Delbrück-Streuung von 17 MeV-Photonen

Differential cross sections have been measured for the small angle scattering ofγ-rays by iron, silver, tantalum, lead and uranium with 17 MeV photons from Li⁷ (p, γ) Be⁸ at mean four momentum transfersq of 0·5mc and 1·3mc and with 7 MeV photons from F¹⁹(p, αγ)O¹⁶ at mean four momentum transfer of 0·5mc. Under these experimental conditions only Compton, Rayleigh and possibly Delbrück scattering are of importance. Extrapolation of known theoretical results to higher energies shows, that Rayleigh and Compton scattering from bound electrons should depend only onq for small angles, smallq and fixedZ. Using this it follows, that at 17 MeV andq≈0·5mc an additional scattering process must be present, which increases with growingZ and which is negligible in the measurements at 17 MeV withq≈1·3mc and at 7 MeV withq≈0·5mc. These results are in qualitative agreement with the approximate theory for Delbrück scattering ofBethe andRohrlich, however experimental cross sections at 17 MeV andq≈0·5mc are about a factor of 1·6 lower than those predicted by this theory. This discrepancy is not unexpected, since exact calculations of Delbrück scattering amplitude fromKessler andZernik at 2·62 MeV and 6·14 MeV show even greater deviations in the same sense.     

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.     

Messungen der van der Waals-Wechselwirkung zwischen Edelgasatomen

Total cross sections for collisions of Helium atoms with other rare gases have been measured by modulated molecular beam technique. The results are used to determine the interaction constants of the van der Waals potential (V(r)～ ?C/r ⁶). For this purpose, an indirect procedure is adopted, since the well known approximation ofMassey andMohr (Q～C ^2/5) is not applicable for Helium scattering experiments at thermal energies. The van der Waals constants obtained are in agreement with values determined from experimental data on transport properties in gases.     

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.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

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.     

Der mittlereg-Faktor der ersten angeregten Rotationszustände der geraden Wolframisotope in natürlichem Wolfram

The average gyromagnetic ratio of the first excited 2⁺ states of the Tungsten isotopes was measured using a target of natural Tungsten. An external magnetic field of 40950±200 Gauss was employed for observing the precession of the angular distribution of the 115 keV deexcitationγ-rays following Coulomb-excitation with an atomic hydrogen beam of 2·18 MeV. The measurement of the angular distribution was carried out with a proton beam at 6 different energies between 1·5 and 3·7 MeV, and was found to be slightly perturbed by internal fields. The measured attenuation coefficients areG ₂=0·966±0·049,G ₄=1·07±0·15. The gyromagnetic ratio was found be\(\bar g = 0 \cdot 264_{ - 0 \cdot 019}^{ + 0 \cdot 023}\), in agreement with the average value of the measurements ofGoldring andVager and the average theoretical value ofNilsson andPrior, but lower than the measurements ofBodenstedt et al.     

Streuung von 25 keV-Elektronen an Gasen

The differential cross section of neon, argon, krypton, and xenon for the elastic scattering and for the excitation of optical transitions has been measured. For neon and argon the elastic angular distribution can be described by the cross section calculated according toWentzel andLenz. For krypton and xenon there are considerable deviations from the Wentzel-Lenz cross section. In these cases it is better to calculate the elastic differential cross section from Slater eigenfunctions, from Thomas-Fermi-Dirac or from Hartree-Fock electron density distribution. The differential cross sections for the excitation of optical transitions, so far as measured here, obey for?<? _c the dipol approximation, i.e. for angles not to small the inverse square angular dependence is valid.? _c is higher for the heavier rare gases. The oscillator strengths for some transitions have been determined from the scattering measurements in satisfactory agreement with theoretical values.     

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.     

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\(\alpha _ \bot = 5.5 {\AA}^3 \).     

The Adler-Weisberger sum rule

Starting from a weak form of the axial current algebra and usingFubini's covariant dispersion method we give a fairly rigorous derivation of the Adler-Weisberger sum rule. Special attention is given to the necessary continuation in the “pion mass”. Combining the sum rule with the forwardπ ^± p dispersion relation we obtain a sum rule containing essentially low energy data. A numerical evaluation is given for two sets of existing s-waveπN scattering lengths. The one reproducesAdler's andWeisberger's results, the other improves the agreement with experiment giving r_A=1.20.     

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.     

Raman spectra of alkali halides

In this article, we present a comparative study of the Raman spectra of alkali halides in relation to the lattice dynamics ofBorn andRaman. It is shown that the experimentally observed limit of the second-order spectra in almost all the cases can be explained well by the Lyddane-Sachs-Teller relation. It is also seen, while, an explanation of the second-order Raman spectrum of a crystal of diamond or zinc blende structure requires the frequencies from the critical points,W, Γ, X andL inBorn's analysis, the frequencies fromΓ, X andL alone are sufficient and necessary for an interpretation of the same onRaman's model. Some similarities in the determination of the long wave properties of crystals like elastic constants and limiting frequencies of the lattice vibrations in the symmetry directions in both the models are pointed out.     

Mobility of electrons in nondegenerate semiconductors considering electron-electron scattering

Spitzer andHärm [1] have investigated the velocity distribution of electrons in the presence of a weak electric field in an ionized gas. Introducing the concept of time of relaxation τ′, due to electron-ion and electron-electron scattering, and using the results ofSpitzer andHärm [1], the authors have obtained an expression for τ′ which is applicable to semiconductors with little modification. In this paper the authors have used this expression for τ′ to obtain the mobility of electrons in nondegenerate semiconductors, taking into account the scattering by lattice vibrations, electron-ion interactions and electron-electron interactions.     

Eine Integralgleichungsmethode zur Behandlung der Streuung an gebundenen Teilchen

First it is pointed out that various methods known for the treatment of multi-particle scattering problems such as the methods ofLax, Watson, andFaddeev are based on the same type ofT-operator equations with eliminated interactions. They only differ by the identification of the interactions. — Then an integral equation treatment for the scattering of a particle by a system ofn bound particles is developed. If the scattering occurs via local two-body forces, the interaction matrix element splits into that of the two-particle case and a momentum-dependent factor. This fact is used to simplify the scattering equations which then get a mathematical structure similar to that of theT-operator equations discussed at the beginning (however, involving sums of bound states rather than sums of interactions) and which, therefore, can be handled in a similar way. When the interactions are eliminated by means of the two-particle scattering amplitudes, the off-shell energy parameter of these amplitudes may be chosen to be dependent on quantum numbers of the bound system. Such a choice shows indeed to be favorable if one likes to keep only the lowest order approximation of the integral equations. The resulting approximate formula leads, after some further approximations, for resonant scattering to a formula ofLamb, and for weakly energy-dependent amplitudes to a formula ofFermi (being related to the impulse approximation). — The resonant scattering formula is applied to a quantum-mechanical derivation of a method for the determination of nuclear lifetimes which had been proposed on semiclassical arguments byCiocchetti et al. — Finally the method developed for the scattering of a particle by a system of bound particles is extended to collisions between composite particles.     

Consistency of new π N phase-shift analyses with dispersion relations

New phase-shift analyses for pion-nucleon scattering are used to check the dispersion relations for the amplitudesB _±(v _L, 0), which are essentially determined by the pionnucleon spin-flip scattering extrapolated to forward direction. Within the experimental errors, the relations seem to be fulfilled. The pion-nucleon coupling constantf ² turns out to be consistent with the value found byHamilton andWoolcock, who obtainedf ²=0,081±0,003. However, in spite of the newer data and less sensitivity of our calculational procedure toward the high-energy behaviour of the amplitudes, the error off ² is still considered as somewhat larger. Our method also gives some information on the high-energy behavior of the spin-flip amplitude.     

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.     

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.     

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.