Showing papers in "European Physical Journal A in 1968"

Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection

Abstract: A new method of exciting nonradiative surface plasma waves (SPW) on smooth surfaces, causing also a new phenomena in total reflexion, is described. Since the phase velocity of the SPW at a metal-vacuum surface is smaller than the velocity of light in vacuum, these waves cannot be excited by light striking the surface, provided that this is perfectly smooth. However, if a prism is brought near to the metal vacuum-interface, the SPW can be excited optically by the evanescent wave present in total reflection. The excitation is seen as a strong decrease in reflection for the transverse magnetic light and for a special angle of incidence. The method allows of an accurate evaluation of the dispersion of these waves. The experimental results on a silver-vacuum surface are compared with the theory of metal optics and are found to agree within the errors of the optical constants.

Transformation of Gorkov's equation for type II superconductors into transport-like equations

Abstract: The stationary behavior of type II superconductors is completely described by Gorkov's equations for a set of four Green's functions, supplemented by two self-consistency equations for gap parameterΔ(r) and vector potentialA(r). Expanding all quantities as usual at the Fermi surface and averaging over impurity positions, this set of equations is transformed into a simpler set for integrated Green's functions (which still contain much more information than is needed in most cases). The resulting equations, when linearized, yield essentially Luders' transport equation for de Gennes' correlation function. The full equations contain all the known results and provide a promising starting point for numerical calculations. The thermodynamic potential is constructed as a functional of the integrated Green's functions and the mean fieldsΔ andA and a variational principle is formulated which uses this functional. Finally, paramagnetic scatterers are included (in Born approximation) as an example for possible generalizations of the new equations.

Zur formelmäßigen Darstellung des Ionisierungsquerschnitts für den Atom-Atomstoß und über die Ionen-Elektronen-Rekombination im dichten Neutralgas

Abstract: Thomson's classical theory for the calculation of ionisation cross sections in electron-atom encounters is applied for calculating the ionisation cross section for atom-atom collisions. A very simple formula is obtained permitting a rapid calculation of the total ionisation cross sections as a function of the kinetic energyEa and the massmA of the ionizing atom, and of the binding energyEi and the number ξi of equivalent electrons in the electronic shell to be ionized. The formula is in good agreement with quantum mechanical calculations and with experimental results. It can be applied to ionization from ground and from excited states. From this formula one obtains an expression for the rate coefficient for ionization in the center-of-mass system of the colliding particles. Then, the method of detailed balancing is applied to calculate the rate coefficient for ion-electron three-body collisional recombination with a neutral atom acting as the third body. This latter formula is applicable to recombination into the ground and into excited states.

Quantum theory of light propagation in a fluctuating laser-active medium

Abstract: The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.

The onset of superconductivity in the time dependent Ginzburg-Landau theory

Abstract: The fluctuations of the local order parameter above the superconducting transition temperature give rise to singularities in the electrical conductivity and the diamagnetic susceptibility. Using the time dependent Ginzburg-Landau equation the fluctuation of the current density is calculated. By means of the fluctuation-dissipation theorem and a dispersion relation the electromagnetic response function is then determined for small frequencies and wave-numbers. The dynamical conductivity for bulk material, thin films, and thin wires shows an increasing peak at zero frequency the width of which decreases as the transition temperature is approached. This structure should be observable in microwave experiments.

An approximation for rotation-projected expectation values of the energy for deformed nuclei and a derivation of the cranking variational equation

Abstract: An approximation is given for the expectation value of the Hamiltonian with functions: where ¦ϕ〉 is a HFB wave function of a deformed nucleus. This is achieved by expanding the overlap function of the energy 〈ϕ¦ HD(Ω)¦ϕ〉 in derivatives of the overlap function of the norm 〈ϕ D(Ω)¦ϕ〉. The cranking equations for even nuclei are yielded by varying the approximate energy.

The quantum fluctuations of the optical parametric oscillator. i.

Abstract: Our treatment is based on a microscopically correct Hamiltonian which contains the Bose-operators of the light modes and the Fermi-operators of the optically active electrons in the medium. The coupling between modes and atoms is taken from quantum-electrodynamics. Besides that, the light modes may interact with external “heat baths” like the mirrors, scattering centers etc., while the atoms interact with lattice vibrations, incoherent light fields etc. Using recently developed methods the effect of these heatbaths is taken into account in a quantum mechanically consistent fashion. In the present paper we apply quantum mechanical Langevin equations for the field and electron operators which contain dissipation and fluctuation terms. The elimination of the electron operators by an iteration procedure finally leaves us with a set of coupled nonlinear field equations which are shown to be quantum mechanically consistent. They are solved in the Heisenberg picture below threshold by linearization and well above threshold by quantum mechanical quasi-linearization. The solutions show that the line width of the signal mode below threshold is due to the vacuum fluctuations in the idler and vice versa, whereas the thermal noise of the resonator and the spontaneous emission noise of the medium may be neglected. Above threshold the linewidth is caused by the undamped diffusion of the phase difference between signal and idler, to which the vacuum fluctuations of both modes contribute in equal parts. The phase sum of both modes adiabatically follows the slow phase diffusion of the external pump light, produced by a laser, and therefore contributes to the linewidth too. Well above threshold the amplitudes are stable. Correlation and cross-correlation functions of their small residual fluctuations are calculated.

Interferenzen bei atomaren Stoßprozessen und ihre Interpretation durch ein modifiziertes Lennard-Jones-Potential

Abstract: The influence of the shape of the interatomic potential on the total and differential scattering cross section, with special consideration given to interference effects, was numerically studied with the help of a 5 parameter modified Lennard-Jones potential. It is shown that the experimental data for the systems Na-Kr and Na-Xe, for which precise measurements are available, can be well reproduced with the use of such a potential. The absolute value and velocity dependence of the total scattering cross section as well as rainbow scattering and rapid oscillations in the differential scattering cross section were all used in the comparison of the calculated with the experimental values. In addition, the modified potential has been used in a re-evaluation of recent experimental results for alkali metal —inert gas scattering.

Berechnung der Energieverluste schneller Elektronen in dünnen Schichten mit Retardierung

Abstract: Regarding the retardation of the electromagnetic field, a semiclassical formula for the energy-loss-probability of fast electrons penetrating a thin foil with a dielectric constantɛ=ɛ(Ω) is derived. This formula is discussed for the special cases of the free electron gas and the occurence of Cerenkov-radiation in substances with high dielectric constants. Numerical evaluations have been made for these cases. Significant deviations from the formula without retardation are found, which are confirmed by the experiments.

Die Emissionskontinua thermischer Edelgasplasmen

Abstract: Absorption cross sections of the rare gases Ne, Ar, Kr, and Xe have been calculated by the quantum defect method. From them absorption coefficients for bound-free transitions in thermal plasmas of 8,000 to 16,000 °K have been derived. The wavelength range considered extends from 2,000 to 7,000 A. The results are compared with those of other authors and with new experimental data. They agree satisfactorily.

Anisotropie der Plasmaschwingungen in Graphit

Abstract: Energy loss spectra of electrons at different incidence angles α against the crystal axis were measured in transmission of thin graphite single crystals The spectra show that the energy and the intensity of the loss peaks are dependent on the angle between the transferred pulseħk p and the crystal axisc

Genaue Potentialbestimmung aus Streumessungen: Alkali-Edelgas-Systeme

Abstract: Recent improvements in precision and the increase in number of molecular beam scattering experiments demand a reanalysis of the experimental data. The commonly used potential functions show a serious lack of flexibility, and fitting procedures are not unambigious. A new potential ansatz (which is a continuous modification of the (12-6)-potential) has been used to fit all available data on the alkali-rare gas systems Li-Kr, Na-Ar, Na-Kr, Na-Xe, K-Ar, and K-Kr. Aχ 2-minimum method is used as the procedure to fit the data and to estimate the errors of the parameters obtained (see Table 1). It turns out, that the shape of the potential is similar for all systems evaluated here but probably different from that derived for rare gas-rare gas systems.

Die Auger-Spektren der L 2 - und L 3 -Schale von Argon

Abstract: TheL 2 MM andL 3 MM-Auger spectra of gaseous argon have been investigated with an electrostatic spectrometer with energy resolution of 017% The ionization in theL 2 andL 3 shell was caused by electron impact It was possible to separate allL 2 MM andL 3 MM lines except the components of transitions to triplet final states The experimental relative intensities of transitions within theL 2 M 2,3 M 2,3 andL 3 M 2,3 M 2,3 groups agree well with theoretical values, calculated byRubenstein, whereas the relative intensities of transitions of the groupsL 2 M 1 M 1,L 3 M 1 M 1,L 2 M 1 M 2,3 andL 3 M 1 M 2,3 differ systematically from theoretical values

Anionische Silberzentren („B-Zentren“) in Alkalihalogeniden

Abstract: It is proposed that negatively charged silver ions on anion sites are responsible for theB bands found in silver doped alkalihalides. Experimental investigations confirming this model of theB center are presented. Optical absorption and emission ofB centers were measured in seven alkalihalides in the temperature range from 450 to 4 °K. Configuration coordinate diagrams were obtained for KCl, KBr, and KI.

Green's function theory of the Kondo effect in dilute magnetic alloys

Abstract: The exact solution of thet-matrix integral equation derived from the self-consistent Nagaoka equations in the theory of dilute magnetic alloys is established. It is shown that the unique solution for thet-matrix involving all Kondo type anomalies can be found under quite general assumptions. Using the exact solution we have calculated thermodynamic properties of dilute magnetic alloys. It is found that the excessive specific heat of the system due to the anomalous scattering of conduction electrons from the magnetic impurities is of the order ofBoltzmann's constant per local moment at low temperatures. In the limit of vanishing temperature the specific heat goes to zero asymptotically as (lnT)−4. Finally the entropy difference of the interacting system as compared to the free system is calculated.

Das Coster-Kronig- und Auger-Spektrum derL1-Schale von Argon

Abstract: The Coster-Kronig and Auger spectrum of theL1 shell of gaseous argon has been investigated with an electrostatical spectrometer. The ionization in theL1 shell of argon was caused by electron impact. Absolute energies and relative intensities of all the Coster-Kronig and Auger transitions have been determined. The relative intensities of transitions within the groupsL1L2, 3M1,L1L2, 3M2, 3 andL1MM agree fairly well with the theoretical values, calculated byRubenstein for extreme Russel-Saunders coupling, if intermediate coupling theory is used properly.

Investigation of the collective potential-energy-surface

Abstract: The structure of the collective potential-energy-surface is discussed. By use of its rotational invariance it is possible to determine the surface explicitly without the necessity of calculating all points in thea 0-a 2-plane microscopically. The contributions of three essential parts, namely the single particle-stiffness, the pairing-interaction and the Coulomb-force, are thoroughly investigated. The surface is compared with experimental data in the rare earth region and yields important results for the structure of the collective vibrations in these nuclei.

Recoupling coefficients of the symmetric group for shell and cluster model configurations

Abstract: Recoupling coefficients of the symmetric group are defined from the reduction of irreducible representations of this group to direct product representations of particular subgroups. These recoupling coefficients are analysed and shown to be identical to the invariants of unitary groups arising from the reduction of Kronecker product representations. The recoupling coefficients have applications in configurations of several shells or clusters.

Range of recoil atoms in isotropic stopping materials.

Abstract: A calculation of the stopping power, range, and range straggling of low energetic atoms (E≲1 MeV) is reported. The computation applied the biatomic repulsive potential of Firsov and thus had to be carried out numerically. The results, however, are presented in an analytical form. — Experimental checks were performed with recoil atoms. 96 keV Ra-224 atoms from the α-decay of Th-228 were used to measure the range distributions in several light gases. — The fast neutron induced reactions, such as (n, p)-or (n, α)-reactions, led to recoils of higher energies (up to more than 1 MeV). Their mean ranges in polycrystalline metals or amorphous oxide layers could be obtained by measuring the fraction of radioactive recoils which had left the target surface. — The experimental data are in good agreement with the theory, except at the highest energies where the observed ranges are slightly larger than predicted.

O−−-Lücken-Dipole in Alkalihalogenidkristallen

Abstract: Dielectric loss measurements are reported for KBr, KCl, and NaCl crystals containing O−− ions. The frequency and temperature dependences can be well represented by a Debye curve.

Spinpolarisation langsamer Elektronen durch elastische Streuung an Edelgasatomstrahlen

Abstract: The angular dependence of spin polarisationP(θ) of electrons elastically scattered by noble gas atomic beams is measured in a double-scattering experiment for electron energies between 40 and 150 eV and over an angular range fromθ=30‡ toθ=150‡. Maximum degree of polarisation measured isP=+ 39.5%±2.6% (Xe; 150eV;θ=60‡). The results are compared with the theoretical values ofCoulthard, which agree approximately with the measurements only for Xenon. For all lower atomic numbers the experimental values are higher than the theoretical ones.

An interpretation of the structure of subthreshold fission cross section of 240 Pu

Abstract: The structure recently observed in the subthreshold fission cross section of240Pu is interpreted as being due to intermediate states of the fissioning nucleus associated with the second minimum of the potential energy as a function of deformation postulated byStrutinsky.

Die differentiellen Anregungsfunktionen der n+2-Zustände von Helium

Abstract: Energy and angular dependences for the electron impact excitation of the Helium 23S, 21S, 23P, and 21P states have been measured using monochromatic (0.05 eV) electrons in the energy range from 19 to 23 eV and for scattering angles ranging from 0 to 110°. The structures near the 23S-threshold have been analyzed in terms of resonant and non resonant i.e. direct scattering phase shifts. The first peak in this excitation function at 19.95 eV is mostly due to the rapid change with collision energy of the directs-wave phase of the inelastic scattering, which in turn is a consequence of the existence of the 22S-resonance at 19.3 eV. The energy position and behaviour with collision energy of the first peak at 20.7 eV in the 21S-channel is in agreement with the predictions for the existence of a virtual resonance state ofBurke et al. A term sceme of the He− resonances with assignments of configurations is presented.

Totale Streuquerschnitte für den Stoß von H 2 , D 2 und He an den Edelgasen Ne, Ar, Kr und Xe im thermischen Energiebereich

Abstract: The velocity dependence of the total elastic cross section has been measured for the scattering of H2, D2, and He beams by Ne, Ar, Kr, and Xe gases. Velocity-selected beams were attenuated by gas in a scattering chamber. A universal detector, with a magnetic mass separator, was used in conjunction with lock-in techniques. The results are compared with quantum mechanical calculations using a Lennard-Jones-(12.6)-potential, and employing suitable averaging over experimental velocity distributions. Potential parameters are presented. These are in good agreement with those expected from other methods of measurement.

Schwingungsanregung von H 2 -Molekülen durch Zentralstoß mit Li + -Ionen

Abstract: An apparatus is described for measuring the inelastic differential cross section for vibrational excitation in collisions of diatomic molecules with monoenergetic ions at laboratory energies between 10 and 50 eV. The method consists of measuring the time of flight of single ions with a time amplitude converter and displaying the results on a 100 channel pulse height analyzer. From the shift in the time of flight relative to that expected for elastic scattering the final state of the molecule excited in a single collision is identified. By studying only central collisions with almost zero impact parameter rotational excitation is strongly suppressed. Measured times of flight after collisions of monoenergetic Li+ ions with H2 show that with increasing energy the most probable vibrational quantum jump increases from 0→1 to 0→2,0→3 etc. Contrary to the usual assumption of a small steric factor for vibrational excitation the results show that the inelastic cross section is larger than the elastic cross section. Using reported potential parameters the energy dependence of the most probable excited state is compared with the calculations of Secrest and Johnson for a one-dimensional collinear collision. The satisfactory agreement suggests that the steric factor is close to 1. From measurements at different scattering angles at 10 eV the integral inelastic cross section is found to be about 0.2 A2 corresponding to a differential cross section of 0.4 A2/sr. Measured values of integral and differential total cross sections for Li+-He andLi+-H2 are reported and compared with theory. Direct dissociation of D2 by Li+ in the energy range from 25 to 55 eV was not observed, yielding an upper limit for the cross section of 4 · 10−4 A2/sr.

Berechnung der Besetzungsdichte und Ausgangsleistung von Ionenlasern

Abstract: Rate equations for the density of excited ions in noble gas discharges are solved for the steady state. The atomistic parameters in the theoretical treatment are replaced by experimental values. Hence inversion density and single pass gain can be calculated as a function of gas pressure, discharge current and geometry of the discharge tube. Conditions for maximum inversion density and power output are calculated and compared with experimentally determined values. The calculation is pointing out large bored tubes to be advantageous for high power operation. Numerical evaluations are particularily given for theA+ line 4880 AU.

The resistivity of a superconductor in its normal state

Abstract: GLOVER 1 has observed (and subsequently STRONGIN et al. 2) that the conductivity of a metal increases as the temperature is lowered towards the transition temperature to the superconducting state. Thus the approach of superconductivity is revealed above the transition temperature. This behaviour was explained later quantitatively by ASLAMAZOV and LARKIN 3, and SCHMIDT 4 by a microscopic theory. In the following I want to show that this effect can also be understood fairly simple on the basis of the Ginzburg-Landau equations 5 and their time dependent generalisation given by the author 6. We will use the concept that in a metal above the critical temperature, (small) superconducting regions will grow and decay in due course of time as a result of fluctuations, similar to the growth and decay of condensed droplets in a gas at temperatures just above the critical point. Let us consider a metal of very short mean free path such that the normal electrons are virtually stuck in the dense jungle of lattice defects. Then, only the superconducting regions (=drople ts) contribute to the current, and the conductivity can be calculated by means of

Zur Dispersion der OberflÄchenplasmaverluste an reinen und oxydierten AluminiumoberflÄchen

Abstract: The dispersion of the surface plasma oscillations is caused by 1. the coupling of the two surfaces of thin foils, that leads to a splitting into two modes of oscillation with different dependence of frequency on wavelength. 2. the influence of thin coating of e.g. oxide, that produces a displacement of the frequency depending on the wavelength of the surface oscillation.

Elektronen-Energieverlustmessungen und Berechnung optischer Konstanten

Abstract: Energy loss measurements on KBr-films applying 51 keV-electrons are reported. The loss spectrum is interpreted in terms of excitonic structure, interband structure, and plasmons. The temperature dependence concerning position and half width, and the angular dependence of the intensity of different energy losses is investigated. From the loss spectrum the energy loss function —Im 1/g3 is calculated. By means of a Kramers-Kronig transform optical constants are calculated from the loss function. Absorption and reflectance, especially, are found to agree very well with optical spectra.