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.     

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.     

Proximity effect of a superconductor on an antiferromagnetic metal

There should be two contributions to the pair breaking energy in an antiferromagnetic metal. The first, already discussed byde Gennes andSarma, is due to disorder on the magnetic sites. The second is a temperature dependent contribution from electron magnon scattering. This term is calculated for the temperature rangeT _N(J/μ)²?T?T _N and found to be of orderT ²/T _N. (T _N = Néel temperature,μ = Fermi energy,J = exchange coupling between conduction electrons and magnetic ions.)     

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.     

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.     

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.     

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.     

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).     

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.     

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.     

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.     

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.     

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.     

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.     

Bemerkungen über relativistische Stoßinvarianten

The relativistic analogue of the theorem ofGrad is proven stating that the general additive collision invariant is given by the expressionβ _a p ^a +c. It is used to determine the equilibrium distribution of a 1-component general relativistic quantum gas. The proof is not analogous to the one initially given byGrad, but covers the non-relativistic case.     

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.     

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.     

Behaviour of some faintK β for elements As(33) to Ru(44)

1. 1.
   It has been shown that the semi-Moseley graphs for theβ ₈,β ₇,β ₆,β ₅,β ₄,β ^?,β ₁₁ ^? andβ ₀ in theK-series for elements over the rangeZ=33 toZ=44 reported byHulubei, Cauchois andManescu become remarkably regular when referred toα ₁ instead ofβ ₁ as the parent line.     
   
   

Concerning internal conversion coefficients in Hf180

The gamma-ray relative intensities from transitions in Hf¹⁸⁰ following the 5.5 hour Hf^180m decay have been measured using a bent-crystal gamma-ray diffraction monochromator and a least-squares fitting technique. From these measurements it was possible to deduce a value for the internal conversion coefficient for the 93.3-keV transition of α _T ⁹³ =4.91±0.23. From previous measurements of conversion electron intensities byEdwards andBoehm and our gamma-ray relative intensities, internal conversion coefficients for all transitions except the 57.5-keV transition were obtained. These coefficients agree well with the previous determinations byEdwards andBoehm, however, our measurements have improved precision, particularly in the case of 501.3-keV transition. The present measurements of α _K for the 215.3-, 332.5-and 443.8-keVE2 transitions are 11% lower than theoretical values while α_K for 93.3 keV E2 transition agrees closely with the theoretical value. These results are in close agreement with the previous measurements ofEdwards andBoehm. The present experimental α_K for the 501-keV transition agrees closely with the theoretical α_K for an E3 multipolarity.     

Relativistic Slater's integrals for theK andL shells

TheZ-dependent form of theSlater's integrals for electrons in theK andL shells is studied by expanding the relativistic hydrogenic radial wave functions in the manner explained byLayzer andBahcall. When screening is not taken into consideration, theseSlater's integrals can be put in the form AZ(1+a Z²) wherea is positive for all integrals considered except G¹(1s, 2p) and G²(2¯p, 2p). Values ofA anda are given.