Showing papers in "Physical Review D in 1967"

All Possible Symmetries of the S Matrix

Abstract: We prove a new theorem on the impossibility of combining space-time and internal symmetries in any but a trivial way. The theorem is an improvement on known results in that it is applicable to infinite-parameter groups, instead of just to Lie groups. This improvement is gained by using information about the S matrix; previous investigations used only information about the single-particle spectrum. We define a symmetry group of the S matrix as a group of unitary operators which turn one-particle states into one-particle states, transform many-particle states as if they were tensor products, and commute with the S matrix. Let G be a connected symmetry group of the S matrix, and let the following five conditions hold: (1) G contains a subgroup locally isomorphic to the Poincare group. (2) For any M>0, there are only a finite number of one-particle states with mass less than M. (3) Elastic scattering amplitudes are analytic functions of s and t, in some neighborhood of the physical region. (4) The S matrix is nontrivial in the sense that any two one-particle momentum eigenstates scatter (into something), except perhaps at isolated values of s. (5) The generators of G, written as integral operators in momentum space, have distributions for their kernels. Then, we show that G is necessarily locally isomorphic to the direct product of an internal symmetry group and the Poincare group.

Mobility of Charge Carriers in Semiconducting Layer Structures.

Abstract: The electrical resistivities and the Hall constants of the compound semiconductors GaSe, Mo${\mathrm{S}}_{2}$, Mo${\mathrm{Se}}_{2}$, and W${\mathrm{Se}}_{2}$, which crystallize in layer structures, have been measured at temperatures ranging from 100 to 700\ifmmode^\circ\else\textdegree\fi{}K. The Hall mobilities derived from these measurements are all of the order of 100 ${\mathrm{cm}}^{2}$/V sec at room temperature, and they exhibit a temperature dependence of the form $\ensuremath{\mu}\ensuremath{\propto}{(\frac{T}{{T}_{0}})}^{\ensuremath{-}n}$, where $n=2.1$ for GaSe, $n=2.6$ for Mo${\mathrm{S}}_{2}$, and $n=2.4$ for Mo${\mathrm{Se}}_{2}$ and W${\mathrm{Se}}_{2}$. A short-range interaction is discussed which couples the charge carriers in highly anisotropic layer structures to the nonpolar optical lattice modes. The relatively low room-temperature mobilities as well as the high values of the exponents $n$ are explained in terms of the proposed interaction.

Structure of Binary Liquid Mixtures. I

Abstract: An exact solution of the Percus-Yevick equation for the correlation functions ${C}_{\mathrm{ij}}(r)$ appropriate to a binary mixture has been given by Lebowitz. We show that the Fourier transforms ${C}_{\mathrm{ij}}(K)$ lead directly to the structure factors ${S}_{\mathrm{ij}}(K)$, the latter being functions of a total packing parameter $\ensuremath{\eta}$, the ratio of the hardsphere diameters and the concentration parameter $x$ describing the relative amount of each component in the mixture. An expression for the compressibility is also given. The results are applied to a discussion of x-ray scattering from mixtures.

Quantum Theory of Parametric Amplification. I

Abstract: The amplification of electromagnetic fields is analyzed in a quantum-mechanical context by discussing the behavior of a simple theoretical model of the parametric amplifier. The statistical properties of the amplifier fields are described by means of the time-dependent density operator for the system. In doing this, extensive use is made of the coherent states and the $P$ representation of the density operator, which provide a quantum-mechanical description of the fields closely resembling their classical description. Explicit solutions are obtained for the density operator for either of the two field modes for a variety of initial states of the modes. Initial states considered include combinations of coherent states, chaotic mixtures, and $n$-quantum states. Particular attention is given the behavior of the amplifier fields in the limit of large amplification. The conditions are established under which the amplification process leads in this limit to the existence of a non-negative $P$ representation for the density operator for a single mode of oscillation.

New Formulation of the Axially Symmetric Gravitational Field Problem. II

Abstract: The field equations governing the gravitational field of a uniformly rotating axially symmetric source are reformulated in terms of a simple variational principle. The new formalism affords a concise unified derivation of the solutions discovered by Weyl and Papapetrou, and permits a simple derivation of the Kerr metric in terms of prolate spheroidal coordinates. More complex solutions are identified by applying perturbation theory.

Photoneutron Cross Sections for Zr 90 , Zr 91 , Zr 92 , Zr 94 , and Y 89

Abstract: Photoneutron cross sections, including σ[(γ, n)+(γ, pn)] and σ(γ, 2n) for Zr90, Zr91, Zr92, Zr94, and Y89, and σ(γ, 3n) for Zr94, have been measured as a function of photon energy up to 30 MeV with a monoenergetic photon beam from positron annihilation in flight. The photon energy resolution varied from less than 300 keV at the lowest to 400 keV at the highest energies. The average neutron energy was determined simultaneously with the cross-section data. Nuclear information extracted from the data includes giant-resonance parameters, integrated cross sections, level densities, and threshold (and hence mass) values. In particular, it is found that a Lorentz-shaped curve gives an accurate representation of the total photoneutron cross section near the peak of the giant resonance, although in several cases there is important structure about 5 MeV above the giant resonance. The variation with neutron number and atomic weight of these quantities is studied for these nuclei near the N=50 closed neutron shell.