the laser modes. Our results apply to the whole threshold region and above up to essentially the same photon number, to which the previous semiclassical theories of inhomogeneously broadened lasers were applicable. For the example of a two-level system we also demonstrate the application of a new technique which allows us to eliminate rigorously the atomic variables (operators), yielding a set of nonlinear coupled equations for the lightfield operators alone. If the elimination procedure is carried out only partially and additional approximations are made, we find essentially the rate equations of McCumber, in a form derived by Lax. When we neglect noise, the nonlinear equation may be solved exactly in the case of single mode operation. By a suitable expansion of the exact multimode equations we find a convenient set of equations, which reduce in the noiseless case to those derived and used previously by Haken and Sauermann as well as Lamb. [ABSTRACT FROM AUTHOR]

In the first part of the paper we derive expressions of the Ginzburg-Landau (GL) type for the local tunneling density of states of superconducting alloys. These expressions are quite generally applicable at high excitation energies. One can see immediately that the density of states, N(r, ω), at any position r and high energies ω is always larger than the local BCS density of states if the space dependence of the order parameter is governed by the GL-equation. This effect is largest for long mean free paths l. In the second part of the paper we calculate the spatial average of the density of states, ¯N, at all energies ω for a lattice of vortex lines in a magnetic field slightly below the upper critical field. The resulting curve of [ ¯N− N(0)]/N(0) versus co shows no gap and has a zero at about the gap value in zero field. Its value at ω=0 depends on l like ln(ξ/l) for l≫ξ [N(0) denotes the normal density of states, and ξ is the BCS coherence length]. [ABSTRACT FROM AUTHOR]

In extension of a preceding paper the correlation function of the amplitude and of the intensity fluctuation are calculated in the threshold region. The laser amplitude is treated as a classical random variable obeying a van der Pol equation with a noise term. In order to get correlation functions, the method of distribution functions is employed. The distribution functions are evaluated by the Fokker-Planck equation. The lowest eigensolutions of the Fokker-Planck equation are obtained approximately by a variational method. [ABSTRACT FROM AUTHOR]

The mode structure and the diffraction losses of a Perot-Fabry-Interferometer filled with an active material are calculated analytically with a Green's function method. The active material is described by a complex susceptibility. The mode pattern and the diffraction losses derived here are in good agreement with the results of Fox and Li, who obtained the mode pattern and the diffraction losses of the decaying modes of a Perot-Fabry-Interferometer by a machine calculation. Furthermore the case of different dielectric constants between the active material and the outer space and the example of a Perot-Fabry-Interferometer with infinite mirrors are discussed. Throughout the paper only a single mode is treated and it is assumed that the inversion in the active material is constant. [ABSTRACT FROM AUTHOR]

The undulatory behavior in the velocity dependence of the total elastic cross-section Q( v) for atom-atom-scattering can be calculated by the semiclassical approximation. In a previous paper J numerical values of the classical deflection function, which are necessary to evaluate the amplitude of the extrema in Q( v), were reported for a Kihara-potential as a function of the reduced energy K and the potential parameter α. The present paper gives the correspondent reduced maximum phase shifts η ( K,α), which determine the location of the extrema. The results for the Kihara-potential are compared with similar calculations for a Lennard-Jones-( n, 6)-potential. [ABSTRACT FROM AUTHOR]

The interaction of N atoms each with 3 levels at random lattice sites with a set of cavity modes is considered. The optical transition between the lowest two atomic levels is taken into account explicitely assuming a Lorentzian line shape, whereas the third level just serves for the pumping process. If homogeneous inversion of the atoms is assumed, only one coherent mode oscillates in the steady state. It is the one being closest to the atomic resonance and having highest Q. If, however, in the next approximation a mode-dependent depletion of the excited atomic states is taken into account, with increasing pumping rate several modes may oscillate simultaneously. The behaviour of two such modes is treated in detail and it is shown, that one obtains a stable configuration. Using a higher approximation the nonlinear interaction between these two modes brought about by the amplifying material is studied in detail. As a special result one obtains a repulsion of the frequencies of the modes as a function of pumping power in accordance with gaslaser experiments. Quantum noise effects are neglected throughout the present paper. [ABSTRACT FROM AUTHOR]