Messungen des van der Waals-Potentials zwischen Alkaliatomen

Total collision cross sections for the interaction between alkali atoms have been measured using a modulated atomic beam technique. Since the determination of the density in the scattering chamber is the main source of error in absolute scattering measurements, particular attention is given to this problem: The cross section for partnersA andB is measured first withA as beam particles anB as target particles, and then withB as beam particles andA as target particles. The data are used to deduce the long rangevan der Waals (inverse sixth power) potential constants, which can be compared with theoretically calculated values of different authors. The interaction constants resulting from the present measurements are in good agreement with those calculated byFontana, while other calculations give much larger values.     

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.     

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.     

On the connection between the decaysπ 0→2γ andπ +→e++υ+γ

A result discovered byVaks andIoffe is newly derived using reduction technique and G-invariance only. It has some consequences concerning the decaysπ ⁰→2γ andπ ⁺→e⁺+υ+γ and various coupling constants of the? and ω particle.     

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.     

Messung der Anisotropie des van der Waals-Potentials durch Streuung von Molekülen in definiertem Quantenzustand

A beam of TlF molecules in the (1,0) rotational state was produced by an electrostatic four pole field. This primary beam was crossed at right angles by a secondary beam in a scattering chamber. By changing the direction of an electric field in the scattering chamber it is possible to produce a (1, 0) or (1, 1) state with respect to the secondary beam direction. In this way it was possible to measure the ratio of the total scattering cross-sections,\(\frac{{Q\left( {1, 1} \right)}}{{Q\left( {1, 0} \right)}}\), for He, Ne, Ar, and Kr as scattering gases. The result, which should be independent of the scattering gas, is\(\frac{{Q\left( {1, 1} \right)}}{{Q\left( {1, 0} \right)}} = 1.0133 \pm 20 and 1.0140 \pm 50\) for Ar and Kr resp., whereas for Ne and He the measured ratios are considerably smaller. The results were interpreted in terms of a van der Waals potential of the form\(V = - \frac{A}{{R^6 }}\left( {1 + q \cos ^2 \Theta } \right)\), whereR is the distance between the scattering partners and Θ is the angle between the internuclear axis andR.A andq are constants. With the Schiff approximation it is possible to calculate the scattering cross section as a function of the angle between the internuclear axis and the collision direction. Using the rotator eigenfunctions the ratio of the matrix elements of this function was calculated for various assumed values ofq. The above experimental result for\(\frac{{Q\left( {1, 1} \right)}}{{Q\left( {1, 0} \right)}}\) for Kr and Ar leads to the anisotropy factor,q=0.40±0.07-A detailed estimate of all interactions contributing to the van der Waals potential shows that it is possible to separate out the dipol-dipol dispersion potential from the observed potential; usingLondon's expression for the dispersion potential of asymmetric molecules one gets for the polarisabilities parallel and perpendicular to the intermolecular axis of the TlF molecule:\(\alpha _ \shortparallel = 7.8 {\AA}^3 \) and\(\alpha _ \bot = 5.5 {\AA}^3 \).     

Contributions to the theory of alpha-decay

The theory of α-decay is reformulated in order to point out the necessary approximations in a rigorous way. The connection between the formulas given byThomas and byMang is easily established.Mang's explicit expressions of reduced widths, valid for shell model wave functions, are brought into a general form. The theory is applied to BCS wave functions and the decay constants of several Po-isotopes are calculated as an example. Furthermore results are presented which favour a spin assignmentI=18 and a predominating (h9/2) ₈ ² (i11/2) ₁₀ ² configuration for the Po²¹² isomeric state. The penetrabilities are calculated numerically, since the WKB-method is found to be unsatisfactory.     

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.     

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.     

Physics results from HERMES

The Hermes experiment at the Desy laboratory in Hamburg, Germany, studies the spin structure of the nucleon. Its unique feature is the combination of a polarized internal gas target with the longitudinally polarized 27.5 GeV electron/positron beam of the Hera accelerator. Recent Hermes measurements include the proton spin structure function g ₁ ^p , the flavor decomposition of the polarized quark distributions in the nucleon, the DIS contribution to the generalized GDH sum rule, the first observation of a spin asymmetry in exclusive vector meson production and the first observation of a single-spin azimuthal asymmetry in semi-inclusive pion production. Additionally, the possibility of using various unpolarized gases as target material broadens the spectrum of physics measurements with Hermes.     

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.     

Das Vorzeichen der Hyperfeinstruktur-Aufspaltung des 3d 5 4s 2 6 S 5/2-Grundzustandes des Mn55

Using a double Fabry-Perot interferometer and an atomic-beam light source, the sign of the hyperfine-structure splitting of the 3d ⁵ 4s ^{2 6} S _5/2 ground state of Mn⁵⁵ has been determined to be negative. The absolute value of the splitting previously has been measured byWoodgate andMartin.     

Measurement of the Lamb shift 42S1/2-42P1/2 of the helium ion

Helium ions were produced in then=4 states by electron collisions with ground state atoms, resulting in simultaneous ionization and excitation. Dipole transitions between the Zeeman levels of the states 4² S _1/2 and 4² P _1/2 were induced by a microwave electric field. The intensity of the emitted Fowlerα line 4686 Å, corresponding to transitions from then=4 to then=3 states was then reduced by about 3%. From the measurements, a value of the Lamb shiftδ=1751±25 MHz was obtained, compared with the theoretical valueδ=1768.23±0.55 MHz, and the results ofLea, Leventhal andLamb ofδ=1765±20 MHz.     

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.     

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.     

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.     

The spin cut-off factor for60Co

Nine experimental isomeric cross-section ratios for the reactions⁵⁹Co(n, γ)⁶⁰Co,⁶⁰Ni(n,p)⁶⁰Co, and⁶³Cu(n,α)⁶⁰Co are analysed in terms of statistical theory by means of the method ofHuizenga andVandenbosch. Theγ-cascades are treated by a new model which was recently published. The results confirm the energy dependence of the spin cut-off factor for⁶⁰Coσ～U^1/4 which should not be neglected. As a mean value (σ=4.3±0.3 is obtained forU=B _n =7.5 MeV in good agreement with a nuclear moment of inertia for a rigid sphere.     

Zur Frage des Grundzustandes im Tb I-Spektrum

Analysis of the optical spectrum of Tb I confirms the conclusion reached byBender, Penselin andSchlüpmann from atomic beam magnetic resonance observations, that the lowest multiplet in the 4f ⁸5d6s ² configuration is⁸ G. The lowest level, however, is not⁸ G _15/2, but⁸ G _13/2, which is the true ground level of the Tb atom, provided the determination of the relative position of 4f ⁹6s ^{2 6} H _15/2 with respect to 4f ⁸5d6s ^{2 8} G _15/2 byBender c. s. is correct.     

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.     

Die Intensität der Bremsstrahlung und der charakteristischenK-Röntgenstrahlung dünner Anoden

The intensities of bremsstrahlung and characteristicK X-rays of thin Al, Mn, Cu, Se, Ag and Sn targets were measured with a scintillation counter. The angle between the 50 keV electrons and the direction of emission was 90°. — The spectral intensity of bremsstrahlung for 20 keV quantum energy was determined in agreement with the theory ofKirkpatrick andWiedmann. The result obtained isi _v=(2.7) · 10^?53.Z ^{2, 0} ergs per steradian, unit frequency interval, bombarding electron and atomper-cm². The cross section ofK-ionisation by electron impact has been found out by measuring the characteristicKX-ray intensity in agreement with known theoretical and experimental values. The result of this work isσ _K=(7.0) · 10^?16 ·Z ^?4,3 cm².