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.     

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.     

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.     

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.     

Zeitliches Abklingen und Anisotropie von p-Terphenyl- undp-Terphenyl-Anthrazen-Mischkristallen bei Beschuß mit α-Teilchen

The time dependence of scintillation intensity from single crystals ofp-terphenyl and mixed crystals ofp-terphenyl and anthracene after bombarding with α-particles was investigated at the two temperaturesT=296 °K andT=92 °K. For the crystals ofp-terphenyl the time dependence of the scintillation anisotropy was also measured. Using the formulas given byKing andVoltz the decay curves ofp-terphenyl were decomposed into two components. Good agreement between experiment and theory was found. The ratio of the prompt intensity to the delayed intensity was determined to be 1∶2 atT=296 °K and 1∶3 atT=92 °K. The diffusion constants for triplet excitons were calculated to beD _T(296 °K)≈10^?5 cm² sec^?1 andD _T(92 °K)≈ 2×10^?6 cm² sec^?1, and the triplet-triplet interaction rate constantsχ _tt(296 °K)≈ 2.5×10^?11 cm³ sec^?1 andχ _tt(92 °K)≈0.5×10^?11 cm³ sec^?1.     

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.     

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.     

Zur Unsymmetrie der Impulshöhenverteilung in einem Szintillationsspektrometer für monoenergetische Röntgenstrahlung

For theK _α1-lines of the elements Ti, Fe, Cu and Mo the pulse-height distributions at the output of a Na I(Tl)-scintillation detector are recorded with an automatically recording single channel pulse-height analyser. The deviation to be observed in this low-energy region of the most probable from the mean value of these distributions is determined and is compared with the computations ofWright. The results may be described by an empirical formula with the energy dependenceE ^?2, whileWright predicts the dependenceE ^?1.     

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.     

Quenching of ππ* triplet states of vaporous polycyclic aromatic compounds by oxygen

The oxygen quenching rate constants k _T ^O2 of the triplet state T ₁ of vapors of polycyclic aromatic hydrocarbons (PAHs) with strongly different oxidation potentials 0.44 eV < E _OX < 1.61 eV and energies of the triplet levels 14800 cm^?1 < E _T < 24500 cm^?1 (anthracene, 2-aminoanthracene, 9-nitroanthracene, chrysene, phenanthrene, fluoranthene, and carbazole) are estimated from the measured dependences of the decay rates and intensities of delayed fluorescence on the oxygen pressure P _O2. It is found that the rate constants k _T ^O2 vary from 4 × 10³ (9-nitroanthracene) to 4 × 10⁵ s^?1 Torr^?1 (2-aminoanthracene) and increase with decreasing oxidation potentials E _OX of PAHs. The rate constants k _T ^O2 for vapors and solutions are compared. The dependences of k _T ^O2 on the free energy of two intermolecular processes, namely, triplet energy transfer to oxygen and electron transfer, are analyzed. It is shown that the rate constants k _T ^O2 increase with decreasing electron transfer free energy, which proves that, along with energy transfer, charge-transfer interactions contribute to the quenching of the triplet states of PAH vapors.     

Sur les propriétés magnétiques de l'adénosine triphosphate (ATP) et de ses constituants

A detailed thermomagnetic study (80°–380°K) has been made on polycrystalline adenosine triphosphate (disodium salt), hydrated, dried, compressed and deeply cooled. The susceptibility-temperature curves exhibit around 180°K an abrupt transition from the Curie paramagnetismχ?χ ₀=CT ^?1,C=1.37·10^?5 cm³ g^?1°K, to a state, which most frequently is a temperature independent paramagnetism of the order of 10^?7 cm³ g^?1 (extremely weak ESR absorption at room temperature according toIsenberg andSzent-Györgyi). The Curie paramagnetism might be related to the acceptor-donor process of charge transfer imagined bySzent-Györgyi to explain the energetic comportment of ATP. Extensive thermomagnetic study of adenosine, KH₂PO₄ and KD₂PO₄ was made. Using a simple model based on these data we have constructed susceptibility-temperature curves for ATP di-Na which approximate the real behaviour fairly well.     

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.     

Crystal structure and magnetic susceptibility of (CuInSe<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(2MnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

The crystal structure of samples in the (CuInSe₂)_{1 ? x} (2MnSe) _x system at room temperature and their magnetic susceptibility in the temperature range 77–1000 K are investigated. It is established that compositions with concentrations 0≤ x ≤ 0.2 form solid solutions with a tetragonal structure, space group I \(\bar 4\)2d (122). The specific magnetic susceptibility χ of samples with 0.1 ≤ x ≤ 0.4 at 77 K lies in the range 9 × 10^?4?1.6 × 10^t-3cm³/g. The temperature dependence of the inverse magnetic susceptibility of the sample with x = 0.4 suggests the presence of a component with antiferromagnetic ordering and a reliably measured Néel temperature that is characteristic of MnSe. The dependences χ = f(T) of the compositions with x = 0.1, 0.2, 0.3, and 0.4 indicate the occurrence of magnetic phase transitions with a change in the spin state.     

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.     

Bestimmung der Atomspinkorrelationszeiten der Fe3+-Ionen in FeNH4(SO4)2·12 H2O mit Hilfe des Mössbauereffektes

The Mössbauer effect studies of⁵⁷Fe in the paramagnetic salt FeNH₄(SO₄)₂·12 H₂O reported byObenshain et al. were extended to higher values of the applied external magnetic fieldH _a. The results are discussed in terms of the theoretical calculations given byWegener. The data can be fitted using a maximum internal fieldH _max=(598±10) kOe and two atomic spin correlation times τ_c=2,4 · 10^?9 sec andτ′ _c=2,1 · 10^?9 sec.τ _c andτ′ _c are independent ofH _a and the temperatureT. It is assumed in the analysis that the distribution w(H) of the internal fields can be described by a continuous function of the Boltzmann factor type with two parameters. These two parameters are determined by the normalization and the macroscopic magnetization.     

Photon distribution functions of the fluorescence photons from a single nanoparticle in various photon counting methods

Simple expressions have been derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. In contrast to the previously derived expressions represented in the form of N multiple integrals, the new expressions contain only single or double integrals of Poisson functions, which makes it possible to easily perform the numerical calculation of the photon distribution. The simplest photon counting method corresponds to the lengthiest function w _N ^M (T); on the contrary, the simplest function w _N ^O (T) corresponds to the most complex photon counting method. The functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) are noticeably different in short time intervals T; however, the distributions calculated using these functions are almost indistinguishable from each other in long T intervals. This circumstance makes it possible to use the simplest function w _N ^O (T) to consider the photon statistics measured by the simplest method. This possibility is particularly important for investigating the fluorescence photon statistics, where the intensity fluctuates.     

Untersuchung des Iridium-191m-Zerfalls

Theγ-radiation of the nuclear isomer Ir^191m (T _1/2=4.5 sec) has been investigated with the aid of a scintillation fast-slow coincidence-spectrometer. Theγ-rays of the 42 keV-transition have been measured for the first time. The conversion coefficient α of this transition was found to be α = 13500 ₊₂₁₁₀₀ ^?5200 in acceptable agreement with the value taken from the tables ofRose under the assumption of anE3-transition. Thus this assignment proposed earlier by other authors has been confirmed. TheK-conversion coefficient of the 129 keV-transition has been remeasured yielding α _K =2.32±0.06.     

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.     

Messung der lichtelektrischen Leitung in Anthrazenkristallen

The drift mobility of holes in pure Anthracene has been measured by the transient photoconductivity technique used byKepler andLeblanc. The mobility is 0.8 cm²/Vsec and varies asT ^?2. In Tetracene-doped crystals the drift-mobility of holes decreases with growing Tetracene concentration and it varies exponentially as-T ^?1, which suggests that Tetracene acts as a trap. The trap depth is 0.45 eV. By pre-irradiation with α-particles or X-rays the photocurrent is reduced and it is supposed that α-irradiation produces deep traps, whereas X-rays produce as well shallow as deep traps.