Volume 28, Issue 3-4

It is shown that poorly converging series of Legendre polynomials or spherical harmonics can be well approximated by the method of the Padé approximation. The improvement of the convergence will be discussed with the help of three model series which can be calculated exactly.

The structure of the Bogoljubov -Valatin transformation and the HFB state is investigated by group-theoretical methods. A direct proof of the Bloch-Messiah factorization theorem shows that the second factor which contains the BCS part of the BV transformation can be chosen always real. An unitary representation of the Bogoljubov-Valatin group in the Fock space is constructed which allows to write down various equivalent expressions for the HFB state vector. The relation between the "unitary form" and the usual form of | HFB〉 is clarified using the "quasispin" concept in connection with a theorem about the factorization of the D(3) Lie group.

Quotient spaces are examined as they occur in canonical formalisms with constraints. Illustrative examples are taken from classical mechanics, from general-relativistic theories, and from the theory of the electron microscope.

The necessary extension of the quantum mechanical Hilbert space to a state space with indefinite metric in a local description of quantum electrodynamics, the Yang-Mills theory and a linearized gravitation theory is illustrated. As one of the essential physical consequences of such an extension we emphasize the fact that the interaction cannot be completely represented by the virtual exchange of particles but always does contain non-particle-like “genuine” parts of nonlocal character. In analogy to these cases the indefinite metric in Heisenberg's Lee model and in subcanonical quantum field theories, like Heisenberg's nonlinear spinor theory, is discussed. The physical consequences resulting from a unitarization of these theories with regard to the effective interaction and its causal character are pointed out.

The manifestly covariant Bethe-Salpeter equation is reduced to relativistic, three-dimensional integral equations suitable for the dynamical treatment of the two-nucleon system at low energies. The reduction is achieved by restricting one of the nucleons to the mass shell. The resulting twonucleon scattering equations and bound state equations are Schrödinger-like field equations containing relativistic kinematical corrections. The transformation of these equations to the ordinary Schrödinger (or Lippmann -Schwinger)-equation is discussed. Intimately connected with the reduction is the derivation of a meson field mediated two-nucleon potential containing meson retardation effects and adequate for the application to the two-nucleon system and nuclear structure problems.

The difference between the absolute value of the Hartree-Fock (HF) single particle energy and the removal energy is studied. This total rearrangement is composed out of the orbital (or spatial) and the Brueckner rearrangement. It is shown analytically within the Pauli-Brueckner HF (PBHF) approach that the saturation potential 〈h | ∂V/∂ρ | h〉 for a density dependent effective force is equal to the Brueckner rearrangement energy of the level | h〉 plus a smaller term. This is in 16 O accidentally numerically roughly equal to the orbital rearrangement energy. The numerical calculation in 16 O of the rearrangement energies for the proton level yields the maximum value (9 MeV) for the Os½ state. The Brueckner rearrangement is from a factor two to twenty larger than the orbital rearrangement.

After briefly reviewing the experimental facts that seem of direct relevance for the question of the origin of cosmic rays, and after quickly going through the “classical” theories of cosmic ray origin, we discuss in some detail those theories that have been put forward over the past few years since the discovery of pulsars. This discovery brought the first observational evidence for the existence of super-strong magnetic fields in nature.

The main properties of neutron star matter and of neutron star models are reviewed with particular emphasis on those aspects that can directly be related to pulsar observations.

The method of generator coordinates is applied to a two level model with pairing and monopole force. The harmonic approximation is investigated. By proper inclusion of the symmetries of the Hamiltonian an improvement over the usual Random-Phase approximation results.

A coordinate-independent formulation of the chiral-symmetric pion theory is developed using a dreibein field which introduces a redundant gauge field into the field equations. There is a particular gauge, where the field variables transform linearly under chiral transformations and the field equations reduce to those of the Sugawara-model. Quantization of Sugawara's field equations is obtained in terms of Green's functions. The field equations for the coordinate-independent Green's functions are translated into equations for coordinate Green's functions by introduction of the coordinates as auxiliary variables. The latter field equations incorporate the additional Feynman graphs discovered before.

It is shown that the cluster expansion formalism previously developed as a basis for a theory of the ground state of correlated systems may be generalised in such a way as to enable the application of the generator coordinate method in the presence of singular interactions, thereby providing also a theory for excited states.

The construction of subalgebras of the set of bilinear products of fermion operators which allow the formation of physically relevant solvable models is investigated. The subalgebras are assumed to be semisimple, hermitean closed and compatible with angular momentum. One obtains two classes of subalgebras, i) the wellknown set of spherical tensors of rank zero and ii) a new class of subalgebras which contain the angular momentum operators. The construction procedure for subalgebras of the second kind is presented in detail (hereby, one starts with the abstract type of the subalgebra and defines the physical model space by the carrier space of a representation) and a number of examples, which provide models not known from the literature, is given.

The coupled-channel contribution of N 33 isobars, which appear in the solutions of the fixedsource strong coupling field equations, are equivalent to an effective scalar N-N potential with the range of the σ-exchange in usual OBE models.

Replacing the Green function of Maxwell's electrodynamics δ(x 2 ) by δ(x 2 + l 2 ) we obtain a Hamiltonian with a finite number of degrees of freedom for the classical motion of a pointcharge in its own electromagnetic field. After quantization we obtain a mass spectrum if we assume that a nonelectrodynamic bare mass M exists. The spectral terms are S 1/2 , P 1/2 ; P 3/2 , D 3/2 ; D 5/2 etc. (k = +1, -1; +2, -2; +3 ...). It is possible to fit the length l in the Green function and the mass M so that the mass ratio of the lowest terms becomes m (P 1/2 )/m(S 1/2 ) = m μ /m e . We then get: l =4,896 · 10 -91 ħ/m p c, M = 15,32m p . Hence the deviation from Maxwell's electrodynamic is extremely small, but not zero, and heavy leptons should exist near m = | M | . Some further leptonic states exist with masses similar to that of the muon. All states, those of the electron and the muon excepted, are γ-instable (life time 10 -17 sec. resp. 10 -26 sec.).

for given values of the total current density j and the cathode spot surface temperature T a unified and consistent calculation of the cathode drop, U c , the electron temperature in the ionization region T _- the electron emission current density j e , the ion current density j + , and the extension of the space charge region l sp are presented. We find that the counter diffusion of plasma electrons into the space charge region plays a decisive role. It causes an effective space charge region extension l sp of a few plasma electron Debey lengths which in general is much less than the ion mean-free-path commonly used. Without the effect of the counter diffusing electrons, the theoretical results deviate from the experimental data by orders of magnitude. For the example of a Cu metal vapour-or vacuum arc the cathode drop is found to be approximately U c = 15 [V], the electron temperature about T- =25000 [°K] and the ratio j+/j= 0.5. Since the analysis allows for multiple ionization the presence of multiply charged ions in the spot area can be calculated. The results of this investigation justify within the E-areas the approximations used in the analysis for the copper arc in an earlier investigation 1 . Outside these E-areas a recalculation with the new results derived here may cause markable changes.

The motion is depicted as a sequence of steps of a finite residence time. The spot motion affects essentially only the energy characteristics T e which in comparison to the stationary characteristics T es are shifted to smaller values. Hereby the critical currents I 0 , I 1 are raised in comparison to the corresponding stationary limits I 0s , I 1s . Particularly attractive are the phenomena found in connection with the dependence of the spot velocity ʋ on the spot current I. If the spot velocity increases with the spot current stronger than ʋ ∞ I 1/2 then the E-diagram reveals the existence of an upper limit l u for the spot current. This result can be used to explain qualitatively the experimentally observed phenomena of "spot multiplicity" and “spot extinction”. Quantitative conclusions are obstructed by the lack of knowledge about the velocity dependence on the spot current, ʋ(I). Experimental and theoretical studies to provide a better understanding of the physical background and the analytical laws describing the motion of the cathode spots are urgently needed.

Accessibility of a plane electromagnetic wave into an inhomogeneous, magnetized plasma column is studied using the complete cold plasma dielectric tensor. It is found that TM (transverse magnetic) waves incident at small angles with the vacuum-plasma interface are almost completely transmitted into the plasma even though the criterion for accessibility to the lower-hybrid resonance is not satisfied. The significance of this result for coupling rf energy into plasma filled waveguides is discussed.

The interaction between an electric arc and a gas flow is governed by the flow of mass relative to surfaces of constant temperature. This fact is used to introduce a new method for the computation of decaying wall-stabilized arcs in which the temperature is used as a free variable instead of the radial coordinate. The method is also applicable to more general cases and gives direct insight into the physical processes involved. An implicit two level scheme is described which guarantees numerical stability for any chosen time step. The method is applied to a decaying wall stabilized arc. The results agree quite well with published experimental curves.

The 4f-shell of Europium was polarized in different rare gas atmospheres by spin exchange with optically pumped Cesium. The estimated cross sections for Europium-rare-gas relaxation turned out to be significantly larger than corresponding Cesium values.

A high-temperature microwave spectrometer has been developed for Zeeman effect measurements in strong magnetic fields up to 50 kG. The absorption cell is placed in a superconducting solenoid and can be heated as high as 1200 °C. The g J -factor and the magnetic susceptibility anisotropy of TIF, CsF and CsCl, the g J -factor of CsBr, and an upper limit for the value of the g J -factor of CsI have been measured. The molecules CsF and CsCl were also studied in higher vibrational states.

The ligand field reflectance spectra of octahedrally coordinated Cu 2+ -ions in different host lattices and at different temperature (300 °K - 4 °K) are critically compared. Especially the band shifts with decreasing temperature are analysed with respect to transitions from a dynamical to a static Jahn-Teller effect (macroscopic Jahn -Teller distortion of the lattice). In addition the square planar coordination of Cu 2+ is discussed and alternative descriptions in the crystal field formalism and the angular overlap model are given.

The preparation and the alloy structure of Nb - Al samples containing σ.-phase are described. Using single-phase material it is shown that the o-phase Nb - Al, independent of composition and heat treatment, is not superconducting down to 1.3 K.

In this paper the splay k 11 and bend k 33 elastic constants for the homologous series 4,4′-di (n-alkoxy)azoxybenzene (from methyloxy to hexyloxy) were measured as a function of temperature by studying the deformation of the liquid crystal in a magnetic field. The values of these elastic constants (10 -6 to 10 -5 dyne) all decrease with increasing temperature. The reduced elastic con­stants C 11 and C 33 which were derived by Saupe and which take into consideration the effect of temperature on the order parameter and on the mole volume should be independent of temperature if there are no changes in short range order. In the region of the isotropic transition temperature the reduced elastic constants of the homo­logous series show a general increase with increasing alkoxy chain length. This trend can be ex­plained by the increasing molecular length. There is still a strong alternation superimposed upon this trend, however, which can not be due to the alternation of the anisotropic polarizabilities. To first approximation, the elastic constant ratios for the homologous series can be summarized on a single universal curve. The temperature behavior of the elastic constants can be divided into four groups, each having its own characteristic short range order structure. Region IV, which is near the smectic phase transition, is characterized by cybotactic groups which exist in the nematic phase and which have a smectic like structure. C 33 as well as C 11 show a very strong increase in this region as the smectic C phase is approached. This abnormal temperature behavior can be explained as a pretransitional effect because in the smectic C phase C 33 and C 11 must be quite large because of the planar structure where the molecules are tilted with respect to the plane. In a smectic A phase where the molecules are perpendicular to the plane a pretransitional effect occurs only in C 33 as Cheung and Meyer have shown. In region III C 33 /C 11 ~ 1 and this ratio is temperature independent. This behavior is in agree­ment with our model calculation if the steric units contain only a few' molecules and are approximately spherical and are arranged to form a planar structure. In region II C 33 /C 11 ~ 2 and C 11 and C 33 are both independent of temperature. The assumptions made for region III are also valid here except that the steric groups in region II are not arranged in a planar configuration. This assumption is in agreement with the model calculation and has been verified through x-ray experiments. In region I, which borders upon the isotropic phase, C 11 is nearly independent of temperature whereas C 33 becomes smaller with inceasing temperature. The model calculation show's that C 33 is more sensitive to structural changes than C 11 . The abnormal temperature behavior of the mole volume in this region is an indication that changes in the short range order structure are occurring.

The ratios of the g I -factors of 85 Rb and 87 Rb and of 111 Cd and 113 Cd have been measured in aqueous solutions of salts by the NMR method with high accuracy. A comparison with the same ratios measured by optical pumping techniques in free atoms shows agreement within the limits of error of 2.3 · 10 -6 in the case of rubidium and of 3 · 10 -7 in the case of cadmium: No difference in the magnetic shielding between the isotopes is observable.

Measurements of the magnetomechanical effects of high permeability materials have not yet been performed because of their smallness. Using a new technique, the Joule magnetostriction of Mumetal is obtained by shear strain measurement. The change of shear modulus and the magnetomechanical damping in dc and ac magnetic fields are investigated and discussed.

The interdiffusion coefficients of the systems NaNO 3 +AgNO 3 at 290 °C in the concentration range 0.25 ≦ x 2 ≦ 1.0 (x 2 mole fraction of the silver nitrate) and LiNO 3 + AgNO 3 at 260 °C in the total concentration range are determined by the diaphragm cell method. The dependence on time of the composition of the melt in the two compartments of the cell is followed up by emf-measurements. To that end we propose a new plotting method.

The anisotropy of electric conductance in nematic electrolytes induces an inhomogeneous field in a rectangular sample. The effective specific conductivity and the cross voltage, which is generated at opposing points of the sample, depend on the ratio between the sides of the cell. The experimental values obtained for the electric properties agree favourably with the theoretical values calculated according to a method previously described. The orientation of the axis of alignment can be determined using this experimental procedure to an accuracy of 0.05°.

In this paper we show that in binary liquid systems with miscibility gaps, the forces related to the formation of spatially ordered regions near the critical solution temperature, T c , prevalently involve interactions of type AA and BB rather than interactions of type AB. A and B being the components of the mixture. For this purpose we have measured the viscosity and proton spin-lattice relaxation as a function of temperature and concentration in water-ethylene glycol monobutyl ether systems. With a method previously described, which allows to determine the contributions to the relaxation that arise from the coupling of protons belonging to molecules of different types, the mixed translational contributions near T c due to interactions of type AB and the mixed translational contributions one would obtain if the same region were not critical, have been calculated. The knowledge of these quantities allowed us to evaluate the viscosity per cent deviation due to the critical phenomenon, considering this to be essentially related to interactions of type AB. Comparison with the per cent deviation of the measured viscosity shows that the two sets of values are quite different. The difference must be due to interactions of tpye AA and BB.

The drift velocities of radiation-induced excess electrons and positive charge carriers in liquid methane were measured at different electric field strengths and several temperatures. For the excess electrons the drift velocity increases up to 1.5 kV cm -1 proportional to the electric field strength and a mobility of (400±50) cm 2 V -1 s -1 at T = 111 °K was obtained. Above 1.5 kV cm -1 the drift velocity varies with E ½ . The temperature coefficient of the mobility is negative. For the positive charge carriers the measurements were carried out up to electric field strengths of 50 kV cm -1 and the drift velocity remained proportional to the field giving a mobility of (2.5 ± 0.5) · 10 -3 cm 2 V -1 s -1 at 7 = 111 °K. The mobility increased with increasing temperature. The reaction of excess electrons with oxygen was also studied and a rate constant of 8.4 · 10 11 l mole -1 s -1 was obtained.

In some recent works a dispersion relation proposed by Feshbach for the generalized optical potential has been used in order to analyse the energy dependence of the strength of the empirical optical potential. In the first part of this report the mathematical problems arising in the derivation of the dispersion relation and the results obtained in this direction are discussed; in the second part the approximations introduced in the application of the dispersion relation are analysed and the results concerning the non-locality of the generalized optical potential are reviewed.

After a short historical introduction it is discussed how far Mach's principle is incorporated into general relativity. The possible role of Mach's principle as a selection rule for the solutions of Einstein's field equations is summarized. Then follows a discussion of Math's principle in theories of gravitation other than Einstein's, mainly the Brans-Dicke theory. Finally the experiments on the isotropy of inertial mass and their consequence for Mach's principle are described. The conclusion is that Mach's principle, though an extremely stimulating thought, has at present little claim to be a basic physical principle.

This is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

The new nuclide 236 Th has been produced via the (γ, 2 p) reaction by irradiation of 238 U with 140 MeV bremsstrahlung. After chemical separation of thorium, the half-life was determined to be 36 ± 3 min -from the growth-decay curve of the strongest γ-ray transition of the daughter nuclide, 9 min 236 Pa.

Since there are discrepancies in the value of the Si -Si-bond length in Hexachlorodisilane the structure has been reingestigated with gas electrondiflraction. The resulting structure parameters are listed and compared with the earlier results.

A simple model for track formation in solide state nuclear track detectors is proposed. According to this model the area of an etch pit is proportional to the etching time and to the square root of the energy of the impinging particle. This conclusion is in agreement with experimental results.

A brief report is given of some recent experiments which have been conducted in order to prove the existence of a gravitational radiation effect proposed by Keith (1963).

Several recent papers have emphasized the current interest in the study of infrared band shapes in condensed phases. The aim of this note is to report the temperature dependence of the half-widths of certain IR bands of succinonitrile, malononitrile and acetonitrile with primary interest in the elucidation of the mechanism influencing the half-width. Generally it is assumed that the main contributions are the vibrational or intrinsic (ΔWv) and the reorientational (ΔW r ) relaxations. The separation of both contributions can be done by Raman spectroscopy 1, 2 but in our work we used the much simpler method due to RAKOV 3 . The half-width is written as: ΔW = ΔW v + ΔW r (1) and only ΔW r is a function of temperature ΔW r ~ exp (-ΔE/k T) where ΔE is the activation energy.