Über die Berechnung der Photoerzeugung von π0 aus Streudaten

The cross section forπ ⁰-production is calculated from the results of the dispersion relation approach ofChew, Goldberger, Low andNambu and compared with the experimental data. The predictions are made using the measured values of all scattering phase shifts. A fit of the theoretical result toσ(90?) between 260 and 370 MeV givesf ²=0,082. There is no systematic deviation from the predictions forσ (90?) up toE _γ =450 MeV. The general behavior of the asymmetry coefficientB is correct. A quantitative comparison which would show the contribution of the unknown electric dipole termN ⁽⁺⁾ ofChew et al. is only reasonable after the calculation ofB and the measurements have been improved.C/A depends strongly on the small phases up to 240 MeV. The effects of the small phases are pretty large forσ(l50?) but there is no discrepancy similar to the results forπ ⁺-production above 290 MeV. The formula for the cross section does not reduce to the results of the phenomenological theories ofBrueckner-Watson, Sachs et al. andFeld, if the simplifications made by these authors are taken into account. The origin of the differences is discussed.     

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.     

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.     

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.     

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.     

Zum Kernphotoeffekt am Ar40 und Ar38

Liquid Argon was irradiated with bremsstrahlung from 18 to 31 MeV endpoint energy in steps of 2 MeV. The yields of the reactions Ar⁴⁰(γ, n)+(γ, p) and Ar³⁸(γ, n) were measured by detecting the 269a and the 35d rest activity with a low-level-counter. Cross section curves for the (γ, n)-processes could be found from the yield values, and they allowed together withσ _N, σ(γ, p) andσ(γ, np) a determination ofσ(γ, 2n) and σ_γabs for Ar⁴⁰. The integrated cross section forσ(γ, n) from threshold to 33 MeV yields (200±40) MeVmb for Ar⁴⁰ and (210±40) MeVmb for Ar³⁸, the corresponding value for σ_γabs being (450±60) MeVmb for Ar⁴⁰.     

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.     

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.     

Untersuchung des ZerfallsBi^{212} (ThC)\xrightarrow{\beta }Po^{212} (ThC')\xrightarrow{\alpha }Pb^{208} (ThD) durch (γ, α)-Koinzidenzen

Theγ-spektrum of Po²¹² (ThC′) has been measured by (γ, α)-coincidences with a fast-slow coincidence apparatus. The results are in excellent agreement with the conversion lines found by theLatyshev group. The absoluteγ-intensities have also been determined in order to get spins and parities of the levels by calculating the absolute conversion coefficients. Theβ-intensity leading to the exited states of Po²¹²(ThC′) is estimated to be about one third of that measured byBurde andRozner by (β, α)-coincidences. Threeγ-lines measured byChinaglia andDemichelis by (γ, α)-coincidences do not agree with our results. The 2⁺ assignment of the first exited state is now well established, but for the other levels in the decay scheme there is still some uncertainty concerning spin and level assignment.     

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).     

Experimentelle Untersuchung zur Fluktuation der Wirkungsquerschnitte für die Reaktionen F19(n,2n)F18, Al27(n,α)Na24 und Cu65(n,2n)Cu64

Using the activation method investigations on the fluctuation of the total reaction cross sections for the reactions F¹⁹(n, 2n)F¹⁸, Al²⁷(n, α)Na²⁴ and Cu⁶⁵(n, 2n)Cu⁶⁴ were performed in the 14 MeV region under similar conditions as in the experiments reported byStrohal et al. and byCsikai on the same subject. In disagreement to the results of these authors no considerable fluctuation amplitudes were found.     

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.     

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.     

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.     

Berechnung des Magnetisierungs-„Ripple“ in ferromagnetischen dünnen Schichten

By means of straight forward analysis a complete calculation is given of magnetization ripple in polycrystalline ferromagnetic films. Wavelenghts and practical relations for ripple amplitude, length of coherence, and angle fluctuation are derived (which were so far only rather incompletely available from a very rough model of the ripple, given previously by the author). The dependence of ripple wavelength (λ ₀) on average crystallite sizea reaches a plateau at a definite critical valuea=a _g ∶λ ₀≈4a fora<a _g ,λ ₀ independent ofa fora>a _g , as has been found most recently byBaltz andDoyle.     

Calculated rates for the reactionμ −+He3→H3+ν

The effective Hamiltonian ofMorita andFujii is used to calculate the muon capture rate\(\mathfrak{W}_\mu \) in He³. The calculation is done including and omitting the “weak magnetic interaction” and for positive and negative sign of pseudoscalar coupling. The results are related to the known value offt for the beta decay of the triton. The r.m.s. radius of the charge distribution in He³ is taken to be 1·55 fm rsp. 1·85fm. (The first value follows from the results of the variational calculation ofKikuta, Morita, andYamada, the last value is based on a variational calculation for a potential with a long tailed attractive part.) The capture rates differ by 10% for the two r.m.s. radii. Our result forv _r.m.s.= 1·55 fm deviates slightly from the corresponding result ofWerntz.     

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.     

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.     

Thermal conductivity in dirty superconducting alloys in high field

This paper discusses the thermal conductivityK of a dirty type II superconductor in the mixed state, for fields close to the upper critical field (H _e2 orH _e3) where the electronic component is dominant and easily separated. To order |Δ|², the conductivity depends only on the space average 〈|Δ|²〉. Our formula is a generalisation of earlier results byMaki andAmbegaokar andGriffin for gapless superconductors. The slope\(\left( {\frac{{\partial K}}{{\partial H}}} \right)_{Hc2} \) is proportional to the slope of the magnetization curve\(\left( {\frac{{\partial K}}{{\partial H}}} \right)_{Hc2} \), the ratio of these two slopes being a universal function of temperature. These results are very different from the predictions of the “effective gap” model.     

Bestimmung der Kernmomente des Ho165 aus der Hyperfeinstruktur des Grundzustandes im Ho I-Spektrum

In an atomic beam magnetic resonance experiment, the hyperfine interaction constantsA andB of the⁴ I _2/15-groundstate of Ho¹⁶⁵ were found to beA=800,58389 (50) MHz,B=?1667,997 (50) MHz. Using an effective value for 〈r ^?3〉, the magnetic moment of the Ho¹⁶⁵ nucleus was calculated to beμ=4·1(4)μ _n . The quadrupolement was determined by use of the 〈r ^?3〉 given byWatson andFreeman. The result isQ=2·4·10^?24 cm².