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The undulatory behavior in the velocity dependence of the total elastic cross-section Q( v) for atom-atom-scattering can be calculated by the semiclassical approximation. In a previous paper J numerical values of the classical deflection function, which are necessary to evaluate the amplitude of the extrema in Q( v), were reported for a Kihara-potential as a function of the reduced energy K and the potential parameter α. The present paper gives the correspondent reduced maximum phase shifts η ( K,α), which determine the location of the extrema. The results for the Kihara-potential are compared with similar calculations for a Lennard-Jones-( n, 6)-potential. [ABSTRACT FROM AUTHOR]

The results of the preceding paper are specialized to three-atomic molecules in which the three atoms are allowed only small vibrations about their equilibrium positions. This restriction to the vibrational amplitudes makes a perturbation calculation suitable. A sketch of the zero order approximation has been given in this paper, and it has been shown - at least for a symmetrical molecule of the type AB - how the limiting case of the rigid body may be obtained for which there exist the well-known formulas of Wang. [ABSTRACT FROM AUTHOR]

The present paper determines the spectral functions of the Greens-functions for quasiparticles defined in a previous paper by a variational procedure minimizing the thermodynamic potential Ω( T, V,μ). An approach for generalizing the results to an inhomogeneous model (e.g., a lattice) is proposed. [ABSTRACT FROM AUTHOR]

In previous papers we have introduced a simple model for backbending nuclei which satisfactorily describes the essential experimental features of those nuclei. In this paper we show that the basic assumptions of this model can be deduced by a more microscopic treatment. [ABSTRACT FROM AUTHOR]

Entropy which is produced in the interior of a non-isolated system during a process is quite different from its total change of entropy. In an earlier paper was given an expression for produced entropy in the statistical theory. This expression is associated with a statistical measure, the 'gain of information' (Informationsgewinn). A special application of the general scheme is the statistical derivation of the principle of Le Chatelier and Braun. [ABSTRACT FROM AUTHOR]

In this paper the analysis of gas heating phenomena in wallstabilized electric arcs with axial gas flow derived in an earlier paper is applied to a nitrogen arc at a pressure of one atmosphere. For this reason the behaviour of the inlet length, the perturbation quantities and the integral characteristic values of such an arc is discussed and their parameter dependences are investigated. The results give the best parameter values for getting the highest enthalpy flux and the best efficiency of the arc heater. [ABSTRACT FROM AUTHOR]

The aim of the paper is the development of a complete macroscopic description (generalized Bloch equations) of multipole resonance and relaxation in terms of multipolarisations, which are the expectation values of normalized multipole operators. These operators are constructed with the help of the Wigner-Eckart theorem. Using a relation for their commutators the reversible part of the generalized Bloch equations is derived, the structure of which depends on the spin quantum number I. The irreversible part was treated in an earlier paper (I). [ABSTRACT FROM AUTHOR]

In the present paper we give a fully quantummechanical treatment of the self-sustained oscillation of one mode in solid-state lasers. The total laser system consists of various subsystems: The lasing mode is coupled to the atoms of the active material and to a loss mechanism. It is assumed to be in complete resonance with the homogeneously broadened atomic transition. The pump of the active atoms, which are assumed to have only two levels, is brought about by their interaction with a large system of negative temperature. The active atoms decay not only by induced and spontaneous emission into the lasing mode, but also by spontaneous emission into the continuum of nonlasing modes (and possibly by nonradiative transitions). This process is fully taken into account. The pumping process and the spontaneous emission into the continuum of nonlasing modes are treated as in a preceding paper. There we have shown that the coordinates of these fields can be eliminated in some sense and give rise to a mean dissipative motion of the atoms and to fluctuations. Using the Heisenberg picture we obtain a system of coupled nonlinear equations of motion for the atomic operators and for the creation operator of the oscillating mode. We then eliminate the atomic operators by the iteration procedure of the semiclassical laser theory. This leaves us with a nonlinear differential equation of the van-der-Pol type for the creation operator of the laser mode, which contains the fluctuations of the pumping process, the spontaneous emission into the continuum and the loss mechanism as inhomogeneities of operator character. Such an operator equation has previously been obtained by Haken, who has shown, that in the neighbourhood of the stationary saturated level of oscillation the amplitude is highly stabilized, whereas the phase undergoes an undamped diffusion process. This process takes the phase in the course of time arbitrarily far from any given initial value. We use Haken's method of solution and demonstrate that the correct commutation rules for the oscillating mode [ b( t), b( t)]=1 are preserved for all times. Besides these quantum mechanical properties our solution contains all the well known results of the semiclassical theory. Our main result is the expression for the linewidth, which is caused by phase diffusion. The half width at half maximum power is in circular frequencies given by κ is the half width of the cavity, Γ the half width of the atomic transition (we have assumed κ ≪ Γ), σ the critical inversion per atom, P the energy radiated per sec and $$n_{TH} = \left[ {e^{\frac{{\hbar \omega }}{{kT}}} - 1} \right]^{ - 1}$$ the number of thermal noise quanta. We prove that $$\frac{1}{{2\sigma _k }} = n_{SP}$$ , where n is the number of spontaneous noise quanta in the mode, n is determined in complete analogy to n+1/2. It arises from the spontaneous emission of the active atoms into the laser mode and is for optical frequencies much more important than n+1/2, which stems from the finite temperature of the cavity walls and the vacuum fluctuations of the cavity. Both noise sources, however, enter our formula entirely symmetrical. The two terms containing the cavity fluctuations represent the old Townes formula corrected by a factor 1/2. The spontaneous noise term on the other hand agrees in the limit κ≪ Γ with Haken's expression, if we account for the different description of the pumping process. Before we study the nonlinear oscillation of the mode above threshold, we investigate its behaviour in the linear or amplification region below threshold. The laser line is shown to grow out of a broad background of spontaneous emission noise. [ABSTRACT FROM AUTHOR]

The present paper contains a mathematically exact, fully quantummechanical treatment of dissipation and fluctuations in a two-level system. We consider an atom with only two levels, which is coupled to the radiation field and to a system of negative temperature. As a consequence, the atom decays to the lower level and is pumped to the upper one alternately. Although the methods, which are developed, do not depend on this model, it has been chosen because of its applicability in laser theory. In fact, we will give in a second paper a fully quantummechanical treatment of a laser, using the results given here. We discuss the motion of the atom in terms of its time-dependent 'spin-flip' and occupation number operators, i.e. we use the Heisenberg picture. In such cases usually one writes down the nonlinear coupled system of equations of motion for the field and atomic operators. We, however, start with a transformation of the time evolution operator of the total system using the technique of disentangling, which has been developed by Feynman. Incidentally this transformation allows for a generalization of the Wigner-Weisskopf theory of spontaneous emission, which will be published in a forthcoming paper. For the present purpose it permits us to write down the equations of motion for the atomic operators in terms of a mean motion, which refers to the coupled fields only through relaxation times and equilibrium values of the occupation numbers, and of fluctuating forces, which give the effect of the quantummechanical fluctuations of the fields on the atom. The mean or dissipative motion agrees with that of a 2×2 density matrix, which describes N identical atoms coupled to our fields. The fluctuating forces are given by operators and they are therefore noncommuting. Their properties are discussed in detail. An important result is, that they are not correlated in time. It is shown that they are responsible for the commutation relations of the atomic operators for all times. Such fluctuations do not occur in a density matrix description, because it contains already an averaging over fluctuations. Our results show clearly that dissipation and fluctuations cannot be split in quantum mechanics, because the neglection of the fluctuations would violate the commutation relations. [ABSTRACT FROM AUTHOR]

In this paper the properties and the dependence upon parameters of those quantities are investigated, which are characteristic for the gas-heating process in electric arcs with axial gas flow. Starting with the equations of the one-fluid-model of plasma physics three various methods are derived, to calculate analytically or numerically the thermal and electrical entities of the inlet region of the arc. With these results expressions can be given for the thermal and electrical inlet length. Further the azimuthal component of the velocity and its inlet length are determined. A discussion of the results will be outlined in a later paper (part II). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to examine the properties and parameter dependences of the electrical, thermal, dynamical and radiation quantities of a Hagen-Poiseuille flow in a cylindrical wallstabilized electrical arc. The basic equations are derived from the single fluid model of plasma physics taking into account the special arc conditions. For this flow it is outlined, that the temperature distribution and hence the electrical and radiation quantities do not depend upon the dynamical entities in the considered parameter region. The determination of these functions can be performed in the same way, which is demonstrated for the electrical arc without convection in a previous paper. Knowing the temperature distribution it is possible to calculate the dynamical quantities, which are modified by the temperature field of the arc contrary to the isothermal flow. Corresponding to this they have different parameter dependences as shown by analytical and numerical treatment for a nitrogen and an argon arc. [ABSTRACT FROM AUTHOR]

The attempt has been made by several authors to clear up the discrepancy between van der Waals constants determined from scattering cross sections for thermal energies and theoretical values using measured oscillator strengths. The present paper discusses three sources of error not accounted for properly in the earlier work. The appropriate corrections discussed in this paper lead to a satisfactory agreement between experiment and theory. [ABSTRACT FROM AUTHOR]

Scattering experiments are often not performed with the ideal set-up consisting of a monochromatic beam and target particles at rest. This is, for instance, never the case in molecular beam scattering, which is of primary interest in this paper. Two arrangements are normally employed, one consisting of a gas chamber as target (case a), the other of a crossed beam, generally at right angles to the incoming beam (case b). In both cases the scattering particles have a Maxwellian velocity distribution. This means that in any such experiment an 'effective cross section' is measured, which is an integral over cross sections for different collision velocities. Other similar integrals are needed, if one works with polarized beams and takes into account the fact that the cross section is angular dependent. A third type of integral is required, when the primary beam is not monochromatized, and one has to average over its velocity distribution too. The functions needed to interpret scattering experiments of all the types mentioned are given in this paper, as well as a table of values for the 24 most important of these functions. [ABSTRACT FROM AUTHOR]

In a previous paper an equation was derived for the attachment of the decay products of radon and thoron to aerosol particles. Considering the deposition to be solely governed by thermal diffusion (not by electrostatic forces) and assuming a quasi-stationary density distribution for the diffusing atoms, it was shown that the attached activity is proportional to where R is the particle radius and h=7·10 cm at NTP. As most aerosols in nature are electrically charged it is shown in the following paper how the diffusion process is modified by the influence of electrostatic forces between diffusing ions and charged aerosol particles. For the frequently occuring case of a symmetrically bipolar charged aerosol and ion diffusion it is furthermore shown that the attached activity is proportional to where x is dependent on the electrostatic charge and the radius of the aerosol particles. Applying this equation to the deposition of natural radioactivity on atmospheric aerosols and assuming that particle size-distribution can be roughly approximated by a law N (R)=const· R in the range 10 cm≦ R≦10 cm calculation shows that 90 to 95% of the total natural radioactivity should be attached to particles smaller than R=5·10 cm and as much as 50 to 75% to particles smaller than R=5·10 cm. It is concluded that the distribution of natural radioactivity on the different particle sizes in atmospheric and artificial aerosols is fundamentally dependent upon the diffusion process, including ionic diffusion. [ABSTRACT FROM AUTHOR]

In the first part of this paper the optical absorption of amorphous films of PbCl, formed by quenching condensation, is shown and compared to the spectrum of PbCl in its normal state. The sharp exciton band of crystalline PbCl in the long wavelength region is considerably broadened in the spectrum of amorphous films. The transition from the amorphous state to the normal crystalline state is indicated by an abrupt, irreversible change in the absorption curve at 260‡ K. This comparatively high temperature of crystallisation seems to be due to the complicated structure of PbCl. In the second part of this paper the optical absorption curves of evaporated films of the system TlCl-KCl are measured. A shift of the absorption bands as a function of the composition is found. The 3,46-eV-maximum of pure TlCl is coordinated to the A-band of the KCl∶Tl-phosphor. On the other hand there is no connection between the 5,82-eV-maximum of TlCl and the known bands of KCl∶Tl. [ABSTRACT FROM AUTHOR]

The small pion-nucleon scattering phase shifts have been calculated by Chew, Goldbeeger, Low and Nameu, using relativistic dispersion relations and the data of the first resonance. The authors introduced several approximations without going into the details of their validity. It is the aim of this paper to give a more accurate treatment, because it turned out that the approximations used by Chew et al. result in pretty large errors, at least for the s-waves. First we retain the neglect of all contributions to the dispersion integral other than the 33-part and consider the s-wave amplitude Re f=(sin 2α−sin 2α)/6q. For 200 MeV (lab.) pions, the correct evaluation of the recoil effects leads to a value 2.8 times lower than the 1/M-approximation and the projection, carried through without an approximation, deviates by 20% from the first terms of the expansion used by CGLN. At zero kinetic energy a comparison with the dispersion relation for forward scattering shows that the above mentioned neglected contributions to the dispersion integral amount to 35±15%. The combination of the s-phases was recalculated, replacing the first two approximations of CGLN by an exact treatment. In order to take care of the main part of the neglected contributions to the dispersion integral, we added the value found at zero kinetic energy. The energy dependence, not accounted for by this procedure, should result in a one-sided deviation from the experimental data. Comparison with these data, however, shows that the absolute values as well as the energy dependence of the calculated curve agree reasonably with the measurements up to 333 MeV. Cini et al. and Hamilton et al. have used an interpolation formula which represents the measured s-wave data by adjusting parameters, whereas in this paper the combination of s-phases is calculated from α and σ. Our result for the s-wave scattering lengths a−a=0.255 is compatible with P=1.60 for the Panofsky ratio and with the measured photomeson cross section which near threshold shows no deviations from the perturbation theoretical values for charged pions (f=0.080). It is doubted that in this energy region the small additional contributions, which follow from the dispersion theory of photoproduction in its present state, are really an improvement of the perturbation theoretical results. The scattering lengths of the p-waves have been calculated, taking into account only the 33-part of the dispersion integral, but without the recoil approximation of CGLN (f=0.080): a=0.189, a=−0.045, a−a=0.0007, a=−0.147. The formulae for these scattering lengths and the corresponding q-coefficient of the s-wave amplitude fulfil Geffens relation identically, if the total cross sections occuring in the integral are replaced by their 33-parts. This changes the value of the integral by 5 to 10%. The approximations of Chew et al. have been used in the discussion of the influence of the ππ-interaction on the πN-scattering phase shifts. Our result makes it worthwhile to reconsider this question. [ABSTRACT FROM AUTHOR]

In a previous paper direct electron-intensity measurements in Debye-Scherrer diagrams of aluminium have been described. A retarding field apparatus was used for investigations into the influence of crystal size and electron energy (15 to 50 keV) on the elastic diffraction intensities. The validity range of the kinematical theory could be determined. By means of a retarding field the inelastically scattered electrons were separated from the elastically scattered electrons (energy loss below 2 eV). In this paper the retarding field apparatus by which scattering intensities can be measured with good accuracy (≈ 2%) is described in detail. It is compared with other arrangements for the measurements of angular and energy distributions of scattered electrons. [ABSTRACT FROM AUTHOR]

In a previous paper a grouptheoretical scheme for the classification of wavefunctions has been developed from a consideration of the group of all transformations, which leave the nuclear hamiltonian invariant thereby taking into account also accidental degeneracies. This scheme is applied here to a translation-invariant hamiltonian with harmonic oscillator forces. The existence of a shell structure for the ground states is proved and the quantum numbers and symmetry properties of the wavefunctions of the ground states and of some excited states are derived. If translation-invariance is neglected, spurious states appear. It is shown how their quantum numbers and symmetry properties can be determined. Some remarks on a translation-invariant formulation of the Elliot-model conclude the paper. [ABSTRACT FROM AUTHOR]

An approximation method proposed by Braunbek for the diffraction of scalar waves by plane obstacles, or apertures in a plane screen, is extended to the diffraction of electromagnetic waves. As an example, the diffraction of a linearly polarized plane electromagnetic wave normally incident on a circular aperture in a perfectly conducting plane screen and on a perfectly conducting plane circular disk is considered in detail. The results are compared with those obtained from the exact solution of Meixner and Andrejewski and with the results of Kirchhoff's approximations. It is shown that, in contrast to the Kirchhoff approximations, Braunbek's method leads in all cases to the correct 'optical' limits and represents a good approximation even for wavelengths comparable with the size of the obstacle. After a general formulation of Braunbek's method in the electromagnetic diffraction problem, we calculate in the present paper the far field of the circular aperture and the transmission coefficient by means of the cross section theorem. The near field of the circular aperture and the circular disk will be considered in a subsequent paper. [ABSTRACT FROM AUTHOR]

The present paper gives experimental and theoretical results which enabel us to determine the absolute values of stacking-fault energies of face-centred cubic metals from the stress-strain-curves of single crystals. The activation energy for the crossslip of screw-dislocations is calculated as a function of the stacking-fault energy γ, the applied shear stress τ, and the size of the piled-up dislocation groups. An experimental value for the activation energy for cross-slip in copper is deduced from the strain-rate dependence of the shear stress τ at the beginning of stage III of the stress-strain-curve. Comparison between experiment and theory gives γ=170 ergs/cm. The determination of the stacking-fault energy of other f.c.c. metals is possible by comparing the temperature dependence of τ. Experimental results are given for Au and Cu. Data from the literature are used for Ag, Ni, and Al. We find γ= 30 ergs/cm. The difference in stacking-fault energy of Cu and Au is much larger than was anticipated. It is substantiated, however, by a number of observations discussed in the paper. Constriction energies calculated on the basis of the newly determined stacking-fault energies are given. [ABSTRACT FROM AUTHOR]

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In order to obtain an azimuthal dependence of the external bremsstrahlung produced by electrons, the electron beam has to be transversely polarized. In first-order Born approximation the differential cross section does not depend on the azimuthal angle φ, but the second-order approximation includes the spin vector of the electrons and yields, consequently, a φ-dependence. This paper deals with a measurement of the bremsstrahlung asymmetry as function of the photon energy and the emission angle Θ. The transversely polarized electron beam was produced by momentum deflection of longitudinally polarized β-decay electrons emitted from aSr source. With a kinetic energy of 300±10 keV and a degree of transverse polarization of 74% the electrons hit a Pb target. Because of the high γ-background it was necessary to detect the emitted bremsstrahlung in coincidence with the incident electrons. We found effects of about 3% in contrast to considerably larger values (13%) published in an earlier paper. The asymmetry was numerically calculated according to Johnson and Rozics. Since at an electron energy of 300 keV the Born approximation gives not yet good results, theory and measurement agree only in order of magnitude, particularly at high γ-energies. [ABSTRACT FROM AUTHOR]

In a previous paper the anisotropy parameter of the attractive part of the intermolecular potential has been determined from total cross sections measured by scattering of TlF-molecules in selected rotational states by rare gases. In this series of papers, further measurements on the systems TlF-He, Ne, Ar, Xe, CH, and CsF-He, Ar will be described. In the case of CsF-He, it has been possible to determine the anisotropy parameter of the repulsive part of the potential additionally, by comparing cross sections related to different rotational states over a large velocity range and by using the high energy approximation. The determination of the anisotropy parameter for the repulsive potential requires knowledge of the parameters of the angle averaged potential. Part I describes the determination of these parameters for a Lennard-Jones-potential from measurements of the velocity dependence and the absolute value of the total cross section by scattering of not state selected CsF-molecules by He and Ar. Since these systems show no glory undulations in the experimentally accessible velocity range, they require an evaluation procedure, which is independent of the appearance of such undulations. The procedure described below only uses the velocity dependence of the cross section itself by fitting of quantum mechanically calculated cross sections. The finite resolving power of the apparatus and the influence of velocity distributions are taken into account. The results are communicated, the parallel evaluation of an experiment on K-Ar serves as a test for the procedure described. [ABSTRACT FROM AUTHOR]

A method is outlined which gives a numerical describtion for some configurations of axially symmetrical constricted electric arcs. For this purpose the equations of single fluid model of plasma physics are decoupled in such a way that only the heat flux potential, the axial velocity, the radial velocity, the average axial pressure gradient, and the average axial electric field have to be calculated simultaneously considering a given set of boundary conditions. In this paper the method is applied to the Koppelmann arc. In addition the paper reports upon some experiences in applying this method to the computation of further arc configurations. [ABSTRACT FROM AUTHOR]

In a previous paper a method has been described to produce thin films of amorphous iron by simultaneous condensation of iron and small additions of oxygen, silicon, or germanium onto a substrate at 20 °K. During annealing the amorphous films crystallize within a narrow range of temperature. In this paper the magnetic properties of these films are investigated. By a new lowtemperature άgnetometer the magnetization curves can be registered for the different states of annealing. It results that even in the amorphous state iron is ferromagnetic. Below a critical concentration of the oxygen, silicon, or germanium admixtures the magnetic moment of the iron atoms is smaller and the coercive force is greater in the amorphous than in the crystalline structure. Above that concentration the magnetic moments in the two structures are equal, whereas the coercive force of the amorphous films is smaller than that of the crystalline ones. The results are explained by a concentration depending short range order in the amorphous films. [ABSTRACT FROM AUTHOR]

In a previous paper (I) the problem of the range of validity and quality of Markovdescriptions in Statistical Physics has been reduced by several assumptions to the question of how to approximate a homogeneous regular Markov Chain (Mc.) R of high order s by a Mc. R of lower order r. A method to approximate R by R has been developed in (I). In the present paper the discussion of this method is continued for the special case s=2, r=1. In particular, the paths any observable A will run through in either of the chains R and R will be compared. Furthermore the conclusions one is able to make from the knowledge of R about the character of the Mc. R, which should be approximated by R, are discussed. It will be shown, that regular Mcs. of different order which are related by the approximation method developed in (I), will have many properties in common. This enables one to understand to a certain extent the success of Markov-description in Statistical Physics. [ABSTRACT FROM AUTHOR]

In a preceding paper a new expression ~ for the charge density of the Klein-Gordon field was constructed which is positive definite if confined to positive frequency solutions only. This is not the case for the usual charge density. The present paper deals with some properties of ~. We propose a generalized definition for macrocausality which can be applied to nonlocal expressions too, yielding a causal behaviour in the case of ~. [ABSTRACT FROM AUTHOR]

In this paper the influence of a radial instreaming gas on electric arcs is investigated. An axial or an azimuthal mass flow may be superimposed to the radial one. Using the basic equations of the single-fluid model of plasma physics the important properties and parameter dependences are numerically calculated and discussed. The results are compared with those of a corresponding arc without an instreaming radial mass flow. Using an arc heater with radial mass flow it is possible to reach much higher axis temperatures and enthalpy densities. Choosing a set of well selected working conditions nearly the whole electric input may be transformed into axial enthalpy flux of the gas to be heated. The paper illustrates the mutual interaction between the dynamic and thermic functions of an electric arc. [ABSTRACT FROM AUTHOR]

The equations derived in a previous paper are discussed in some greater detail, in order to correct an erroneous impression, to which this paper may have given rise. [ABSTRACT FROM AUTHOR]

In an earlier paper we have extended the new Tamm-Dancoff method to the 'New Tamm-Dancoff method with intermediate states'. This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In addition to well-known approximations, such as the Hartree-Fock theory and the Hartree-Bogoliubov theory, we obtain a series of new approximations. The 'Hartree-Fock theory with intermediate states', which is the subject of the present investigation, is one of these. By using time reversal invariance we have succeeded in clarifying its structure, and we give the solution procedure. The exchange terms in the N-particle intermediate states can be represented by an additional potential Y, which (as is the case for the generalized density matrix ρ) has to be determined selfconsistently. In this way we have overcome the difficulties, that Kerman and Klein met in their 'generalized Hartree-Fock approximation', which has some close similarities with our Hartree-Fock theory with intermediate states. We demonstrate our method for the exactly soluble rotational-vibrational model of Klein et al. Hereby we show how to treat conservation laws and the degeneracy of levels. The Hartree-Fock equations with three intermediate states turn out to give analytical expressions for the energies and the matrix elements. These agree excellently with the exact values in the rotational part of the spectrum. [ABSTRACT FROM AUTHOR]

On introducing relative and centre-of-mass coordinates, the Hamiltonian H of a system of n identical particles with two-body interaction separates into a centre-of-mass Hamiltonian and a centre-of-mass-independent Hamiltonian H formally describing a system of n-1 'reduced' particles. The objective of this paper is firstly to investigate the connection between the symmetries of the actual and the reduced system and secondly to discuss the consequences of symmetries of H on the classification and construction of the eigenstates of H. Angular momentum and parity properties are found to be coincident in the actual and the reduced system. Group-theoretical considerations lead to a method for the determination of reduced vectors with simple transformation properties under permutations of the position vectors which define the reduced vectors. The method is used to construct 'optimal' reduced vectors for the three- and four-body-problem. It is proved that similar 'optimal' reduced vectors do not exist for n>4. [ABSTRACT FROM AUTHOR]

For the elastic scattering of ion beams at atoms the diffraction of the matter wave at the atom can be observed in the region of small scattering angles and high energies. The diffraction causes undulations in the differential scattering cross section. In this paper a general solution of the diffraction effect is given. The solution holds for the Yukawa type screened Coulomb potential which is well suited for the small angle scattering of-ions at atoms and which contains two parameters. The computations have been made using the partial wave method and the Jeffreys-Born-approximation for the scattering phase shifts. The solution is presented in a form in which the amplitudes and characteristic constants of the first four undulation maxima and minima are given in dependence of a product which contains one of the potential parameters. The characteristic constants are correlated in a characteristic equation with the second potential parameter and the positions of the diffraction extrema. The conditions for the appearance of the diffraction effect are discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the determination of the potential parameters from experimental results. The potential parameters are determined from the amplitudes and the positions of the experimental diffraction pattern by applying the general solution of the diffraction effect in [1]. All existing experimental results up to date are referred and evaluated. For the following scattering systems the potential parameters were determined and are presented in a table:Li-He,Li-Ne,Li-Ar,Li-Kr,Li-Xe,Li-Ar and H- Ar. [ABSTRACT FROM AUTHOR]

In several papers we recently obtained simple high-energy asymptotic expansions for the solutions and eigenvalues of wave equations containing generalized superpositions of Yukawa potentials. In the present article we extend these investigations to the calculation of phase shifts and eigenvalues of the Lippmann-Schwinger kernel. We also calculate corresponding Padé approximants and illustrate, by means examples, their usefulness, even in regions of low energies. [ABSTRACT FROM AUTHOR]

Extending the results of a preceding paper the excited vibrational states of the H ion are calculated. To this end we employ an improved Born-Oppenheimer-approximation. [ABSTRACT FROM AUTHOR]

The hyperfine structure of the Re I-lines λκ 4889 å (5d 6s 6p zP−5d 6s aS) and 5275 å (5d 6s 6p zP−5d 6s aS) was measured by a photoelectric recording double Fabry Perot spectrometer using enriched isotopes of Re and Re, which have been excited in liquid air cooled hollow cathodes. Besides the usual recording the signal was also measured by a digital voltmeter and punched into paper tape making it possible to evaluate the measurements by a computer. The linewidth obtained in the experiments was small enough that besides the splitting of theP states also the splitting of the ground state could be detected in asymmetries of the hyperfine structure components. By the mathematical analysis of the components it was possible to derive the quadrupole coupling constant B of the 5d 6s aS ground state: 5=1.6(8)· 10cm for Re and Re. The quadrupole moments of Re and Re have been estimated from B (zP) with LS coupling eigenfunctions considering relativistic effects: Q(Re)=2.30 (4) [90] · 10 cm Q (Re)=2.20 (4) [90] · 10 cm. (Figures in round brackets are experimental errors, those in square brackets are estimated uncertainties introduced by the theoretical evaluation.) Using these results and the known B (aS) of Re and Re also the nuclear quadrupole moments of these isotopes were derived. Q(Re)≈Q(Re)≈0.4 · 10 cm. [ABSTRACT FROM AUTHOR]

In the nonlocal part of the single particle potential of bound nucleons the Gaussian nonlocality, which was used in earlier papers, is replaced by a Yukawa- and an exponential potential. The nonlocal parameters are fitted to the nucleon scattering experiments and the results are used for a calculation of single particle levels of Pb and Pb. The nonlocality required by the Pauli-exclusion-principle is compared with the phenomenological approach. It turns out that the form of this nonlocality is essentially given by the supposed nucleon-nucleon potential. The range of this potential is determined by the experimentally known energy-dependence of the single particle potential. [ABSTRACT FROM AUTHOR]

Two fundamental inequalities in the theory of nonequilibrium systems are the second law in its generalized form stating that entropy-production is always positive and the so called thermodynamic passivity relation. In a statistical theory these inequalities can be derived under very general conditions. Thus certain results contained in a preceding paper are put on a new basis and shown to be independent of the Markovian property of the stochastic laws of motion. In the new formulation the results refer especially to systems under the influence of an environment variable in time. (4.4) ist die bekannte Formulierung der Passivitätseigenschaft des Netzwerkes. [ABSTRACT FROM AUTHOR]

Molecular beam measurements of total scattering cross sections require a very high angular resolving power of the measuring apparatus, which is often not attainable to a sufficient degree for reasons of beam intensity. Consequently the measured cross sections need a correction. The problem becomes complicated, if, as is customary, the geometry of beam and detector has no rotational symmetry about the beam axis. In this paper the average detection probability η(Θ), as defined by Kusch, is calculated for all common shapes of beam and detector. By use of the semiclassical differential cross section for an r potential, the correction to the total cross section is computed. At thermal energies and with an angular resolving power of about one minute of arc, the correction amounts to several percent and is therefore considerably greater than commonly assumed. [ABSTRACT FROM AUTHOR]

The paper gives a simple, classical derivation on the effective differential scattering cross section concerning the scattering of neutrons in a monatomic gas. [ABSTRACT FROM AUTHOR]

The transition temperatures of superimposed films of copper and lead are measured at very low temperatures by means of a helium-cryostat. The double films are condensed in situ inside the cryostat at 200 °K, and have never been warmed up or brought to air before measuring. Careful measurements of the residual resistivities, film thicknesses and the choice of l

The dynamic collective theory has been developed for vibrational nuclei in a previous paper. Here the details are studied and compared with experiments. For this purpose the structure of the dipole operator has been established, the energy matrix of the dipole-quadrupole interaction has been diagonalized and the various approximations are discussed quantitatively in detail. It is interesting that this systematic theory gives the details of the γ-absorption cross section in many nuclei. [ABSTRACT FROM AUTHOR]

The relations between multiple-beam interference and normal oscillation modes in a parallel-plate resonator are clarified in a preceeding paper. Based on experiments with cm-waves, here diffraction and shadowing effects are investigated for interferometers containing diaphragms before, between or behind the mirror-plates. It is shown, that the observed phenomena can be fully understood on the basis of the mode concept mentioned above. [ABSTRACT FROM AUTHOR]

In a preceding paper it was reported on the photoemission of multialkali photocathodes with temperatures of about 77 °K, where nonlinearities, discontinuities and hystereses of the emission current were observed when the wave length and the intensity of the light was varied. In the following a detailed account is given on measurements of hystereses with alternating light intensities. Furtherly the absorption of the photocathodes was measured, while the emission current was at a discontinuity with a jump of the current by a factor of two and more. The absorption was independent of the jumps. From this and from a detailed discussion of the intensity hystereses it can be concluded an independence of the effect of: a) the primary interaction of the light with the cathode, b) the conduction mechanism of electrons through the cathode (for then otherwise a band gap of 7.05 eV should follow), c) the potentialstep at the cathode surface. Observed quantum yields of 100% are not due to electron multiplication by the initial energy of the excited photoelectrons but seem to indicate an exciton mechanism and/or field effect, the latter being quite different from the Malter effect. The intensity at which the upward jump occurs increases by a factor of ten when the cathode temperature rises by 0.36 °K. This temperature sensitivity is interesting in application as radiation detector. [ABSTRACT FROM AUTHOR]

In this paper the solution of the Dirac equation, for a free particle moving in a uniform external magnetic field is obtained by using the Schrauben-functions. In case the magnetic field tends to disappear, all physical quantities tend to the corresponding quantities of the completely free particle. [ABSTRACT FROM AUTHOR]

The high laser intensity allows colliding-beam Compton scattering experiments of high-energy electrons with the photons of the red ruby laser light by which the latter are transformed into γ-radiation photons. Detailed calculations are given in this paper for the 'average' polarization over the scattered beam and for the energy spectrum of the γ-rays. [ABSTRACT FROM AUTHOR]

Using the generalized Bloch equations of the preceding paper (II) transient and steady-state experiments in pure quadrupole resonance of spin 1 and spin 3/2 systems are discussed. A method of time averaging is employed to replace the use of auxiliary circular fields. The free induction signal after a short pulse of the radio frequency field as well as the quadrupole echo amplitude after a sequence of two pulses is calculated. For the case of a steady-state rf field the complex susceptibility in terms of relaxation coefficients is given. [ABSTRACT FROM AUTHOR]

A polar c-axis must be attributed to the wurtzite structure of zinc oxide. The sign of the c-axis can be determined by cleaving perpendicular to this axis and subsequent etching of the exposed {0001} surfaces. The present paper reports how this can be achieved without cleavage, merely by etching the prism faces {10¯10} which are the principal surfaces of hexagonal needles and of thin platelets. The etch patterns unambiguously point into the direction of the positive c-axis. This method is applied not only to the prism faces but also to cleaved surfaces of the same orientation. A close relation between etch patterns and lattice defects is apparent. [ABSTRACT FROM AUTHOR]

The coupled spin-lattice and lattice-bath differential equations are solved numerically for the special case of terbium ethyl sulfate. The relaxation decay shows non-exponential behaviour if the lifetime τ of the phonons in direct contact with the spin-system is equal or greater than T/b. T is the spin-lattice relaxation time and b the ratio of the specific heats of the spin-system and the phonons in contact with the spin-system. The effective (measured) relaxation time T depends on the initial disturbance of the spin-system. In a second paper measurements are published which show these predicted effects. In these experiments there has been found a severe phonon bottleneck in the terbium ethyl sulfate. [ABSTRACT FROM AUTHOR]

Collision alignment has been found in a beam of thermal Gallium atoms of P-state emerging from an oven through a channel being wide compared with mean free path inside the oven and narrow compared with that one outside. Alignment effect is ascribed to 'loss impacts' in the channel and the difference in scattering cross section for states of different orientation having been the subject of a previous paper. Calculation of the effect in linear approximation is discussed together with experimental data. [ABSTRACT FROM AUTHOR]

Dielectric dispersions at low and audio frequencies and ferroelectric after effects in Rochelle Salt are due to ordering of point defects as recently has been shown by Unruh and the author. It is possible to describe all these effects in terms of an intrinsic electric field. This paper deals with the influence of the intrinsic field on the motion of ferroelectric domain walls. Preliminary measurements are consistent with the conception of the intrinsic field, but some details are to understand only by the assumption of permanent imperfections of the crystals. [ABSTRACT FROM AUTHOR]

The results of susceptibility measurements on single crystals of anhydrous CeCl and PrCl, published in a preceeding paper, are analysed in terms of a static crystalline electric field of approximate D symmetry acting upon the Ce and Pr ions. For each of the two salts a set of crystal field parameters V, V, V, V was adjusted to fit the susceptibility data. To get agreement within experimental accuracy a small reduction of the Landé g-factors had to be introduced, indicating the influence of factors which are omitted in the simple crystal field model, presumably covalent bond and configurational interaction. [ABSTRACT FROM AUTHOR]

In a thermal plasma, consisting of one component only, it is possible to calculate an accurate relation between electron pressure and temperature. In the present paper it is tried to give an approximate solution for plasmas composed of several elements under condition that the electron pressure is less than 10% of the atmospheric pressure and that only one element is singly ionized. The results are controlled by measuring the temperature in a copper arc with addition of alcali or earth-alcali elements. Theory and experiment show that the ionization potential divided by the temperature is a constant term in the plasma for certain groups of elements. [ABSTRACT FROM AUTHOR]

The beta-gamma directional correlation between the inner beta-group and the following 84.2 keV gamma ray was measured as a function of the energy of the beta-particles. Details of the apparatus and the experimental procedure are given. The results are corrected for the contribution of internal bremsstrahlung and the attenuation of the directional correlation due to the relatively long lifetime of the excited state in Yb and the presence of crystal fields. The measurements of these corrections are described in the following paper. The directional correlation results were used with the results of measurements of the longitudinal polarization of the electrons and the shape of the beta-spectrum given by other authors to determine the nuclear matrixelements. The computer calculations showed that there are two physically different types of solutions. One is the so called modified ∫ B solution which is, however, unsatisfactory in the framework of the Bohr-Mottelson theory. By including higher order nuclear matrix elements we get a solution which is in agreement with this nuclear model. [ABSTRACT FROM AUTHOR]

During the last years several experiments on small angle scattering have been made the results of which are not in agreement with Lenz's theoretical results commonly used in electron microscopy. These measurements having been made on foils, a possible reason for the discrepancies seemed to be that scattering did not take place on isolated, spherical, neutral atoms as theory assumes. These conditions were fulfilled, however, at the experiments of the following paper. In spite of this there is no agreement with theoretical results basing on Lenz's scattering cross sections except in the case of neon, where Lenz's cross sections give very reliable values. The discrepancies are shown not to be explainable by a breakdown of Born's approximation as seems to be obvious because of the systematic increase of the discrepancies with atomic number. [ABSTRACT FROM AUTHOR]

An apparatus is described, which enables us to measure the thicknesses of films immediately after condensation at low temperatures and in different stages of annealing by means of a multiple beam interferometry technique ( Tolansky). The film thicknesses are also measured by the temperature dependence of the electrical resistance. Measurements of Pb- and Cu-films are given as an example, and the sources of errors are discussed. In the case of Pb-films both the methods give the same thicknesses at any condensation temperature. This leads to the conclusion that Pb-films have a density of the compact material. At low condensation temperatures the disorder in the films turns out to be thickness dependent, and the distribution of defects seems to be inhomogeneous. Cu-films condense at low temperatures with high porosity. This may be the cause of the often observed getter effect of freshly condensed Cu-films. The filling factor of Cu-films is studied at different condensation temperatures. The temperature dependence of the resistivity of thin metallic films is discussed in the appendix of this paper. [ABSTRACT FROM AUTHOR]

Cross sections for small angle scattering of electrons are determined from the absolute measurements of the foregoing paper. Lenz's approximation of the cross sections proves to be valid but in a very limited angular range for most elements. Deviations from results calculated with Lenz's theory can be ascribed to this reason in all in vestigated cases. Determination of the cross sections shows that the Thomas-Fermi-Dirac-model describes small angle scattering much better than is commonly assumed, disregarding a very small range near the angle 0 into which but a very small portion of the electrons is scattered. Lenz's method, however, yields only in special cases the correct cross sections and must not be as commonly used as is general practice. [ABSTRACT FROM AUTHOR]

Macroscopic relaxation phenomena of a magnetic spin system in a magnetic field are related to microscopic fluctuations and the corresponding correlations by the systematical theory of relaxation. In the paper presented here this relationship is investigated experimentally for some typical examples in the field of nuclear magnetic resonance by means of the frequency dependence of nuclear magnetic relaxation times. A short description of a pulse spectrometer which operates on 12 different frequencies from 50 kc to 160 Mc is given. From the dispersion of both T and T in various paramagnetic solutions, as well as in pure liquids, correlation times of the relaxation process are evaluated. The form of these dispersion curves is especially suitable for distinguishing between translational and rotational power spectra and allows for conclusions about the corresponding molecular motions. [ABSTRACT FROM AUTHOR]

In a way similar to that of a former paper, the Schrödinger equation of the four-body problem has been transformed to appropriate coordinates. Besides those of the center of mass, these are the six distances between the four particles and the Eulerian angles describing the orientation of the instantaneous ellipsoid of inertia. By introduction of the angular momentum operators L, L, L the wave equation - in contrast to the more special three-body problem where the configuration needs must be plane - becomes fully symmetrical not only in the distances but also in these three operators. The solution can again be written as a linear combination of the eigenfunctions D of the rigid rotator with coefficients depending upon the particle distances. The system of differential equations for these coefficient functions has been given; its behaviour under parity transformation turns out to be rather more involved than in the three-particle case. [ABSTRACT FROM AUTHOR]

Pure single crystals of KCl quite homogeneously doped with known amounts of Tl were prepared in this laboratory by a method described in the preceding paper. Optical absorption was investigated over a range of Tl concentration from 4.10⋯1.10 mole percent at 90°K and at 293°K. The absorption cross section does not depend on Tl concentration within this range. The A and C bands are structured. For the A, B and C bands, oscillator-strength was determined with an accuracy of 2 to 4%. A procedure for the exact determination of Tl concentration from absorption measurements is stated explicitly. [ABSTRACT FROM AUTHOR]

Neutrons scattered at deuterons will distort the deuteron wave function. This effect is of special interest in the S state where a step towards formation of an intermediary triton is possible. In this paper we deal with a distortion consisting of a spherically symmetrical contraction of the deuteron. It can be shown that under reasonable assumptions the contraction does not go as far as to reduce the average nucleon distance to triton size, but that the effect on S phase shifts is remarkable and leads to a much better agreement with the results of the empirical phase shift analysis. Results have also been obtained for the S phase shifts. [ABSTRACT FROM AUTHOR]

In an earlier paper, the radial eigenfunctions R= R,( p) of theH-atom were determined by means of the Laplace Transform. They were obtained this way in a series-representation. The present work completes the foregoing considerations: It will be shown that the well known closed expression (23) for R can be obtained directly (i.e. without emploing any tables) but using only three rules of the Laplace Transform. [ABSTRACT FROM AUTHOR]

In two earlier investigations it has been shown that the discrepancy between some new measurements of the spectrum of the μ-mesic Bi-atom and the calculations of Ford and Wills as well as the discrepancy found by fitting the electron-scattering data from Bi to a density function of 'Fermi'-type, may be explained if one takes into account explicitly the charge density of the 83-rd proton in the shell-model. The present paper deals with the Tl nucleus where a similar 'shell structure effect' seems to occur. [ABSTRACT FROM AUTHOR]

Copyright of Zeitschrift für Physik is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Zeitschrift für Physik is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In studies of gas adsorption on metals with the aid of the field emission microscope influences of the electric field or the current on the adsorption have been reported. In the present paper we succeed in seperating the effects of field and current by using pulsed field emission with a variable voltage in the interval between pulses. We find that the electric field is of no influence, that larger currents, however, result in an increase in the speed of adsorption. Possible mechanisms are discussed. A new method for measuring the change in work function on adsorption is reported. With this method the change in work function during the adsorption of O on tungsten has been measured. [ABSTRACT FROM AUTHOR]

The theoretical differential cross section for the elastic scattering and for the excitation of optical transitions in helium by electron impact has been refined in Born approximation by use of the two parameter Eckart eigenfunction for the ground state and for the excited states. The angular distributions of 25 kev electrons scattered elastically and inelastically by helium were measured in the angular range 2·3·10≦ ϑ≦4·10. The intensity distribution of the elastically scattered electrons is in accordance with the theoretical curve for ϑ>7·10 and is disturbed at smaller angles by the primary beam. Normalization of the experimental values to the theoretical elastic differential cross section leads to agreement between the experimental differential cross section for the excitation of the 2 P and 3 P state and the scattering formulae given in this paper. There are small systematic deviations (<20%) for the 2 P differential cross section in the angular range 3·10< ϑ<1·10 only. The oscillator strength of these two transitions has been determined from the scattering measurements: f=0·312±0·04 and f=0·0898±0·006. [ABSTRACT FROM AUTHOR]

In Silicon and Germanium one finds three types of characteristic energy losses: the plasma loss at 17 eV in transmission of electrons through thin films, the 10 eV loss in reflection at cleavage surfaces, and the 5 eV loss in transmission through extremely thin films. The present paper is concerned with the 5 eV loss. It is found that the intensity of the 5 eV loss does not depend on variation of thickness of the foils. Thus, it is concluded that the 5 eV loss is due to surface plasma oscillations. In fact, measuring the angular distribution, there is found a dependence of ∼ ϑ in good agreement with that given by the theory. In the case of non-normally incident electrons it is found that the intensity of this loss is not symmetric about the direction of the incident electrons. This is in agreement with the theoretical considerations of Stern and Ferrell, and represents a further typical feature of surface plasma losses. [ABSTRACT FROM AUTHOR]

The specific heat for constant pressure, constant volume and their ratio behind a strong shock wave in helium with initial pressures of p=0·1 and 1·0 mm Hg have been calculated. At shock-velocities up to Mach 150 both ionizations have to be considered. Lowering of ionization potential and exitation energy can be neglected for this range. The specific heats show typical maxima as first found by Möglich, Riewe und Rompe for c of hydrogen. The second part of this paper deals with a method of iteration applied to the Rankine-Hugoniot equations. Hence they can be evaluated continuously over the range of both ionizations including the lowering of ioniziation potential. [ABSTRACT FROM AUTHOR]

This paper deals with exterior solutions of the field equations of Jordans x-theory. The Bianchi identities are set up and brought into a simple form. All solutions with vanishing conform tensor are determined. There are three classes of solutions characterized by a timelike, spacelike, or lightlike gradient of the gravitational scalar x. [ABSTRACT FROM AUTHOR]

Using results of a preceding paper, the wavefunctions of nuclear vibrations in muon molecules have been calculated by numerical integration, especially at small nuclear distances. These functions have then been used to determine reaction rates of nuclear fusion. The effect of nuclear forces on the wavefunction at very small distances has been estimated and taken account of. The numerical results reasonably agree with ( pμd) experiments. [ABSTRACT FROM AUTHOR]

The radiative decay of the charged π-meson π→ e+ ν+ γ is calculated using dispersion relation techniques. It is assumed that the weak interaction producing the decay has a V-A structure. The decay through the vector variant has been reinvestigated and found to be different from the result of Vaks and Ioffe. The theoretical prediction of this paper is in agreement with a preliminary experiment recently performed at CERN. [ABSTRACT FROM AUTHOR]

In the presented paper the behaviour of mixtures of ionizing atomic gases in the direction of electric current as a function of space and perpendicular to the current as a function of temperature is studied. The ionization energies of the 'constituents' being either extremely different from each other or equal (isotopes), simple solutions of the problem can be given which may be useful for the understanding of effects of mass separation being found in such mixtures. [ABSTRACT FROM AUTHOR]

An apparatus to measure differential scattering cross sections using crossed molecular beams is described and results for the scattering of potassium atoms by different heavy atoms and molecules are presented. The experimental data are compared with theoretical calculations for a Buckingham-(exp-six)-potential and the parameters of this potential are determined. To carry out this comparison, it was necessary to average the existing calculations of E. A. Mason over the Maxwellian velocity distribution in the potassium beam. These averaged differential cross sections are tabulated for various angles and temperatures in the appendix of the present paper. Using crossed beams of molecules containing halogens, we can observe chemical reactions. Methods to determine total and differential reaction cross sections are discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the analysis of quantum-mechanical modes of description for extremely complex systems such as found in biology. Starting from Max Born's recent statistical approach to classical mechanics we proceed to a discussion of the limits of measurement and prediction in the corresponding quantum-theoretical problems. A main concept here is that of temporary constants of the motion, long-lived parameters of the system which have the property that they can be measured without appreciable perturbation. Knowing these, microscopic structure can only be estimated by means of inductive inferences which are intrinsically indefinite. The part played by such inferences can be diminished only by more thoroughgoing measurements which, however, perturb the system and thereby prevent it from being representative of a class of similar systems that have not been so perturbed. This may be taken as a quantitative expression of Bohr's concept of generalized complementarity. The pragmatic value of an effective description lies in its forming the basis for prediction. In quantum mechanics there are limits of prediction engendered by the indefinite nature of certain elements of the description. The importance of these limitations of predictability for theoretical biology is outlined. [ABSTRACT FROM AUTHOR]

The quantum theory of relativistic particles is developed in close analogy with that of nonrelativistic ones. In §1 we show how the Hilbert-space for the states of a physical system can be derived immediaty from experience. It turns out that both theories, the relativistic as well as the nonrelativistic one belong to the same Hilbert space. Lorentz invariance does not enter until we consider the transformations induced in the Hilbert space by the motion of the particles. These are formulated in §2. They form a representation of the inhomogeneous Lorentz-group or even of the Klein-group of conformai transformations in space-time. In §3 we develop the Hilbert-space from the so called 'basic space'. This space is spanned by simultaneously observable quantities of specific single particles which we call 'simple particles'. The characteristics of these single particles are: particle type (mass), momentum, spin, isotopic spin, etc. The configuration-space of a many particle system is taken as a set of all occupation numbers in the basic space. The Hilbert space is then the manifold of all square-integrable functions in the configuration space. In this paper the simple particles are considered to have zero rest-mass. Those having finite mass require the assumption of internal interactions and thus lead to complex structures. Mereover, particles of mass zero are distinguished by a higher degree of symmetry, i.e. by their invariance under transformations of the Klein-group. Taking into account further group-theoretical properties of the Klein-group, we assume that all aprticles are built up from neutrinos of two types. Only these we consider as simple particles. To begin with, we consider the simple case of a world with one kind of simple particles having no internal degrees of freedom. In §4 operators are given representing the inhomogeneous Lorentz-group and the Klein-group. For particles without any interaction these can easily be determined. In the case of particles with interaction it is possible to derive all operators of the inhomogeneous Lorentz-group from the interaction energy operator. This operator must satisfy certain conditions, one of which is quite involved and leads to a nonlinear operator equation. A special and rather simple approximate solution is given in §5. The resulting two-body-equation given in §6 leads to some interesting features concerning scattering and virtual and bound states. The cross-section and the wave function of the virtual state of the particle-pair, as well as the mass of a resonant state are finite. There is no bound state after a limiting process. The whole is strictly Lorentz-invariant, although we started from an expression only approximately Lorentz-invariant. Finally we state the corresponding field equations in §7. Our specific expression for the interaction energy leads to a strictly local coupling between the particles. However, the kinetic terms (which are bilinear in creation- and annihilation-operators) are of a non-local type, perhaps describing something like an interaction between the particles and the vacuum. [ABSTRACT FROM AUTHOR]

In strong electric fields the acceleration of the electrons by the field exceeds the deceleration by collisions with neutral molecules. Thus run-away or beam electrons are produced. This paper investigates the motion of the beam electrons in a neutral gas considering ionization processes by electron-molecule-impacts. We start with a time independent current of primary electrons (case a) and a space independant density of primary electrons (case b). The further development of the velocity distribution is calculated. For a molecular hydrogen gas the amplification of the initial electrons, the average ionization, and the velocity distribution of the electrons as a function of space or time respectively is given. The average ionization has an asymptotic solution, which becomes valid, when one primary electron has produced by ionization an avalanche of approximately 100 electrons. The Townsend coefficient α for high values of the field strength is independant of space only in the region of this asymptotic solution. [ABSTRACT FROM AUTHOR]

This paper gives a report on measurements of the coefficient of absorption and intensities of a gas-ionizing radiation, which is emitted by a gas discharge. Earlier measurements in oxygen with a discharge in a cylindrical electrical field had yielded components of radiation with values of μ≈550, μ≈250, and μ= 38 cm according to 760 mm Hg. By new measurements using a spark discharge an additional component with a value of μ=2,5 has been found, which already has been measured by other authors. Measurements with mixtures of oxygen and nitrogen are compared with results of measurements in air. From this it may be deduced that the gas-ionizing radiation effective in air is essentially emitted by nitrogen and ionizes oxygen, the coefficient of absorption being about μ≈5 cm. The number of ionizing quantums emitted per ionizing collision of electrons in the discharge tube is about 10 for oxygen, nitrogen, and air. In oxygen this figure proves to be essentially independent of E/p. In air, however, this figure is reduced with increasing values of E/p. The absorption of the ionizing radiation in air is increased by the addition of methane ( μ=960 cm for 760 mm Hg of methane). In carbon dioxyde several components of ionizing radiation are found, with coefficients of absorption in the range 200< μ<800. [ABSTRACT FROM AUTHOR]

In a device described in a previous paper the angular dependence of the 14.7 eV energy loss of aluminum has been measured. - The dispersion coefficient and the angular dependence of the intensity of this energy loss are in good agreement with the plasma theory. The cut-off angle was found somewhat smaller than expected. [ABSTRACT FROM AUTHOR]

The interaction of the nuclear electric quadrupolemoment with an electric field gradient at the position of the nucleus changes the angular correlation of two successive γ-rays and should also produce a circular polarization of the γ-rays. By measuring this polarization it should be possible to distinguish between electric and magnetic attenuation of the γ-cascade. In the electric case this measurement leads to determine not only the absolute value of the interaction product $$Q \cdot \frac{{\partial E}}{{\partial z}}$$ but also the sign of it and therefore the sign of the nuclear quadrupolemoment. In the following paper the measurement of the circular polarization of the 247 kev γ-ray of Cadmium-111 is described. A polarization of P=(0.8±0.2)% leads to the determination of the quadrupolemoment of the first excited state to Q=+0·9·10cm. [ABSTRACT FROM AUTHOR]

The behaviour of mixtures of reacting gases can be described by means of different principles. In this paper the thermodynamics of irreversible processes is confronted by a method based on the mechanics of particles. Here the conception of the 'constituents' as the building elements, composing the several components of the mixture, can be used profitably. Taking into consideration the thermal diffusion and the terms due to reactions in the equations of force, when the mechanical or 'dynamical' method is used, and formulating the kinetic quantities more precisely, when the thermodynamics of irreversible processes is regarded, the forces of inertia, hitherto missed, appear in the phenomenological equations, and the two systems can be proved to be equivalent. [ABSTRACT FROM AUTHOR]

In lattices, in which the Fermi surface is simply closed, the saturation values of the electrical resistivities in longitudinal/ transversal magnetic fields are equal to the approximate values for the resistivities, obtained from the variational method of Kohler using rotation symetrical trial functions/ constant relaxion times. - Depending upon the magnetic field direction the changes of the longitudinal and transversal resistance and of the Hall coefficient are proportional to the anisotropies in k-space perpendicular to the magnetic field direction. Depending upon the current direction the change of the transversal resistance is larger in the direction perpendicular to the smaller anisotropy. - By generalization of the results of part II of this paper (concerning special elliptic models) one can conclude, that the saturation of the transversal resistance vanishes in the direction of the axis in presence of cylindrical dispersion surfaces and perpendicular to the open orbits in presense of open oblate Fermi surfaces. [ABSTRACT FROM AUTHOR]

Work already published under the above topic by W. Ludwig and the author was limited to crystal temperatures above the Debye temperature, as it treated the lattice vibrations by classical statistics. In this paper, a complete quantum-statistical treatment is presented. The essential features of the high temperature results remain unchanged: New, temperature dependent dispersion curves may be introduced which, for long waves, are determined by the isothermal elastic constants. [ABSTRACT FROM AUTHOR]

Single crystals of anthracene and trans-stilbene when irradiated by α-particles show a strong dependence of their scintillation light yield on the impact direction of the α-particles with respect to the crystal orientation. This having been established in earlier papers, further investigations of 11 other compounds confirm this effect which now seems to be a common feature of monocrystalline organic scintillators. For explanation a possible relation between the anisotropy of the scintillation light yield and that of the electronic conductivity is proposed. [ABSTRACT FROM AUTHOR]

The β-spectrum of Na was measured with a scintillation spectrometer. To avoid source absorption and scattering troubles the Na source was built in in the lattice of NaJ(Tl)-crystals. The observed β-spectrum of Na has a statistical shape. The Fierz term b is obviously zero the value obtained in this paper is (+0,8±6,0)·10 m c. [ABSTRACT FROM AUTHOR]

The internal field emission (Zener-tunneling) is examined from two directions, using a onedimensional model. In section I the transition probability is calculated using the Houston expansion, but without perturbation theory, as has been used in previous papers by other authors. The calculation permits an examination of the various perturbation approximations. It is found, that the validity of the first approximation depends critically upon the residue of the interband coupling function. This residue contains the Keldysh factor, which is determined here. In section II the transition probability is calculated using free electron functions, again without perturbation theory. The same transition probability is obtained in both cases. [ABSTRACT FROM AUTHOR]

The process of deceleration of electrons by the field of neutral atoms is investigated by the aid of a model approximating the neutral atom by a constant potential U in the interior of a sphere of radius γ. The free-free emission coefficient is determined in the general case for an isothermal plasma; in the special case of an impenetrable sphere it is compared with the emission coefficient of the ion bremsstrahlung as obtained by the 'soft' approximation. The results show that electron-atom radiation may not be neglegible as compared with electron-ion radiation, and this fact may be used to explain the experimentally observed increase of the emission coefficient with pressure which is more rapid than linear. This is verified numerically in the limiting case of an impenetrable sphere. In addition the bound-free absorption coefficient is determined both in general and in the special case of the H ion; a comparison is made with the absorption coefficient as obtained by Chandrasekhar. By the aid of the method of 'best approximation' given in the concluding part of the present paper the quantities U and γ may be determined for any neutral atom. [ABSTRACT FROM AUTHOR]

A simple method of measuring the degree of polarization achieved by optical pumping has been described recently for the case of sodium vapor, illuminated with the single circularly polarized D line. The assumption had to be made, however, that the atomic absorption cross section Q, depending on the degree of polarization P and the frequency of light ν, may be approximated by Q( P, ν)=(1− P)· Q( P=O, ν). The purpose of this paper is to discuss the qualification of this assumption. A theoretical analysis of the pumping process is tried, showing that the measured polarization corresponds in good approximation to the degree of the valence electron spin polarization. - For the case of weak absorption and equal intensity of the two hyperfine components of the D line a diagramm is given, relating the measured polarization to the polarization of the nuclear spin. [ABSTRACT FROM AUTHOR]

The orbital and spin energy of a Fermi or Bose gas with different orbital and spin temperature depend on both temperatures. This new thermodynamic behaviour demands a new formulation of the foundations of thermodynamics for such systems. In the present paper the fundamental thermodynamic notions (variables of state, work, adiabatic processes) are formulated and the definition of an empirical orbital and spin temperature is given. The first law of thermodynamics, the definition of orbital and spin heat, and resulting conditions of integrability are discussed. There are four heat capacities (instead of the one for normal systems), the relations of which are stated. [ABSTRACT FROM AUTHOR]

A Dehmelt type experiment is performed in which sodium vapor and argon as a buffer are employed. The pumping radiation consists of the circularly polarized D line. Since the strongly absorbing magnetic sublevels are depopulated, the vapor becomes more transparent to the pumping radiation with growing polarization. The transparency of the vapor is measured with and without optical pumping as a function of the sodium vapor density. The degree of polarization is determined in simulating the increase in transparency due to polarization by decreasing the sodium vapor density of the unpumped sample. This method requires the knowledge of the exact sodium vapor density in the temperature range of interest (100 to 200° C). The determination of the degree of polarization is based on the assumption, that the atomic absorption cross section Q, which depends on the degree of polarization P and the frequency of light ν, can be written in the form Q(P,ν)=A(P) · B(ν), where A(P) is a linear function of P, while B (ν) must not be changed by optical pumping. As will be shown in a following paper, the degree of polarization determined under this assumptions, describes in good approximation the polarization of the sodium valence electrons. [ABSTRACT FROM AUTHOR]

The elastic scattering of deuterons in deuterium has so far only been treated in Born approximation, at rather high energies. In the present paper the authors derive integro-differential equations to deal with the scattering phenomenon at low energies of a few MeV. The mutual distortion of the two deuterons at close distance turns out to have a large influence on the angular distribution. A simple and plausible assumption has been made, concerning this distortion, and the results have been compared with experiment for two energies. [ABSTRACT FROM AUTHOR]

This paper concernes the problem of development of plaine waves in a gas plasma without external fields. The question has been recently treated by Landau, v. Kampen, Berz and o. m. The equation of Boltzmann is discussed and solved for the case with initial conditions (Anfangswertproblem) explicitly. With the usual expression for the collision term exist no 'Eigenlösungen'. Nevertheless in a short time long waves develop with λ>30 l ( Debye-Length) from the initial distribution; the statistical damping cancels down the development of shorter waves. Changing the collision term, one finds true Eigenlösungen too. This different behaviour of the solutions seems to be less a physical problem than a question of the used mathematical formalism. [ABSTRACT FROM AUTHOR]

The procedure of quantum mechanical treatment of a three-body problem described in the preceding paper by Diehl, Flügge, Schröder, Völkel and Weiguny has been specialized to the ground state in which the eigenfunction only depends upon the three distances between the particles. The solution of the Schrödinger equation has been approximated by variational methods, using the electronic functions of Finkelstein and Horowitz, and of Guillemin and Zener, but including the nuclear vibration in the trial function. [ABSTRACT FROM AUTHOR]

Using the variational method developped in the preceding paper of Diehl and Flügge, the binding energy and molecular parameters of the muon molecule ppΜ have been calculated. The vibrational amplitudes of the protons turn out to be much larger in comparison to their equilibrium distance than in the electronic molecule H. The equilibrium distance is about 40% larger than it would have come out from a simple two-center calculation with fixed nuclei. A dissociation energy of 211 ev has been found; this value may be enlarged by something between 10 and 20 ev in consequence of plausible corrections. [ABSTRACT FROM AUTHOR]

The nucleons liberated in a ( d, p)- or ( d, n)-stripping-reaction are generally polarized even if unpolarized deuterons are used. In this paper however these reactions are examined for polarized deuterons in order to provide more detailed information concerning the interactions between the reaction products. [ABSTRACT FROM AUTHOR]

Electron avalanches in uniform fields are studied by means of a short duration spark light source. Electron drift velocities ν are measured in hydrogen, nitrogen, oxygen, and some vapours. It is shown, that in hydrogen and nitrogen the number of electrons increases exponentially by gas amplification with a time constant 1/αν, in accordance with a conventional assumption and with previous measurements in methane, α is the first Townsend coefficient. In oxygen and air it is, however, demonstrated that the number of electrons increases considerably less than exp (αυ·t), and the multiplication process takes longer time. This is evidently due to time losses of the electrons on their paths across the gap. Thus the mean time interval for successors, started by photons at the cathode, is increased. - In addition, this paper gives details of some measurements of the first Townsend coefficient α, the electron diffusion coefficient, and ionic drift velocities for certain gases. [ABSTRACT FROM AUTHOR]

An excited nuclear state can decay by three different modes of double quantum emission, namely double γ-emission, γ-electron emission and double conversion electron emission. The emission of two γ-quanta has been considered in an earlier paper. The purpose of the present work is to treat all three processes together in a systematic manner. It is shown that the connection between the transition rates for γ-electron emission T and double γ-quantum emission T is more complicated than in the case of single quantum processes. However, T can still be expressed in terms of the usual conversion coefficients. This is also true for the transition rate T for the emission of two K-shell electrons, although only approximately. For the emission of electrons from different atomic shells the formulas become rather complicated, because of interference effects. The electron and γ-quantum spectra in all of the three second order processes are discussed in detail for the decay of the isomeric level in Xe. [ABSTRACT FROM AUTHOR]

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Parametric amplifiers have been developed during the last years to get a low noise amplification of weak electromagnetic signals. This paper describes simple experiments to demonstrate the basic principles by an electrical arrangement with variable capacity and by a mechanical set-up with capillary-gravity waves on a water surface. An explanation of the parametric oscillation and amplification is given in connection with these experiments. [ABSTRACT FROM AUTHOR]