Volume 11, Issue 4
October 1978, pages 359-517
pp 359-377 October 1978 General Relativity
Charged particle motion in an electromagnetic field on Kerr background geometry
In this paper we study the trajectories of charged particles in an electromagnetic field superimposed on the Kerr background. The electromagnetic fields considered are of two types: (i) a dipole magnetic field with an associated quadrupole electric field, (ii) a uniform magnetic field. The contribution of the background geometry to the electromagnetic field is taken through the solutions of Petterson and Wald respectively. The effective potential is studied in detail for ther-motion of the particles in the equatorial plane and the orbits are obtained. The most interesting aspect of the study is the illustration of the effect of inertial frame dragging due to the rotation of the central star. This appears through the existence of nongyrating bound orbits at and inside the ergo surface. The presence of the magnetic field seems to increase the range of stable orbits, as was found in a previous study involving the Schwarzschild background.
pp 379-388 October 1978 Solids
General linear response analysis of anelasticity
Linear response theory is used to express the anelastic response (creep function and generalized compliance) of a system under an applied stress, in terms of the equilibrium strain auto-correlation. These results extend an earlier analysis to cover inhomogeneous stresses and the tensor nature of the variables. For anelasticity due to point defects, we express the strain compactly in terms of the elastic dipole tensor and the probability matrix governing dipole re-orientation and migration. We verify that re-orientations contribute to the deviatoric strain alone (Snoek, Zener, etc. effects), while the dilatory part arises solely from the long-range diffusion of the defects under a stressgradient (the Gorsky effect). Our formulas apply for arbitrary orientational multiplicity, specimen geometry, and stress inhomogeneity. The subsequent development of the theory in any given situation then reduces to the modelling of the probability matrix referred to. In a companion paper, we apply our formalism to work out in detail the theory of the Gorsky effect (anelasticity due to long-range diffusion) for low interstitial concentrations, as an illustration of the advantages of our approach to the problem of anelastic relaxation.
pp 389-409 October 1978 Solids
Theory of the Gorsky effect for low interstitial concentrations
The formalism of the preceding paper is applied to work out the theory of the Gorsky effect, or anelastic relaxation due to the long-range diffusion of interstitials in a host lattice, for non-interacting (low-concentration) interstitials (e.g., H in Nb). It is shown how linear response theory (LRT) provides a number of advantages that simplify the solution of the problem and permit the handling of complications due to specimen geometry and stress inhomogeneity. The multiple-relaxation time creep function of Alefeldet al is first re-derived. Next, the dynamic responseand the short-time behaviour of the creep function are deduced exactly, and theω^{−1/2} fall-off of the internal friction at high frequencies is exhibited. Finally, it is pointed out that the true asymptotic behaviour of the dynamic response must be found by going beyond the diffusion equation model. A two-state random walk analysis is used to predict a cross-over to a trueω^{−1} asymptotic behaviour, and the physical reasons for this phenomenon are elucidated.
pp 411-422 October 1978 Solids
The optic mode Gruneisen parameters in silver, caesium and thallium halides are calculated using the Born model for interionic forces and the Szigeti theory of dielectric constants. The strain derivatives of the electronic and static dielectric constants are also evaluated and compared with experimental data. The strain derivative of static dielectric constant reveals the inadequacy of the Born model for the crystals under study. Possible modifications have been suggested to improve the situation. The theoretical values of the optic mode Gruneisen parameters closely agree with recent experimental data. An appropriate process has been adopted to evaluate the average values for the Gruneisen parameter.
pp 423-433 October 1978 Solids
Sound attenuation in doped displacive ferroelectrics
An expression is obtained for the sound attenuation constant in a doped displacive ferroelectrics in the presence of an external electric field, using double-time temperature-dependent Green’s function technique. The mass and force constant changes due to impurity atoms, are taken into account along with higher order anharmonic and electric dipole moment terms, in the Silverman-Joseph Hamiltonian. The attenuation constant increases with an external electric field. The soft mode is responsible for the anomalously increasing behaviour of the attenuation constant in the vicinity of the Curie temperature. The results agree with those attained by Tani and Tsuda and Heuter and Neuhaus.
pp 435-440 October 1978 Solids
Optical, etching, and interferometric studies on ferroelectric PbNb_{2}O_{6}
Optical, interferometric and etching studies of (001) surfaces of ferroelectric PbNb_{2}O_{6} are presented. It is found that crystal growth takes place mainly by layer formation. The layer boundaries can be distinguished from the domain lines by interferometric studies. Thermal etch pits are found near 90° domain walls and the layer boundaries. The etching studies show that these pits are at the sites of dislocations, and it is deduced that no extensive motion of dislocation takes place at the Curie-temperature in the process of domain formation.
pp 441-455 October 1978 Nuclear And Particle Physics
The polarization of the fragments from binary fission or of scattering or fusioning heavy nuclei is investigated in the liquid drop model. Due to the mutual Coulomb repulsion near contact the fragments may be polarized with respect to their charges (electric dipole moments from inhomogeneous charge distributions) as well as with respect to their shapes (quadrupole and octupole deformations). The lowering of the minimum energy near contact due to charge polarization is in the order of 1 MeV if one takes into account the energy from the giant dipole restoring force derived from the volume symmetry energy in addition to the liquid drop energies. The question whether one obtains prolate or oblate shapes is entirely due to the restriction in deformation space (fixed distance between centers-of mass or between the tips of the fragments).
pp 457-469 October 1978 Nuclear And Particle Physics
A classical microscopic description of the collision between two bound particle clusters, interacting via a suitable two body force is presented with a view to extend the analogy to nuclear collisions. It is shown that with a proper choice of the parameters of the two body force, the model calculations can bring out qualitatively all the essential features of low energy heavy ion collisions such as complete fusion, deep inelastic scattering and nucleon transfers. The model avoids some of the limitations of purely hydrodynamic descriptions connected with the shape parametrization, compressibility and viscosity effects, etc.
pp 471-477 October 1978 Nuclear And Particle Physics
Negative muon capture in^{3}He
We compute the partial capture rate of negative muons in^{3}He by following the analysis of Peterson to include the relativistic corrections and the exchange effects, for various values of theg_{p}/g_{A} ratio. We also calculate the total capture rate. The ground state of^{3}He is assumed to be spherical. The radial dependence of the ground state wave function is taken to be (a) one parameter Irving function, (b) a modified three-parameter Irving function and (c) a function having ‘soft-core’, whose parameters have been fixed in a variational calculation of the binding energy of the triton using a non-local momentum-dependent potential involvingp^{2} terms. The calculated values of the capture rates are compared with the experimental data to find a value for theg_{p}/g_{A} ratio.
pp 479-489 October 1978 Nuclear And Particle Physics
An experimental study of angular distribution of fast secondaries in 50 GeV/cπ^{−}-Em collisions
V Kumar S C Varma N S Verma A P Sharma
The pseudo-rapidity distribution has been studied for 50 GeV/cπ^{−}-colliding with various groups of target nuclei in emulsion. These data are compared with the published data onp-A collisions. It is observed that leading component multiplicity inπ^{−}-Em collisions decreases withN_{h} in highη-region. It is also observed that nearly 20% of the interactions proceed via single cluster formation at this projectile energy.
pp 491-506 October 1978 Nuclear And Particle Physics
On the alleged equivalence of certain field theories
We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.
pp 507-517 October 1978 Nuclear And Particle Physics
U_{3}(W)-gauge theory IV. The Kolar events
Pursuing the starting motivation of the recently proposed U_{3}(W)-gauge theory of weak and electromagnetic interactions, we attempt a rough quantitative description of the origin of the unusual Kolar events reported in deep underground cosmic ray neutrino experiments by Krishnaswamiet al. These events are interpreted as due to production, inν_{μ}-nucleon collision, of a charged heavy muonic leptonM^{−} in association with hadrons carrying new heavy quark flavours named grace and taste (g, t), followed by the decayM →E +e +μ, whereE is another heavy lepton of the electronic type. The production cross-sections are estimated by using the standard quark parton model. The long life of the Kolar particle is explained by taking the mass difference of theM and theE to be sufficiently small. With suitable illustrative choices of the masses of the proposed new particles involved, it is shown that the threshold for production could be rather high so that neutrinos with energy of several hundreds of GeV upwards, available in cosmic rays, may be responsible for the processes suggested here for explaining the Kolar events. Comments are made relating to the currently available accelerator neutrinos in this context. Attention is also drawn to the possible role of the above heavy leptons in interpreting the events recently observed in cosmic ray experiments at Tbilisi.
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