Second and third virial coefficient of a quantum gas from two-particle scattering amplitude

Starting from the cluster expansion of the partition function the second and third virial coefficient of a quantum gas is expressed in terms of the two-particle scattering amplitude. In the case of spherically symmetric interaction the result forB(T) agrees with the well known expression ofBeth andUhlenbeck, but the method given here is also valid for non-spherically symmetric and even for non-local potentials. For the third virial coefficientC(T) an expression is derived in lowest order in the two-particle scattering amplitude which is suitable for numerical calculations.     

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.     

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.     

Difficulties with a unified treatment of nonleptonic weak interactions

The isospin selection rule in a unified treatment ofCP-conserving andCP-violating nonleptonic weak interactions proposed byNishijima andSwank is investigated and compared to that of a modified version.     

L/K-Einfangverhältnis von65Zn

A multiwire proportional counter was constructed to measureL/K-capture ratios. The length of the counter is 90 cm, the diameter 14 cm, and it works with pressures from 1 to 6 atm. — The counter was proved by measuring theL/K-capture ratio of³⁷Ar. The result obtained is 0,098±0,003, in agreement with the calculated ratio 0,100 ofBahcall and the results of many other measurements with multiwire proportional counters. — Gaseous radioactiv Zincdiethyl was the substance to determine theL/K-capture ratio of⁶⁵Zn. The result obtained is 0,111±0,006, in agreement with the calculated ratio 0,109 ofBahcall, while 0,119±0,007 measured with a multiwire proportional counter bySantos Ocampo andConway is somewhat above the calculated ratio.     

Der Einfluß der Krümmung eines Schirmrandes auf die Beugung elektromagnetischer cm-Wellen

The diffraction of electromagnetic cm-waves passing by the straight edge of a metal screen was experimentally investigated. The diffraction which depends on the polarisation of the waves and the thickness of the screen was measured within a range of about 20 wavelengths around the edge of the screen. The results agree with the theory ofSommerfeld and the investigations ofFranz andDeppermann. The intensity function of the waves near the edge of the screen shadow depends — according to our measurements — on the curvature of the screen edge. This agrees with the theoretical postulation ofArtmann: if the radius of the screen edge isa>λ the diffraction fringes appearing around the shadow of the screen edge are shifted towards the light area whenσ-polarized radiation is used. When usingπ-polarized radiation a shift towards the shadow area ist observed.     

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.     

Quantum mechanical solutions of the laser masterequation

We treat a laser consisting of one mode described by a running wave and a set of atoms with two optically active levels which are homogeneously broadened. We start from the laser density matrix equations ofWeidlich andHaake and define a distribution functionf for lightfield and atomic variables, where we use for the lightfield the coherent state representation and for the atomic system a modified version of the distribution function used bySchmid andRisken in a previous paper. We derive a partial differential equation forf which is completely exact and is of the type of a generalized Fokker-Planck equation, i.e. it contains higher derivatives. Using a recently stated theorem ofHaken andWeidlich we show that this distribution function allows to calculate single-time as well as multitime quantum mechanical correlation functions. If the leading terms of the generalized Fokker-Planck equation are retained we find the semiclassical Fokker-Planck equation ofRisken,Schmid andWeidlich. Our treatment can be extended to several modes connected with standing waves and multilevel atoms.     

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.     

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.     

W-induced anomalous magnetic moment of leptons,calculated with ξ-limiting formalism

The influence on the anomalous magnetic moment of leptons of a charged intermediate vectorboson, mediating weak interactions is discussed, using theξ-limiting formalism ofLee andYang.     

Untersuchung derK-Strahlung beim Elektroneneinfang des Ge71 mit einem Diffraktionsspektrometer mit gebogenem Kristall

The intensity of satellites in the Gallium-x-rays emitted inK-capture of Ge⁷¹ has been measured and found to be (1,3±0,5)×10^?4 perK-capture. A curved-crystal X-ray spectrometer with a radius of curvature of 27 cm was used for the measurement. The satellites are found to be due to double ionisation ofK-shell accompanyingK-capture as described by the theory ofPrimakoff andPorter. The theoretically calculated intensity of X-ray satellites emitted due to double ionisation ofK-shell — (0,9)×10^?4 perK-capture — is in fair agreement with experiment.     

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.     

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.     

Test of a sum rule for the nucleon magnetic moments

It is shown that the original version of the sum rule relating the isovector part of the nucleon magnetic moment to aπ N scattering amplitude is not consistent with the experimental data. However there is good agreement for the corrected version ofMaiani andPreparata.     

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.     

Separation of surface- and volume-vibrations in quadrupole-deformed nuclei and consequences on isotope shifts

Starting from the complete hamiltonian for a system ofN nucleons, the problem of separating volume and surface vibrations inpermanently deformed nuclei is investigated. The required “volume” variable which allows this separation turns out to be the mean square distance of a nucleon with reference to the center of mass. Our investigation confirms the concept ofpure surface vibrations, as is used in the rotationvibration model ofFässler andGreiner, and leads to a theoretical argument in favour ofFradkin's idea of “compressibility under deformation” forced upon him by experimental evidence in calculating isotope shifts in deformed nuclei.     

The anisotropy of conductivity of n-type germanium in strong d.c. fields

The electric conductivity ofn-type germanium at large d.c. field intensities has been measured in three directions of symmetry of the cubic lattice. From these data the repopulation of valleys of the conduction band has been determined. Measurements were done with three materials of different purity. The variation of repopulation between these materials can be explained qualitatively by the influence of Coulomb scattering at ionized impurities. The data are compared with those ofNathan and theoretical data ofFranz andReik et al. The relations of these data to those of the current component perpendicular to the field direction (Sasaki et al.) are also given.     

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.