Wigner Theory Research Articles

Anomalous Neutron Diffraction inαCadmium Sulfide

Anomalous neutron scattering (failure of Friedel's law) was observed in experiments with alpha Cd containing neutron-absorbing Cd/sup 113/ and a space group Pomc, in which the integrated intensities of (hkl) and (hkl)-bar mates of a series of reflections were measured at several wavelengths. The I/sub 002//I/sub 002/ ratio showed a strong energy dependence, due t o the variation of the complex amplitude of cadmium with the wave length, which agrees with the Breit- Wigner theory. The intensity inequalities were compared for x rays and neutrons on one CdS crystal; the direction of the phase shift was found to be the same for both. Possible applications of anomalous neutron scattering are discussed. (D.L.C.)

Statistical Theory of Chemical Reaction Rates

A ``statistical'' theory of chemical reaction rates based on ``scattering theory'' in the strong coupling approximation is presented. The theory is developed explicitly for reactions involving the dissociation and recombination of a diatomic molecule in the presence of an atomic catalyst but is also readily applicable to other reactions. The theory formally includes Wigner's theory of three-body recombination and the classical theories of both recombination and dissociation. A limited comparison with experiment shows reasonable agreement.

Symmetry Effects on Nuclear Dipole Radiation with Application to a Bound Excited State ofHe42

The effect of nuclear symmetry properties on electric dipole transitions is investigated using the independent particle model and Wigner's theory of the symmetric Hamiltonian. Methods are given for the construction of completely symmetrized wave functions for the nuclear states on this model. Symmetry selection rules are found to operate, in addition to the usual selection rules, to reduce the amount of nuclear dipole radiation. A detailed study of the ${\mathrm{He}}^{4}$ nucleus leads to the conclusion that if a resonant state at 21.6 Mev does exist with a strong dipole transition to the ground state, then a bound, excited state of the alpha-particle also exists. Spin-orbit and tensor forces are introduced to give a possible explanation of the angular distribution of gamma-rays when protons are captured by tritium.

The Catalytic Conversion of Parahydrogen by Paramagnetic Complex Ions in Aqueous Solution

Rates of conversion of parahydrogen by paramagnetic complex ions of copper (II) and chromium (III) in aqueous solution have been measured at 25°C. The results are discussed in terms of the Wigner theory, which predicts the effects of magnetic moment and collision distance. Owing to the planar configuration of the copper (II) complexes, only a qualitative test of theoretical predictions is possible. The rate effects produced by various symmetrical octahedral complexes of chromium (III) can be explained in terms of the theory if one evaluates the various collision distances for H2 from a detailed examination of the complex structure in each case.

XXXI. A note on the analysis of the nuclear binding energies

Abstract The function L(A), appearing in Wigner's theory has been calculated by two different methods : from the observed mass defects and from the chemically determined atomic weights of the elements. It has been found that most probably the curve L(A) is not a smooth function of A, but the accuracy of the individual values of L is insufficient to give the exact shape and character of the irregularities. An empirical two-constant formula, disregarding the oscillations, is suggested. The discrepancy of the values in the region where the two methods overlap is probably caused by the fact that the most abundant nuclei have higher proton content than the most stable ones, which supports the view that the nuclei were formed from the proton side of the stability curve.

The Analysis of Nuclear Binding Energies

The fine structure of the mass defect curve has been studied, especially with reference to the nuclear symmetry character. From the analysis it has been found possible to obtain satisfactory empirical curves for the functions $L$ and ${E}_{0}$ appearing in Wigner's theory. The behavior of these curves allows deductions to be made regarding nuclear shells, and binding energies of both known and as yet unknown, unstable, nuclei. About 150 masses have been computed in this way.

The Difference in Vapor Pressures of Ortho and Para Deuterium

The difference between the vapor pressures, ΔP(e — n), of the 20.4°K equilibrium mixture and the normal mixture of the ortho and para varieties of D2 were determined from 15° to 20.4°K. ΔP(e — n) varied from 0.3 mm of Hg at 15°K to 3.8 mm at 20.4°. ΔP(e — n) for deuterium is small as compared with ΔP(e — n) hydrogen, but [ΔP(orthopara)/P(n)] for deuterium is approximately equal to [ΔP(para-ortho)/P(n)] for hydrogen at the same temperature. Further measurements were made on the uncatalyzed change with time of the vapor pressure of liquid normal deuterium. The change for deuterium is less than one mm of Hg in 200 hours, whereas the vapor pressure of liquid normal hydrogen increases one mm in 4 hours. This large difference in rates is attributable to the difference in magnetic moments of the proton and deuteron. If Wigner's theory of the ortho-para conversion by paramagnetic molecules in the gaseous phase is extended to the liquid phase to calculate the relative rates of change of the vapor pressures of liquid normal deuterium and liquid normal hydrogen, a ratio of 1/1000 is obtained for the ratio of the rate of change for deuterium to the rate of change for hydrogen.