Dynamics of probability distributions over classical fields

It is shown that the original Hopf formulation for the time evolution of probability distributions over classical fields follows deductively from the space-time version of the theory.This work was supported by a grant from the National Science Foundation.     

The role of coincidence experiments in studying the nuclear continuum with high-energy electrons and protons

The Lee model of π-nucleon interactions is very simple, and, in a certain case, an exact solution of the problem of a meson scattering on two “nucleons” can be obtained. However, graphs involving crossed pions are absent in that solution. Because such crossed graphs are crucial in determining the form and character of the physical π-nucleus scattering solution, the Lee model should not be used in testing field theories of the pion-nucleus interaction.     

Comment on the low temperature specific heat of ferroelectrics,antiferroelectrics, and related materials

Lawless has reported accurate, low temperature (2–30°K) specific heat measurements (C_Exp) of a large number of ferroelectrics, antiferroelectrics, and related materials. A plot of C_Exp T^?3 vs. T (T is temperature) reveals an “excess’ specific heat in the 10–30K range. Lawless has interpreted and fit this excess heat with an Einstein term determining the number of oscillators and the Einstein frequence for each material. He has related these large number of extra oscillators to modes observed in some Raman experiments. Using a more realistic density of states, we suggest that the experimental data can be understood in terms of straightforward harmonic lattice dynamics and that there are no extra modes. The “extra” heat capacity merely arises from the differences between the more realistic density of states and that of a Debye solid.     

Elastic constants and softening of acoustic modes in A2MX6-crystals observed by Brillouin scattering

Room-temperature Brillouin-scattering measurements of the longitudinal and transverse sound velocities for the cubic crystals K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆ and (NH₄)₂SiF₆ are presented. The elastic constantsc ₁₁,c ₁₂ andc ₄₄ are determined from the angular variation of the Brillouin line shifts. Furthermore, for K₂SnCl₆ the sound velocities in the [100]- and [111]-direction are investigated as a function of temperature, 256K≦T≦330K. A strong softening of thec ₁₁–c ₁₂ mode is observed in the para-distortive phase as the temperature approaches the phase transition temperatureT _c1=262K from above, whilec ₄₄ shows no anomaly within the experimental error. These acoustic anomalies are interpreted theoretically by a mechanism based on the coupling of the elastic strain field to the fluctuations of the soft-mode coordinates.     

Isobar dynamics and pion-nucleus elastic scattering

A new formalism is developed for studying pion-nucleus scattering in a model which takes into account the dynamics of the (3, 3) pion-nucleon resonance, or Δ isobar. This treatment is used to calculate π⁺ elastic scattering from ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb at energies from 114 to 240 MeV. Some results for π^? elastic scattering are also given. From fits to π⁺ scattering data it is found that the Δ-nucleus interaction is well described by a spherical local complex potential proportional to the nuclear density. The central strength of this potential depends on energy but not on nuclear mass number. Some difficulties in determining the parameters of this potential from elastic scattering are discussed.     

Investigation of the gas phase reaction of dinitrogen pentoxide with water vapor

The gas phase reaction of N₂O₅ with water vapor was investigated in a 17.3-m³ Teflon lined chamber. Temporal concentration profiles for ozone, total nitrogen oxides, and nitrogen dioxide were measured. Concentration profiles for N₂O₅ and HNO₃ were calculated from a combination of measurements of nitrogenous species. A kinetic mechanism with an adjustable value for the rate constant of N₂O₅ + H₂O was used to model the experiments. From this analysis an upper limit value of k ? 4 × 10^?7 ppm^?1 min^?1 for the gas phase reaction N₂O₅ + H₂O → 2HNO₃ was derived.