Spezifische Wärme und magnetische Suszeptibilität supraleitender,binärer komplexer Phasen von Übergangsmetallen

Measurements of the electronic specific heat in the normal and superconducting state of 15 superconducting binary complex phases of theσ- andχ-structure are presented. The alloys have been prepared under high vacuum in an electron-beam melting apparatus described in detail. In the investigated range between 6 and 7 valence-electrons, the obvious correlation betweenT _c, the superconducting critical temperature, andγ, the coefficient of the electronic specific heat, leads to agreement with the empirical rules, found byMatthias. Recently,Morel andAnderson andGarland have calculated the values of the deviation of the normal isotope-effect. With these values it is possible to relate the observedT _c-data for most of the transition metal alloys investigated so far to the density of states at the Fermi level and to a systematically varying electron-phonon interaction parameter. In the superconducting state, an exponential dependence of the electronic specific heat on 1/T is found in the range betweenT _c/2 andT _c/6. However the parameters are somewhat different from those predicted by theory. The values ofγ observed also account for the lack of any correlation between the total magnetic susceptibility and the superconducting critical temperature for these phases.     

Konversion der 238,6 keV-γ-Linie des ThB und Vergleich mit den Tabellen von Sliv und von Rose

The conversion ratiosK/L _I andK/L _II of the 238.6 keVγ transition of ThB have been measured with the new Heidelbergπ/2 √13Β-ray spectrometer. For this transition there are great discrepancies between the values as given bySliv andBand, and byRose. The experimental resultsK/L _I=5.96±0.26 andK/L _II=60.3±7.1 are in excellent agreement with the values ofSliv andBand.     

Paramagnetische Resonanz von Zentren mit den Symmetrienn,\bar n undn/mundn/m

The consequences of applying the spin-Hamiltonians ofAbragam andPryce to paramagnetic centers with the low symmetriesn,\(\bar n\) andn/m(C _n ,C _nh ,S _n ) are examined. The asymmetry of theg- and the hfs-tensors, described in an earlier paper, is considered in this context. The point is that for the symmetries under consideration the coordinate systems are not determined by the symmetry elements. For this reason it is possible to introduce separate coordinate systems for the magnetic field, the electron spin and the spins of the nuclei and this allows the symmetrisation of the tensors under certain conditions. This procedure also leeds to an understanding of the independent parameters found in the Hamiltonians. Ambiguities between the spin-Hamiltonians and the esr-spectra indicate the limits of theAbragam andPryce formalism. The application of the theory to paramagnetic centers under the influence of external, electrical fields is discussed and reveals interesting aspects.     

Kohärenzeffekte in Doppelschichten aus verschiedenen Supraleitern

Films of lead are deposited on a superconducting substrate. The transition temperatureT _c of this sandwich is measured as a function of the lead thicknessD _Pb . In different experiments the properties (thickness, transition temperature, mean free path of electrons) of the substrate are varied. It is especially interesting that the initial slope (small lead thickness) of theT _c (D _Pb )-curve is independent of the electronic mean free path of the superconducting substrate and inversely proportional to its thickness. The results for different thicknesses of the components in the system indium — lead can be well described by a theory ofdeGennes andWerthamer.     

Der Einfluß von Plasmawellen auf das Reflexionsvermögen von Metallen (I)

The wellknown derivation ofFresnel's formula for the reflection coefficient of a metal surface in the case of an oblique incident wave polarized parallel to the plane of incidence includes a mistake concerning the boundary conditions and neglecting the possibility of optical excitation of plasma waves. The right formula for this case is derived in the following paper byForstmann. The discussion of an approximate formula obtained by a simplified method leads in the case of vanishing reflectivity forΩ>Ω _p to a real Brewster-angleα _B . ForΩ<Ω _p there exists another solution with a complex Brewster-angle, representing a surface wave in form of a Zenneck-wave. For large wave numbers and for light velocity ? electron velocity the dispersion formula for these surface waves is nearly identical with that obtained byRitchie andWagner, while for small wave numbers there is a great difference between these two formulas. In the middle region the frequenceΩ is nearlyΩ _p /√2.     

Zur Änderung der übergangstemperatur verschiedener Supraleiter durch Elektronenentzug

The growing of oxid layers on pure metal films at low temperatures may be explained by acceptor levels at the oxid-oxygen interface. These surface states produce an electrical field of high strength by extracting about 10¹⁵ electrons per cm² out of the metal film. As had been shown in earlier experiments, this capturing process shifts the superconducting transition temperature to higher values for the 3-valent metals Al, In and Tl and to lower values for the 4-valent metals Sn and Pb. Extended studies on Tl show that this change in transition temperature is proportional to the relative decrease of the electron density in the metal film. The constant of proportionality has the valuek _Tl=?4.4 deg. With reasonable assumptions, this constant could be determined for Sn too:k _Sn=7.9 deg. These values agree quantitatively with the results ofGlover andSherill who investigated the charge effect on superconductors by a condenser method. They also fit the data calculated byGinsberg from experimental results on superconducting compounds with his extension of the theory ofMarkowitz andKadanoff.     

Supraleitende Bleischichten mit Zusatz von Übergangsmetallen und ihren Oxiden

The influence of small additions of 3d-metals (Cr, Fe, Co) on the superconducting transition temperature of lead has been studied. Both components are condensed simultaneously on a quartz substrate, held at 10 °K. With this “Quench evaporation technique” we get a statistical distribution of the impurity atoms in the lead matrix. As in early experiments on In and Sn the superconducting transition temperature of Pb decreases linearly with increasing 3d-metal content. This is in agreement with the theoretical results ofAbrikosov-Gorkov andSkalski et al. For the first time an influence of 3d-metal oxides (Cr-, Mn- and Co-oxide) on the superconductivity of Pb has been found. The transition temperatureT _c decreases linearly with increasing oxide content (c) as in the case of the pure metals. For Mn and Co the slopesdT _c /dc are nearly equal for the pure metal and its oxide. In the case of Cr the influence of the oxide is about seven times greater than that of the pure metal. Furtheron it is shown by annealing experiments that the degree of precipitation has also an influence on the transition temperature in the system of lead with Fe, Co and CO₂O₃.     

Schrödinger equation in multiply connected spaces and phase optics

The magnetic vector potential\(\vec A\) in a field free spaceR ₀ cannot be removed by gauge transformations in general, ifR ₀ is multiply connected.Aharonov andBohm ¹ have noticed recently that\(\vec A\) therefore should have more physical meaning than only to give the magnetic field by differentiation. They could show that\(\vec A\) inR ₀ may influence the phase ofSchrödinger'sψ-function in an observable manner. We want to point out here that this influence can be expressed in a simple, general form: “A closed magnetic field line operates uponψ like ae Φ/?-phase-shifter placed on any area bounded by the field line.” Surface like phase shifters are familiar in phase optics. There exists a narrow relationship between electron scattering at magnetic fields and some special problems of phase optics. An electron phase contrast microscope is discussed.     

Zur Theorie der infinitesimalen Holonomiegruppe in der Allgemeinen Relativitätstheorie

Starting from the infinitesimal holonomy groupH _i of aV ⁴, (+++?) the spinholonomy group\(\tilde H_i \equiv \bar \sigma ^1 (H_i )\) defined by the covering isomorphism\(\sigma :G \to L_ + ^ \uparrow \) is introduced. In Einstein-spaces we may replace its real Lie-algebra by a complex one. With the complex calculus we may reproduce the results ofSchell, Goldberg andKerr with very much simplified proofs. A theorem on non-empty Einstein-spaces is given. In part 4 we prove a theorem on the connection between theH _i -behaviour of a vector (spinor) and its covariant derivative in aV ⁴. With its help we get in a simple manner the metiics of aV ⁴ with givenH _i and Dim (H _i ) <6; our results agree with those given byGoldberg andKerr, Cahen andDebever. Finally we make some new statements on imperfect holonomy groups.     

The proton-antiproton annihilation at rest as predicted by theSU 6-covariantS-matrix formalism and byW-spin analysis

The proton-antiproton annihilation at rest into two mesons is calculated by two methods: (i) on the basis of theSU ₆ -covariantS-matrix formalism recently proposed byRothleitner andStech, and (ii) by assuming the additional invariance under the group (SU ₆) _W proposed byLipkin andMeshkov. In the first case the calculations give only few relations between transition amplitudes, whereas the larger symmetry group (SU ₆) _W actually determines all amplitudes up to a common factor. While agreement with experiment seems to be poor in some cases for the (SU ₆) _W , so far there are no experimental data available to test the relations of case (i).     

Quasielastic kaon knockout from a proton and momentum distribution of virtual kaons in the proton

The momentum distribution of kaons in the proton and the coupling-constant ratio fKΛN/fKΣN are determined on the basis of the ³P₀ quark model of meson-baryon coupling. The longitudinal cross section for kaon electroproduction is calculated. The results of the present study are compatible with available experimental data, but more detailed data on the longitudinal cross section would make it possible to refine the absolute values of the coupling constants fKΛN and fKΣN.     

Absorptionsquerschnitte und Transmissionskoeffizienten für Protonen und Neutronen nach dem optischen Modell

T _l -values and absorption cross sections for protons and neutrons are calculated with optical potentials, which have been fitted to experimental scattering data. Values are given forZ=10, 20, 30, 50, 70, 90, and energies between 0.1 und 25 MeV. For protons we used the local optical potential ofPerey and for neutrons the nonlocal optical potential ofPerey andBuck. The results are compared with those of other optical potentials. In addition it is shown, that the spin-orbit-interaction leads toT _{l j} -values which sometimes differ appreciably depending whetherj equalsl+1/2 orl?1/2.     

Vergleich der Photoerzeugung von π0 am Proton mit der Voraussage nach der Dispersionstheorie

The real parts of the photoamplitudesE 1S _1/2,M 1P _1/2,M 1P _3/2 have been calculated from the angular distribution of the reactionγ+p→p+π⁰ recently measured byGoldansky et al. at 160 to 240 MeV. One of the solutions fits pretty well to the theoretical prediction for theM 1P _3/2-amplitude according to the dispersion method ofChew, Goldberger, Low andNambu. There is a discrepancy forM 1P _1/2 ifα ₁₁ is taken from the effective range formula, but the positive values ofα ₁₁, necessary to give agreement, are not excluded by the results of the phase shift analysis, especially sincePontecorvo et al. have recently found positive values at higher energies. The prediction for the real part of theE 1 S_1/2-amplitude agrees with the experimental data, if pretty large recoil corrections are added which had been neglected byChew et al.     

Untersuchungen zur Mehrfach-Emission von Sekundärelektronen

CuBe- and NaCl-targets are bombarded by single electrons (100–600 eV). The secondary electrons accelerated by 40 kV strike the crystal of a scintillation counter, backed by a multichannel analyser. The probabilityP _n of emission ofn=0, 1, 2, 3, ... secondaries can be found from the pulse height distribution. The probability distributionP _n =f(n) shows a characteristic deviation from aPoisson's distribution. There was no evidence that there is a preference for even numbers ofn as found byBarrington andAnderson.     

Einfluß der Pion-Pion-Wechselwirkung auf Pion-Nukleon-Streuphasen

The isospin dependent part of theS-wave pion-nucleon amplitude is calculated according to the CGLN approach, but recoil and projection on the partial waves are treated exactly. Then the difference against the experimental data is approximately a constant up to 100 MeV and amounts to 1/3 of the total value. It is shown, that at low energies the main corrections of the CGLN equations are taken into account by a subtraction of theπ+π→?+\(\overline \Re \),J=I=1 amplitudesf _± ¹ (t) as proposed byMandelstam andFrazer. Calculations have been done forS, P andD pion-nucleon amplitudes. The main result is a prediction of theS-wave amplitude obtained without adjusting free parameters up to 100 MeV. The relations of this method to the equations derived byBowcock, Cottingham andLurié according to the Cini-Fubini approach are discussed.     

Aussagen der Theorie von Kraichnan für die isotrope hydromagnetische Turbulenz

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g _m (k, τ) and the time-correlationsr(k, τ), r _m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE _m (k) obeys aE(k)k ^?2-law in accordance with results ofGolitsyn andMoffatt.     

Meissner effect in superconductors with a finite pair momentum

The features of the Meissner effect in superconductors with a finite pairing momentum are analyzed. Response to a weak magnetic field is calculated for various cases covering a pair momentum range from q ? Δ/v ₀ to q ～ p ₀, including q = Δ₀/v ₀ (v ₀ is the velocity on the Fermi surface and Δ₀ is the order parameter at zero temperature; the system of units where ? = 1 is used). The response of a superconductor carrying the transport current at a temperature close to the critical temperature T _c is determined. It is shown that, at a certain critical momentum (current), the response parallel to the momentum vanishes and the London length is infinite. The response perpendicular to the momentum remains unchanged. The response of the superconductor in the current state at zero temperature is calculated. A new contribution to the paramagnetic current is found, and its mechanism is determined. This contribution can be large for high momenta q ～ p ₀. The Meissner effect is analyzed in detail for the state proposed by Larkin and Ovchinnikov, Zh. Éksp. Teor. Fiz. 47, 1136 (1964) [Sov. Phys. JETP 20, 762 (1964)], as well as by Fulde and Ferrel, Phys. Rev. A 135, 550 (1964). It is shown that the response parallel to the vector q is nonzero and diamagnetic. On the contrary, the response perpendicular to the momentum vanishes at the optimal momentum q ₀. The sensitivity of the Meissner effect to the fine features of the superconducting state such as the quasiparticle spectrum, coherent factors, etc. is demonstrated.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

A decoupling experiment on the α-γ correlation in Am243

The directional correlation betweenα particles from the decay of Am²⁴³ to the 75 keV level in Np²³⁹ and the deexciting 75 keVγ-rays has been studied. The recoiling atoms were allowed to escape into vacuum. This brings about a strong hfs interaction between the heavily ionized daughter atom and the nuclear magnetic moment, which has been shown earlier to result in an almost isotropic correlation pattern. By the application of a magnetic field along the direction of the emission of theα-particlesAsaro andSiegbahn showed that the correlation pattern could be restored to, or almost to, the theoretical value, depending on the theory chosen. This is interpreted as a decoupling of the Ms-interaction, where the degree of decoupling is dependent on the strength of the applied field. The highest field used in the earlier experiment was 12 kG. For this experiment a decoupling magnet giving 24 kG was constructed. Applying this magnetic field on three different sources gave a result (A ₂=_?0.404±0.010) which confirms the so called quadrupole correction ofChasman andRasmussen to the theory ofBohr et al. of alpha decay of deformed nuclei. The decoupling magnet used in the experiment is described.     

Dispersion of the stress optic coefficient of the alkali halides

The dispersion of the stress optic coefficient C=n³/2 (q₁₁?q₁₂) of the alkali halides, NaCl, KCl, KBr and KI have been measured from the visible to the ultraviolet region. In general the value of “C” decreases with wavelength for all crystals. While the dispersion is only a few per cent in the visible region of wavelengths, it is enormous in the ultraviolet. NaCl shows a dispersion of about 100% from 5800 to 2400 Å; KCl about 200% from 5000 to 2400 Å; KBr about 300% from 5000 to 2400 Å; and KI about 400% from 5000 to 2800 Å. Also the potassium halides exhibit a change in sign of their “C” values in the ultraviolet. In KCl the sign reversal occurs at about 2550 Å; in KBr at 2760 Å and in KI at 3380 Å. Below these wavelengths, the potassium halides belong to the same class inMueller's classification as sodium chloride. The theory ofRamaseshan andSivaramakrishnan based on the assumption that a stress causes a change in the frequencies and oscillator strengths of atoms is unable to explain the observed behaviour of the alkali halides. On the other hand, the mere variation of the ionic refractivities with wavelength is also unable to explain the observed dispersion onMueller's theory. One is forced to assume that the strain polarisability constantK inMueller's theory varies with wavelength. When “K” is calculated from the experimentally observed values of “C”, it is found to increase with decreasing wavelength for all alkali halides. The variation with wavelength of “K” for all the alkali halides can be fitted up well by a formula of the type given byRamaseshan andSivaramakrishnan. Hence it appears that the total dispersion ofC can be explained only when we take into account the variation with wavelength of 1. theLorentz andCoulomb contributions fromMueller's theory and 2. the strain polarisability constant fromRamaseshan andSivaramakrishnan's theory.