Showing papers on "Symmetry (physics) published in 1968"
TL;DR: In this paper, a superconvergent combination of weak baryon form factors is constructed from the assumptions that the usually adopted transformation properties of the baryons and the vector and axial vector currents are exact for matrix elements in the limit of infinite t, and that the direct vector and the axial-vector form factors are convergent.
113 citations
IBM1
TL;DR: In this paper, the symmetry of bound electron states in GaP depends upon the choice of origin for the group operations and hence upon the location of impurity in the crystal lattice.
Abstract: We show that the symmetry of bound electron states in GaP depends upon the choice of origin for the group operations and hence upon the location of impurity in the crystal lattice. This provides an explanation of the discrepancy between the high radiative efficiency associated with group VI donors and group V isoelectronic centers and the low efficiency of group IV donors (Si) in GaP.
112 citations
101 citations
TL;DR: In this paper, the problem of the accumulation and storage of the energy released in solar flares is discussed; it is proposed that convective energy of the photosphere is transformed into magnetic energy of chromosphere and corona and the consequences of a large ratio of magnetic pressure to gas pressure are investigated.
Abstract: The problem of the accumulation and storage of the energy released in solar flares is discussed; it is proposed that convective energy of the photosphere is transformed into magnetic energy of the chromosphere and corona. The consequences of a large ratio of magnetic pressure to gas pressure are investigated. In this case the field must be approximately force-free. The only suitable force-free fields which allow an analytical treatment are those of cylindrical symmetry. The stability of these fields is studied with the energy principle. It is shown that they are always unstable due to kink type instabilities. The shape of the unstable perturbations is described in detail and an upper limit for their amplitude is estimated. The consequences for the proposed mechanism of energy storage are briefly discussed.
96 citations
TL;DR: In this article, it is shown that the symmetry group of the ordered phase cannot be any subgroup of the symmetry groups of the disordered phase, and that the elastic constants of the second-order phase transition can be computed.
85 citations
69 citations
TL;DR: In this paper, a method for finding the matrix elements of trees correction term in cubic symmetry in the strong field scheme is given. But this method is not suitable for the d5 configuration for which this term has been found quite significant.
Abstract: A method is given for finding the matrix elements of Trees correction term in cubic symmetry in the strong‐field scheme. The correction matrices have been calculated for d5 configuration for which this term has been found quite significant.
65 citations
TL;DR: In this article, the breakdown of Friedel's law in electron diffraction, using the single-crystal intensity distribution from cadmium sulfide in the [21 −bar 3 −0] orientation, was investigated.
Abstract: Detailed observations are made of the breakdown of Friedel's law in electron diffraction, using the single-crystal intensity distribution from cadmium sulfide in the [21{\bar 3}0] orientation. It has been found by experiment that no breakdown of Friedel's law occurs in the zero-order beam distribution. An analysis of the problem due to Moodie, using multiple-scattering diagrams, has also led to this result. Multiple-scattering diagrams are used here to illustrate the symmetry properties of the zero-beam distribution. Rules are given for the deduction of the other symmetry elements of the projected structure from the diffraction-pattern symmetry, and from the occurrence of dynamic extinction bands in the kinematically forbidden reflections. These are illustrated by further pictures from cadmium sulfide. This analysis is simplified in the present work by neglecting non-zero-layer interactions. Results obtained by n-beam calculation using the multi-slice method show the possibility of quantitative interpretation, and of absolute orientation determination. The limitations of the systematic dynamic approximation and also of a systematic approximation using corrected scattering potentials are examined for this substance.
56 citations
55 citations
44 citations
TL;DR: In this paper, the problem of the scattering of an electromagnetic plane wave, incident along the axis of symmetry on a cylindrically symmetric, though otherwise arbitrarily shaped conductor, is solved exactly by means of a perturbationexpansion technique developed for this purpose.
Abstract: The problem of the scattering of an electromagnetic plane wave, incident along the axis of symmetry on a cylindrically symmetric, though otherwise arbitrarily shaped conductor, is solved exactly by means of a perturbation-expansion technique developed for this purpose The solution obtained is an exact analytical solution, equally valid in the near and far zones, as well as over the entire frequency range, including the resonance region The general solution is obtained, and several special cases are treated in detail The term-by-term agreement of the perturbation-series solution with the known exact solution is demonstrated analytically for the case of a sphere The form of the solution is particularly well suited for methodical numerical evaluation by machine calculation
TL;DR: In this paper, a theory for the small deformations superposed on the large deformation of an elastic rod is given, and some aspects of material and geometrical symmetry are discussed.
TL;DR: In this paper, the splitting of atomic energy levels in a crystalline field with the symmetry of one of the magnetic (Shubnikov) point groups has been studied, and the cases of various possible relative strengths of the crystal field and of spin-orbit coupling are considered.
Abstract: Two pieces of theory which have so far remained unconnected, crystal field theory and the theory of corepresentations of non-unitary groups, are brought together here for the study of the splitting of atomic energy levels in a crystalline field with the symmetry of one of the magnetic (Shubnikov) point groups. The cases of the various possible relative strengths of the crystalline field and of spin-orbit coupling are considered. Tables are presented which enable the splitting of any atomic energy level to be obtained very easily in a crystalline field with the symmetry of any one of the 58 magnetic point groups. Examples of the use of these tables are given. A discussion is given of the relevance of Kramers' theorem to the energy levels of electrons in surroundings with the symmetry of any one of the 58 magnetic point groups.
TL;DR: A generalization of the idea of Killing Fields to spaces which are not symmetric is given in this paper, where a real functional associated with every vector field ξ, measures some parameters associated with the radiation.
Abstract: A generalization of the idea of Killing fields to spaces which are not symmetric is given. The field so defined specifies coordinate lines along which the variation of the metric tensor is the slowest possible in a global sense. Thus it generalizes the Killing fields in spaces with a symmetry where the metric tensor does not change along Killing trajectories. Several examples are given, and the method is then applied to spaces containing gravitational radiation of the type considered by Issacson.For spaces containing radiation, it is shown that a real functional λ[ξ], associated with every vector field ξ, measures some parameters associated with the radiation. In the simplest case this parameter is the ``energy density'' of the radiation, but, if a sufficient number of vector fields can be invariantly defined in the background, the average gravitational ``stress'' associated with the wave may also be measured. We conclude with some conjectures about further application of these ideas to the theory of grav...
TL;DR: In this paper, it is shown that for certain broad classes of motions the requirements of material symmetry and frame-indifference greatly simplify the form of constitutive equations and these simplifications are derived without invoking integral expansions or other special hypotheses of smoothness for material response.
Abstract: This paper is concerned with general, compressible, isotropic materials, solid or fluid, characterized by functionals which give the stress when the history of the strain is specified. It is shown that for certain broad classes of motions the requirements of material symmetry and frame-indifference greatly simplify the form of constitutive equations. These simplifications are derived without invoking integral expansions or other special hypotheses of smoothness for material response. Among the motions considered in detail are those which are locally equivalent to pure extensions and sheared extensions.
TL;DR: In this paper, the possibility of constructing a relativistic spectrum-generating algebraic scheme for hadrons is re-examined, interpreting the symmetry operators in terms of local weak currents.
TL;DR: It is shown that the equations relating the radial profiles of the volume emission and absorption coefficients to the transmission and emitted intensity profiles in self-absorbing cylindrically symmetric sources, can be written in such a way that the problem of spatially resolving theVolume emission coefficient gives rise to a Volterra integral equation of the second kind in a standard form.
Abstract: It is shown that the equations relating the radial profiles of the volume emission and absorption coefficients to the transmission and emitted intensity profiles in self-absorbing cylindrically symmetric sources, can be written in such a way that the problem of spatially resolving the volume emission coefficient gives rise to a Volterra integral equation of the second kind in a standard form. The theory of equations of this type is invoked to show the formal convergence of an iterative solution to the problem, subject only to a finite transmission and bounded slope to the absorption coefficient. A prescription for applying this iterative procedure is given that involves a series of numerical integrations and Abel inversions, and the convergence of some numerical solutions is demonstrated.
TL;DR: In this article, a theoretical study of axially symmetric oscillations in a bounded beam-plasma system is presented, where the external magnetic field is assumed to apply along the symmetry axis and the dynamic character of wave fields is taken into account.
Abstract: A theoretical study has been made of the axially symmetric oscillations in a bounded beam-plasma system. The external magnetic field is assumed to apply along the symmetry axis and the dynamic character of wave fields is taken into account. The excitation of plasma oscillations in a waveguide is investigated in the presence of a low density beam passing near the axis. Frequencies and growth rates have been obtained for the quasi-static approximation, for `whistler mode' and magnetohydrodynamic waves.
TL;DR: In this article, the non-leptonic decay of hyperon has been investigated from a new view-point where, the algebra of currents, asymptotic SU(3) symmetry, Regge poles and dispersion relations are heavily utilized.
TL;DR: In this article, the role of time-reversal symmetry in determining the possible forms of macroscopic laws has been clarified, as well as the criteria for the occurrence of spontaneous electric and magnetic moments.
Abstract: In an earlier paper [Amer. J. Phys. 36, 735 (1968)] of the same title one of us described a particularly simple method by which symmetry considerations can be applied to determine the possible forms of macroscopic laws. In this sequel we clarify the role of time-reversal symmetry, describe more fully the criteria for the occurrence of spontaneous electric and magnetic moments, discuss the application of the method to magnetically ordered systems, and correct a number of errors in the tables.
TL;DR: Mean amplitudes of vibration and Coriolis coupling coefficients are calculated for all XY 4 type molecules and ions with T d symmetry for which reliable frequency data are known in this article.
TL;DR: In this article, it is shown how symmetry properties of the potential function may be utilized to find normal modes of vibration in a non-linear system with nonlinear equations of motion.
Abstract: Conservative mechanical systems having non-linear equations of motion are considered. It is shown how symmetry properties of the potential function may be utilized to find normal modes of vibration. If the systems consist of space arrays of masses interconnected by springs, and they have certain geometrical symmetries, then these will be reflected in symmetry properties of the potential function. This theory is applied to a number of examples.
TL;DR: The exact solution to the problem of axially invariant elastic wave propagation in an infinitely long cylinder of isotropic material having a traction-free curved surface was first given by Pochhammer in 1876 as mentioned in this paper.
Abstract: The exact solution to the problem of an axially‐invariant elastic wave propagating in an infinitely long cylinder of isotropic material having a traction‐free curved surface was first given by Pochhammer in 1876. The solution has been extended by Redwood and others to include axially variant waves. In the present work, we have derived expressions for the propagation of waves in an infinite circular cylinder of material having hexagonal crystal symmetry, where the axis of the cylinder coincides with the crystallographic c axis. Normalized plots of phase velocity vs frequency are shown for representative isotropic and hexagonal materials. The plots have been extended to sufficiently high order that the form of all higher modes can be extrapolated. For materials of hexagonal crystal symmetry, we have found that the phase velocity plots do not change in form from those of isotropic materials, but are displaced by small amounts dependent upon the particular elastic constants chosen.
TL;DR: In this paper, weakly coupled superconducting chains with overall cubic symmetry were shown to have a high and strongly anisotropic upper critical field at temperatures only slightly below Tc.
TL;DR: In this paper, the third-order elastic coefficients of a polycrystalline quasi-isotropic aggregate of the same material were derived explicitly, and three linear invariants associated with the coefficients were derived.
Abstract: The three linear invariants associated with the third‐order elastic coefficients are derived explicitly, and are used to relate the elastic parameters of a single crystal of arbitrary symmetry to those of a polycrystalline quasi‐isotropic aggregate of the same material.