Table of contents

The solution of Dirac equation in interaction representation and the Feynman function S_F are generalized in the β-plane, β being a parameter characteristic of the Reisz potential. It is then shown that by using the generalized function y_F^β(x) instead of S_F, divergence arising from the lowest order photon self-energy graph can be eliminated, though the result obtained is not gauge invariant and contains the Wentzel term.

In metals at high temperatures the time τ spent by an electron between two consecutive scatterings is smaller than the duration of the collision t_c, if one defines t_c as that time after which one can be sure that the interaction with the scattering centre (or lattice wave) is less than kT. Hence the customary theory of conductivity is not justified a priori because it considers the scatterings to be independent. Yet its results are confirmed by experiment. In this paper the correction terms for scattering by two centres are calculated. They are shown to be negligible for a Fermi gas.

The magnitude of the change in the nuclear magnetic resonance frequencies in metals, with respect to the resonance frequencies of the same nuclei in chemical compounds, depends upon the nature of the electronic states at the surface of the Fermi distribution. In this paper it is shown that the observed `Knight-shifts' are in good agreement with the results of cellular-type calculations of the electronic states in metallic lithium and sodium.

A brief discussion of the previous work on the subject is given. A general expression for the exchange integral in the collective electron approximation is obtained in terms of the Fourier coefficients of the exchange charge density. These coefficients are evaluated for a particular case of tightly bound electrons and it is shown that the exchange integral is a strong function of the difference of the wave vectors characterizing the two states between which exchange is considered. The significance of this result is discussed and the inadequacies of the collective electron approximation in dealing with problems involving exchange are pointed out.

A theorem is proved which enables a class of known electrostatic solutions of the field equations to be adapted to the magnetostatic case. Exact solutions referring to a uniform magnetic field and to a magnetic dipole are given.

The solution for a circular loop of wire carrying a steady current is considered, and it is shown that if the mass of the wire be neglected, both the magnetic and gravitational fields at great distances are equivalent to those of a magnetic dipole.

The paper concludes with a short discussion of the significance of the solutions presented here, and in an earlier paper, for relativistic electromagnetic theory.

A very simple model of an imperfect gas, analogous to the Weiss model of a ferromagnetic, is used to check various conflicting conclusions about the relationship between the condensation of an imperfect gas and the divergence of Mayer's virial series. For this model, the divergence of the virial series has no physical significance, and the interpretations of this divergence suggested by Mayer and by Born and Green are both incorrect. The model also turns out to be one for which care is necessary in going to the limit of a very large assembly.

Irreducible tensors in the spherical coordinate representation, in contrast to the cartesian representation, are discussed. The greater simplicity of this representation, especially when one deals with eigenstates of particles or radiation fields of sharp angular momentum, is emphasized. Applications to the theory of beta-transitions, gamma-ray emission, angular correlation and the static interaction of a multipole with a surrounding spin system or field are considered.

A beam of filtered neutrons with an average wavelength of 7.0 Å has been used to measure the total cross section of iron as a function of temperature from 290°k to 1170°k. The cross section is found to have a sharp peak at the Curie temperature, 1043°k. At this temperature the measured scattering cross section is 8.6 barns, while the calculated value of the cross section due to nuclear scattering alone is 3.8 barns.

A similar experiment carried out for nickel reveals only a slight increase in the cross section at the Curie temperature, 631°k. At this temperature the calculated value for the nuclear scattering cross section is 7.5 barns. The observed additional scattering is (0.11±0.05) barn.

The electron capture decay of ²⁰³Pb has been studied with a scintillation spectrometer using coincidence techniques. Gamma-rays of energy 280 ± 5, 400 ± 7 and 685 ± 10 keV are found in the approximate proportions 1: 0.047: 0.0087. The whole of the spectrum is in coincidence with the x-rays following electron capture and the 280 and 400 keV gamma-rays are in coincidence. A level scheme with shell model configurations is suggested for ²⁰³Tl; it is: ground, s_1/2; 280 keV, d_3/2; 685 keV, d_5/2. The angular correlation between the 280 and 400 keV gamma-rays is discussed in relation to the published internal conversion data on the 280 keV gamma-ray. Evidence is presented that part of the decay goes by L-capture. There is no appreciable electron capture to the ground state of ²⁰³Tl - this enables the shell model assignment f_5/2 to be made to the ground state of ²⁰³Pb.

Measurements have been made (i) of the absolute intensities of the internal conversion lines of the 57, 78, 97, 127 and 184 keV γ-rays of MsTh₂ and (ii) of the absolute intensity of the associated L-Auger electrons. The K/L conversion ratios for the 127 and 184 keV transitions are respectively 0.023±0.005 and 4.7. Difficulties are encountered in attempting to attribute spins and parities to the two lowest excited levels of the RdTh nucleus.

A formula is given for the absolute magnitudes of (d, p) reactions on the basis of the single particle model (square-well potential) of the nucleus and the Butler stripping theory. On comparison with experimental data for the reaction ²⁸Si(d, p)²⁹Si it is seen to give cross sections which are too large, but there is reasonable agreement on relative values. This is consistent with the recent work on absolute magnitudes of Horowitz and Messiah and of Thomas. The stripping cross section given here leads to a simple single particle formula for the reduced width, which is approximately the same as the Wigner sum-rule limit for resonance reduced widths.