Showing papers in "European Physical Journal in 1965"

A model for streamer propagation

Abstract: A model is presented to describe the propagation of positive corona streamers in the low field region of a non-uniform field gap in atmospheric air. It has been assumed that the growth is a property solely of the streamer tip, uninfluenced by the channel conductivity. Calculations from the model indicate that the criterion for propagation of a streamer in zero external field is that the number of ions in the tip be 108 and the radius about 3×10−3 cm. It is proposed that the streamer ceases to propagate as a result of the loss of energy of the tip due to the formation of ion pairs in the channel. The results of previous experimental observations of streamers are compared with calculations derived from the model, and a prediction from the model of the lifetime of streamers after voltage removal is discussed.

Distribution- and correlation-functions for a laser amplitude

Abstract: 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.

Principles and design of Laue-case X-Ray interferometers

Abstract: A theory of the interference mechanism in the Laue case interferometer is presented. Owing to the strong Borrmann effect a straightforward plane wave approach yields complete agreement with observed fringe patterns. The problem of coherence is discussed in some detail. It is shown that the geometrical precision of actual interferometers does not have to be better than 1 to 10 micron. The theory demonstrates that the “ideal” geometry can also be obtained with the transmission mirrors in different planes, allowing the construction of a modified interferometer with especially long and separated beam paths. This type is particularly suitable for practical interferometry.

Coherence-Properties of the Statistical Operator in a Laser Model

Abstract: Fur ein Lasersystem werden die Koharenzeigenschaften des statistischen OperatorsR des Lichtfeldes untersucht. Die Bewegungsgleichung $$\dot R = - \frac{i}{\hbar }[H,R] + \left( {\frac{{\partial R}}{{\partial t}}} \right)_{incoh}$$ enthlat zwei Anteile.\( - \frac{i}{\hbar }[H,R]\) beschreibt die koharente Bewegung in Wechselwirkung mit den Laseratomen. Fur\(\left( {\frac{{\partial R}}{{\partial t}}} \right)_{incoh}\) wird ein Ausdruck hergeleitet, der die inkoharente Bewegung vonR unter dem dissipativen Einflus des Warmebades der Umgebung beschreibt. Die gesamte Gleichung furR wird gelost. Der sich ergebende statistische Operator beschreibt fast einen Glauberzustand, wodurch die entsprechende, den bisherigen halbklassischen Theorien zugrunde liegende Annahme gerechtfertigt wird.

Messung der Driftgeschwindigkeiten von Elektronen und positiven Ionen in Gasen

Abstract: Values of the drift velocities of electronsv − and positive ionsv + in gases were measured under uniform electric field conditions atE/p-values ranging from some 100 to several 1000 volts/cm Torr. — For oxygen, nitrogen and also for acetone and benzene the velocityv − is prop, to √E/p whereas for methane, carbon dioxide and other organic vaporsv − is prop, to (E/p) v withv between 0.5 and 0.8. The individual constants are given. Besides a diagram shows the valuesv − obtained for hydrogen. — The drift velocities of the positive ions in oxygen, nitrogen, and several other gases and vapors were found to hold the square root relationv + prop. √E/p at highE/p changing over to the linear relationv + prop.E/p which is valid in the lowerE/p-region. The factors for the gases are given. By comparing the experimental results with the various theoretical approaches for the ionic mobility it is shown that at lowE/p polarisation forces are governing the interaction between ions and molecules whereas at highE/p the hard sphere model gives good agreement except for oxygen and nitrogen, in which charge exchange is the main interaction process.

Stoßionisierungskoeffizient α, mittlere Elektronenenergien und die Beweglichkeit von Elektronen in Gasen

Abstract: From the analysis of oscillograms of electron avalanches values of the ionization coefficient α for electrons were determined for oxygen, methane, carbon dioxide, and some organic vapors atE/p-values between some 100 and several 1000 volts/cm Torr. Over a certainE/p-region the values satisfy the relation α/p=A exp(-Bp/E)for which the constants are given. — Values of the mean diffusion energyD/b of the electrons were determined for oxygen, nitrogen, hydrogen, and some other gases and vapors ranging from 4 evolts atE/p≃50–100 to some 20 evolts atE/p of several 1000 volts/cm Torr. These values of the diffusion energy are in agreement with those obtained from values of the ionization coefficient α. — The mobility of the electrons is calculated in dependence on the energyD/b and compared with experimental values. It is shown that satisfactory agreement is obtained only when the first two terms of the expansion of the velocity distribution are taken into account.

Der Regenbogeneffekt und Interferenzerscheinungen bei molekularen Stößen

Abstract: Crossed beam measurements of differential elastic scattering cross sections for collisions of alkali atoms with mercury and xenon atoms as well as with different molecules are presented. Special attention is given to the rainbow effect including supernumary rainbows and to interference effects connected with rainbow scattering.

Über die Hyperfeinstrukturaufspaltung der Mößbauerstrahlung durch zeitlich fluktuierende Magnetfelder

Abstract: In magnetic materials the time fluctuation of the atomic spin causes a fluctuation of the internal magnetic fieldH acting on the nucleus. The Mossbauer radiation in such materials suffers a magnetic hyperfine structure splitting, which displays the field fluctuation in a twofold way: (a) an anomalous line broadening $$\gamma (m_a m_g ) = (\mu _a m_a /j_a - \mu _g m_g /j_g )^2 \cdot \overline {(H - \bar H)^2 } \cdot \tau _c$$ and (b) an anomalous line displacement $$\delta (m_a m_g ) = 2(\mu _a m_a /j_a - \mu _g m_g /j_g )^3 \cdot \overline {(H - \bar H)^3 } \cdot \tau _c^{'2} /3.$$

Transition Radiation, Bremsstrahlung und Plasmastrahlung

Abstract: The visible and ultraviolet radiation emitted from electron bombarded metal targets was investigated for normal and oblique electron incidence in the range of primary energiesE=6⋯40 keV. For normal incidence the observed spectra could be separated in transition radiation and bremsstrahlung because of their different energy dependences. When silver targets were bombarded at oblique incidence a third radiation was observed which is peaking nearλ=3500 A (half widthΔ λ=200⋯300 A). For grazing indicence (α=0,5° against the target surface) under UHV conditions the peak intensity is 100 times greater than transition radiation at normal incidence. Due to the wavelenght, the dependence on the angle of incidence, and the strong dependence on surface contaminations this radiation is assumed to be caused by surface plasmon excitation in the silver target.

Auger- und Coster-Kronig-Übergänge der M-Schale von Krypton

Abstract: The Auger spectra of theM 2,M 3,M 4,M 5 subshells of krypton and the Coster-Kronig spectra of theM 1,M 2,M 3 subshells of krypton were measured with an electrostatical spectrometer. The ionization in theM shells was caused by electron impact. The use of a gaseous target made it possible to measure the Auger lines even at energies as low as 25 eV. The absolute energies and relative intensities of a great number of transitions were determined: 22 of theM 4, 5 spectrum, 14 of theM 2, 3 spectrum and 2 of theM 1 spectrum. Only in the case of theM 2, 3 spectrum a comparison between the relative intensities, determined experimentally, and those calculated byRubenstein forZ=47 was possible. The agreement is only qualitatively. Moreover, from the Auger electron energies measured, the following binding energies were calculated:E(M 1)=(292,1±1,0) eV,E(M 2)=(222,1±0,6) eV,E(M 3)=(214,6±0,6)eV,E(N 1 N 1)=(62,81±0,05) eV.

Ableitung verallgemeinerter Ginzburg-Landau-Gleichungen für reine Supraleiter aus einem Variationsprinzip

Abstract: It is shown that generalized Ginzburg-Landau equations follow from the expression $$\Omega = \user2{Sp}\rho (H + T\ln \rho ) + \frac{1}{{2\mu _0 }}\int {(B - B_a )^2 d^3 r}$$ for the thermodynamic potential if the BCS-Hamiltonian is used forH and if Inρ is a certain operator which contains only the functionsΔ(r) andA(r) besides quadratic expressions ofψ andψ+. When selfenergy expressions are suppressed, the stationarity condition forΩ is exactly equivalent to the well known Gorkov equations.Ω is expressed in terms of a thermodynamic Greens function which is then calculated by an elementary but gauge invariant method of solving the Gorkov equations approximately. The second approximation leads directly to the thermodynamic potential whichWerthamer derived from his generalized Ginzburg-Landau equations.

Elastic strain and coloration pattern in natural quartz crystals

Abstract: Very small elastic strains (tilts of the order of 0.25 sec of arc and dilationsΔd/d≃10−6, whered is the spacing of net planes) have been observed in natural quartz crystals. According to their rocking curves which are of almost theoretical width, these crystals were commonly expected to be practically perfect crystals. On double crystal X-ray topographs a pattern was revealed of uniformly strained layers parallel to the rhombohedron faces (10¯11) and with thickness ranging between 20 and 200 microns. This fine structure strain pattern was correlated to the pattern of the optical coloration which could be produced by irradiating the originally transparent crystals with X-rays. A localincrease of coloration matched with a localcontraction of the lattice. Tilts occurred in transition zones between adjacent layers with slightly different lattice spacings. Strain and coloration patterns probably have as a common cause the deposition of layers with different impurity concentrations during the growth process of the crystals. Although no change of the strain as a result of the X irradiation could be detected in the colored layers in particular, experimental evidence has been found for anoverall expansion of the lattice of the order ofΔd/d≃5×10−7 due to X irradiation. This expansion seems to saturate at this low value and is probably caused by electronic processes connected with the coloration. Some aspects concerning the nature of the color centers have been discussed. It seems likely from the results of the strain measurements that both sets of layers, colored and transparent ones, play a combined role in coloration.

Master-equation for the statistical operator of solid state laser

Abstract: In extension of a preceding paper we derive a masterequation for the complete statistical operator of a laser model. The whole system containing atoms, field and several thermal reservoirs, the latter providing loss effects and pumping, is treated quantummechanically. The masterequation is at first solved in the selfconsistent field approximation (SCFA). The results essentially confirm those given by quasiclassical theories, including the coherence properties of the lightmode (comp. (4)). Secondly, an approximate treatment is given of particle-field correlations which go beyond the SCFA and therefore beyond the quasiclassical approach. It is shown explicitly that such correlation effects influence the coherence behavior of the lightfield, i.e. we get a further small deviation from the pure Glauber state.

Optische Absorption und photochemisches Verhalten von SH−-, S−- und S−−-Zentren in KCl-Kristallen

Abstract: SH−-centers are investigated for the first time. New other centers can be produced by photochemical reaction or by reducing treatment with an excess of potassium (F-centers). They are interpreted as S−- and S−−-centers.

Entfernung von sauerstoffhaltigen Anionen aus Alkalihalogeniden

Abstract: Es wird eine Methode zur Vorbereitung von Alkalihalogeniden ohne sauerstoffhaltige Verunreinigungen mittels der Einfuhrung von kohlenstoffhaltigen Halogenierungsmitteln in die Schmelze beschrieben. Die vorbereiteten Einkristalle wiesen keine Absorptionsbanden auf, die den sauerstoffhaltigen Ionen zugeschrieben werden.

Wirkungsquerschnitte für elastische und unelastische Elektronenstreuung an amorphen Kohlenstoff- und Germaniumschichten

Abstract: Absolute intensities of electrons scattered by amorphous carbon and germanium foils were measured for various energies (20–60 keV) and foil thicknesses (200–800 A). Electrons scattered elastically were separated from those scattered inelastically by means of a retarding field. Thus total cross sectionsσe for elastic scattering andσu for inelastic scattering were obtained. Agreement of observed and theoretical values is satisfactory, especially regarding the dependence on electron energy.

Aharonov-bohm scattering of a wave packet of finite extension

Abstract: The scattering of an electron from a thin, shielded solenoid (Aharonov-Bohm effect) is studied by means of the time-dependentGreen's function of the problem. The structure of theGreen's function reveals in a lucid way the nonidentity of canonical and kinetic angular momentum as the origin of the Aharonov-Bohm scattering. The time development of a Gaussian wave packet is studied in some detail to investigate the validity of certain objections against the original work ofAharonov andBohm. In an appendix some results are given for the case of finite radius of the solenoid and finite shielding potential.

Isomerieverschiebung im Eu151

Abstract: The isomer shift of the 21.7 keVγ transition in Eu151 has been studied for various divalent and trivalent europium compounds using the Mossbauer technique. Theγ energy is lower by up to 1.1·10−6 eV in divalent compounds than in trivalent compounds. Using data from atomic spectroscopy it is estimated that the electron density at the nucleus is larger by about 1.9·1026cm−3 for the configuration 4f6 than for 4f7 due to different shielding of thes2 shells. The difference of the mean square radii of the 21.7 keV state and the ground state is thenδ〈r2〉=+0.03 fm2.

Ionisation innerer Elektronenschalen bei fast-adiabatischen Stößen schwerer Ionen

Abstract: Characteristic X-rays produced in nearly adiabatic collisions when fission products of 5–80 MeV energy are stopped in various materials have been studied using proportional counter detection. The cross sections for the ionization of inner electronic shells of both the colliding particles were measured as a function of the velocity and the mass of the fragments and the atomic number of the target atoms. The measured cross sections range from 10−22 to 10−16 cm2. There is no agreement with the values predicted on the basis of a simple Born approximation description. Characteristic maxima were found in the dependence of the cross section on the atomic number of the projectile whenever the binding energy of the excited electron equals the electron binding energies of the various inner sheils of the projectile. The cross sections depend less strongly on the velocity of the projectiles than predicted by the simple theory. The measured X-ray quanta have energies from 1.2 to 11.4 keV. The observed energy values exceed the theoretical ones by about 0.10 keV for projectile atomic numbers >10. A qualitative explanation of the various effects is presented.

Symmetry violating trial wave functions

Abstract: A variational procedure using trial wave functions projected on to symmetry eigenstates is investigated. In the individual particle model it leads to generalized self-consistent single-particle equations being dependent on the symmetry eigenvalue. A perturbation expansion appropriate for the case of strong symmetry violations is described. Model independent expressions for the moment of inertia and the decoupling parameter are derived by applying the method to rotational symmetry.

Plasmaschwingungen gebundener Elektronen: Der charakteristische Energieverlust von 3,6 eV in dünnen Silberfolien

Abstract: Es wird experimentell gezeigt, das der charakteristische Energieverlust von 3,6 eV in Silberfolien aus einem Oberflachenverlust und dem 1955 vonFrohlich undPelzer vorhergesagten Volumen-Plasmaverlust von 3,75 eV zusammengesetzt ist.

Dielektrizitätskonstante, Permeabilität, elektrische Leitfähigkeit, Wärmeleitfähigkeit und Diffusionskonstante von Gemischen mit kugelförmigen Teilchen (gitterförmige und statistische Anordnung)

Abstract: Es wird eine exakte Methode zur Berechnung der Dielektrizitatskonstanten, Leitfahigkeit usw. eines Gemisches mit kugelformigen Teilchen in beliebiger Anordnung entwickelt. Fur eine regelmasige Anordnung der Kugeln fuhrt die Theorie auf ein unendliches Gleichungssystem, das hier fur zwei kubische Gitter in verschiedenen Naherungen ausgewertet wird. Die Konvergenz des Verfahrens ist sehr gut. Im Falle einer statistischen Anordnung der Kugeln gelangt man zu einer gut konvergenten Reihenentwicklung, in der Verteilungsfunktionen auftreten, die die statistische Anordnung der Kugeln beschreiben. Sowohl fur die statistische als auch fur eine regelmasige Anordnung (unabhangig vom Gittertyp) erhalt man als nullte Naherung die bekannte Formel vonMaxwell. Die Auswertung der Reihenentwicklung bis zur zweiten Ordnung mit genaherten Verteilungsfunktionen liefert eine Formel fur die statistische Anordnung, die sehr gut mit einer ganzen Anzahl von Experimenten ubereinstimmt.

Absolutmessung der kohärenten Streulänge von Quecksilber mit dem Neutronen-Schwerkraft-Refraktometer am FRM

Abstract: Es wird das am Forschungsreaktor Munchen der Technischen Hochschule errichtete Schwerkraft-Refraktometer fur die Absolutmessung koharenter Streulangen von Materie fur Neutronen beschrieben. Mit diesem Gerat wurde das Spektrum der langsamen Reaktorneutronen im Bereich von 170–900m/s gemessen und durch Reflexionsmessungen an einem Spiegel aus flussigem Quecksilber die koharente Streulange des Hg-Kerns absolut bestimmt. Sie betragta coh=+(12,69±0,02) 10−13cm.

Elektronenlawinen bei hohen E/p

Abstract: Current shapes of electron avalanches are calculated for low-pressure and high-E/p uniform electric field conditions. It is shown that drift velocities of electrons and positive ions and the ionisation-coefficient α for electrons can be obtained from low to highE/p-values of over several 103 volts/cm Torr by analysing the current pulses which are measured using fast oscilloscopic techniques. Moreover, values of the diffusion energy (diffusion coefficient over mobility) of the electrons can be determined from the diffusion-broadening of the current shapes. — Values of the diffusion energy are given for methane ranging fromkT≅4 to 15 evolts corresponding toE/p≅40 to 2000 volts/cm Torr.

Der Quartett-Zustand des R-Zentrums in Kaliumchlorid-Kristallen

Abstract: Optical absorption and paramagnetic resonance of KCl crystals containing preferentiallyR-centers have been studied during and after excitation with 430 mμ or 365 mμ light at 90 °K. A partly metastable, partly stable state has been detected and identified as the quartet state of theR-center, which proves to be an association of threeF-centers forming an equilateral triangle in the (111) plane of the crystal as proposed byvan Doorn andHaven andPick. — The crystals used were additively colored to 6.6·1017 F-centers/cm3 and illuminated withF-band light at room temperature until theR/M-ratio reached its maximum value. During light excitation the optical spectrum in the region of theR-bands shows characteristic small changes. A part of these changes disappears spontaneously with a time constant τ=14.5 sec when the light excitation is removed (“temporary bleaching”). The remaining part has a similar spectral distribution. It is completely stable in the dark, but can be bleached within a few seconds by illumination with 840 mμ light. — Electron spin resonance of the crystal under light excitation shows in addition to theF-center line a seven-line spectrum with strong angular dependence, if the field is rotated in a (110) plane. The maximum splitting is 674 G, the width of the individual lines 35.5 G. The angular dependence of the spectrum can be fitted to a fine-structure spin Hamiltonian $$H = g\mu _B \vec H_0 \vec S + D[S_z^2 - \tfrac{1}{3}S(S + 1)]$$ withg=1.996,D/g μ B=+168.5 G,S=3/2 and thez-axis in any of the four 〈111〉 directions of the crystal. After switching off the excitation light the seven-line spectrum decays with the same time constant as the optical changes to a stable level of approximately 20% which can be destroyed by illumination with 840 mμ light. (ΔM=2)-transitions are expected on the basis of the above Hamiltonian and have been observed. — In the ENDOR spectrum the lines of theK Iα nuclei which are nearest neighbours to the threeF-centers of theR-center have been analysed. Their hyperfine interaction is purely isotropic witha/h=17.85 Mc/sec. — General expressions are derived for fine structure and hyperfine structure of the (S=N/2)-state of anN-electron center with negligible spin-orbit coupling. The hyperfine interaction of the nucleusK Iα is very well understood on the basis of an Heitler-London approximation of theR-center. For the fine structure the Heitler-London approximation using the known fine structure of theM-center triplet state predicts a value ofD which is roughly a factor of 2/3 too small. The mechanisms of excitation and decay between the doublet ground state and the quartet state of theR-center are not yet understood.

Lebensdauermessungen von angeregten Kernniveaus mit der Methode der verzögerten Koinzidenzen

Abstract: The lifetimes of several excited nuclear states were measured with the method of delayed coincidences and a time-to-pulse-height converter. The following results were obtained:

The decay of potassium-40

Abstract: Mit KJ(Tl)-, CsJ(Tl)- und NaJ(Tl)-Szintillationskristallen wurde die spezifischeβ −-undγ-Aktivitat des K40 zu $$K^{40} zu\sigma \beta ^ - = \left( {28,26 \pm 0,05} \right)dps/g - K_{nat} $$ und $$\sigma _\gamma = \left( {3,25 \pm 0,07} \right)dps/g - K_{nat} $$ . Das Verzweigungsverhaltnis von Positronen- zuβ −-Emission wurde zu (1,5±0,5)·10−5 ermittelt. Aus diesen Daten ergibt sich fur die Halbwertszeit des K40 (1,266±0,007)·109 Jahre und fur das Verzweigungsverhaltnis von Elektroneneinfang zuβ −-Emission 0,117±0,002. Auf Grund dieser Ergebnisse wird der Fehler, der aus den Zerfallsdaten des K40 in die Alterbestimmungen nach der K-Ar-Methode eingeht, auf ±2% herabgesetzt. Dasβ −-Spektrum wurde mit KJ(Tl)-Szintillationskristallen im Energiebereich von 100 keV bis 1100 keV auf ±3% genau gemessen. Innerhalb dieser Fehlergrenzen stimmt es im angegebenen Bereich mit dem theoretischenβ −-Spektrum fur den dreifach unique verbotenen Ubergang uberein.

Die Hyperfeinstruktur in den 4f7 6s 6p-Termen des Eu I und die elektrischen Kernquadrupolmomente von Eu151 und Eu153

Abstract: The hyperfine structure of the statesz10P11/2,z10P9/2,z10P7/2,z8P9/2,y8P9/2,y8P7/2,y8P5/2,z6P7/2,z6 6s P5/2 of the 4f7 6p configuration of EuI was investigated with a photoelectric recording Fabry Perot spectrometer using enriched isotopes of Eu151 and Eu153, which have been excited in liquid air cooled hollow cathodes. From the measurements the values for the nuclear quadrupole moments $$Q(Eu^{151} ) = (1.16 \pm 0.08) \cdot 10^{ - 24} cm^2 $$ and $$Q(Eu^{153} ) = (2.92 \pm 0.20) \cdot 10^{ - 24} cm^2 $$ could be derived.

Computational improvements in phase shift calculations of elastic electron scattering

Abstract: A method of calculating the scattering phase shifts from the Dirac radial equations containing a rather general potential is described. The method takes advantage of the fact that a system of linear differential equations can be solved with the help of power series. Application of the method is demonstrated for the case of low-energy scattering (uniformly distributed nuclear charge screened by the atomic electrons) and for the case of high-energy scattering (uniform or more complicated nuclear charge distribution without atomic screening).

Die Eigenleitung hochreiner KCl- und KBr-Kristalle

Abstract: The intrinsic conductivity of zone refined KCl- and KBr-crystals is measured as a function of temperature. Plotting logσ versus 1/T the slope is composed of two straight lines which show a knee at 500 °C. The possibility of dominant anionmobility at higher temperatures is discussed. — Below 300 °C there is a nonlinear dependence of current on voltage. The shape of theV-J characteristic is a hint to space charge limited electron currents, which are influenced by quasi continuously distributed traps.