Search

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]

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 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]