Showing papers in "Reviews of Modern Physics in 1963"

Structure of Fermion Density Matrices

Abstract: : A new approach is presented to the many-particle problem in quantum mechanics by proposing a method of finding natural orbitals and natural geminals of a system without prior knowledge of the wave function. It expounds hitherto unpublished results of the author's work. (Author

The octet model and its Clebsch-Gordan coefficients

Abstract: The Clebsch-Gordan (CG) coefficients of SU(3) are derived for the products of the most important irreducible representations. Useful symmetry relations for the CG coefficients are derived. The Wigner-Eckart theorem for this group is given and applied to derive a general mass formula for the octets. The Gell-Mann-Okubo mass relation and a mass relation foi the octets that is very well satisfied by the vector mesons, if one takes as the K/sup */ the 730-Mev (K- pi ) resonance, are given. The Yukawa couplings between baryons and mesons are considered. The mathematical framework of the octet model for strong interactions is examined. (C.E.S.)

The Theory of Small-Angle Multiple Scattering of Fast Charged Particles

Abstract: A systematic unified review is given of the basic statistical theory of the multiple scattering of fast charged particles in the small-angle range. The approximation considered is that of the Snyder-Scott-Moliere theory, and only slight attention is given to the less accurate Gaussian approximation. The single-scattering formulas of Moliere are derived, along with the modifications of them given by Nigam, Sundaresan, and Wu. Moliere's multiple-scattering calculation is presented by an improvement of Bethe's method, and the work of Nigam is given by the same method with newly computed tables. Snyder's calculations are outlined, and previously unpublished work on spatial-angle scattering is reported with tables. Calculations by Keil, Zeitler, and Zinn for very thin films are given, as well as a detailed discussion following Lenz on scattering at very small angles. The work of Muhlschlegel and Koppe on the multiple scattering of polarized electrons is included, with the important correction that no depolarization appears in the approximation to which they worked. The distributions of lateral deflections and other characteristics are considered, but the details of applications to emulsions, cloud and bubble chambers, etc, are not entered into, nor are the electron-penetration and pathlength problems handled. Asymptotic formulas for relatively large anglesmore » are treated, as are various types of mean values. (auth)« less

Relativistic invariance and hamiltonian theories of interacting particles

Abstract: Relativistic invariance may involve two different theoretical postulates: symmetry of the theory under the relativistic transformation group reflecting the invariance of physical laws under changes of reference frame, and explicit transformation properties or manifest invariance of certain quantities. A Lie group formalism, for classical or quantum mechanics of particle variables or fields, is introduced and used to show how symmetry under the Lorentz (or Galilei) group is provided by ten generators satisfying the characteristic Lie bracket equations. For a classical mechanical theory of a fixed number of particles, the Lorentz transformatlon formula is assumed for the coordinates of the space-time events that comprise the world lines of the particles as defined by their positions as a function of time. This assumptlon of manifest invariance is expressed in terms of equations involving the Poisson brackets of the canonical position coordinates with the generators of the Lorentz group. For a theory of two particles it is shown that the only generators satisfying these latter equations plus the Poisson bracket equatlons characteristic of Lorentz symmetry are those descriptive of free particle motion; the combined assumption of Lorentz symmetry and Lorentz transformation of particle positions rule out any interaction. (auth)

Electric and Magnetic Form Factors of the Nucleon

Abstract: The charge and magnetic form factors, G/sub E/(q/sup 2/) and G/sub M/(q/ sup 2/), are discussed with emphasis on their use in electron-nucleon experiments. Electron-proton scattering and proton-antiproton annihllation are discussed with the appropriate form factors. Neutron form factors are also given. (R.E.U.)

Nonadiabatic Theory for Diatomic Molecules and Its Application to the Hydrogen Molecule

Abstract: The electronic -vibrational wave functions are obtained from the Schrodinger equation for the relative motion of the electrons and nuclei in a diatomic molecule. Numerical computation for the ground state of the hydrogen molecule is carried out. (R.E.U.)

Determination of pion-nucleon parameters and phase shifts by dispersion relations

Abstract: The application of single variable dispersion relations to calculate the main parameters of low-energy pi -N interactions and the low-energy phase shifts is discussed. Data on the total cross sections and the dominant resonances of the pi -N system are also given. Numerical values of the parameters and phase shifts are presented. (C.E.S.)

Generalized perturbation theory in operator form

Abstract: It is proposed to formulate any quantum mechanical perturbation theory in operator form and to take advantage of the fact that such a theory can be completely formulated in the domain of a Lie algebra. The concept of a T- operator is generalized and used to compose a solution of a complicated quantum mechanical problem from subproblems connected therein. (R.E.U.)

Evidence for the Occurrence of Violent Events in the Nuclei of Galaxies

Abstract: A number of phenomena, all associated with the nuclei of galaxies, which may suggest that in these nuclei there may take place violent events manifested by a very large energy output and a time scale as short as 10/sup 6/ years, are investigated. Optical and radio data that lead to these conclusions are analyzed. (C.E.S.)

Theory of extended fine structure of x-ray absorption edges

Abstract: The Kronig, Kostarev, Hayasi, and Sawadi theories of extended fine structure of x-ray absorption edges are discussed. The essential features of each theory and its success in interpreting experimental curves are outlined. The shortcomings of each theory are pointed out, and a general evaluation and comparison with experimental data are made. (C.E.S.)

Alkali Hydride Molecules: Potential Energy Curves and the Nature of their Binding

Abstract: Investigation of the potential energy curves of the alkali hydride molecules is reviewed. Values of the rotational constant, vibrational constant, and the ionic binding energy are calculated using seven ionic potentials, and the results are compared. The nature of the binding is examined in terms of classical models and quantum mechanical calculations. (D.C.W.)

The Structure of Light Nuclei

Abstract: Nuclear size parameters, nuclear phenomena, and nuclear interactions are discussed in terms of cluster, shell, liquid drop, and collective representations of nuclei. Results obtained by the several means are evaluated and are compared when posslble. The appropriateness of each model for certain applications is also examined. 334 references. (D.C.W.)

Systematics of deformations of atomic nuclei

Abstract: >In a search for new regions of nuclear deformation and for theoretical verification of experimentally observed re gions, the equilibrium deformations for a large region of the periodic table have been analyzed. The procedure that involves eigenvalues of the Nilsson-model hamiltonian for the self-consistent energies is outlined, and Coulomb and pairing force considerations are discussed. Deformations and energies of deformation are plotted versus neutron and proton numbers. Extended deformation regions are noted where both neutron and proton numbers go from 50 to 82 and where neutron amd proton numbers go from 82 to 126. (D.C.W.)

Properties of fermion density matrices

Abstract: An investigation is presented of basic properties of fermion density matrices and their importance in quantum chemistry. An advanced study of properties of the first-order density matrices and the general properties of higher-order ones is presented. (R.E.U.)

Interpretation of the rapid convergence of correlated wave functions

Abstract: The effect of correlation on the functional form of the wave function pertaining to the structure of the Coulomb hole is presented. The advantages of the correlated wave function for the description of the Coulomb hole over the superposition of configurations are discussed. (R.E.U.)