Table of contents

The hyperfine structure of the ground state 3d⁵4s²⁶S_5/2 of ⁵⁵Mn has been measured in a resonance experiment with an atomic beam. The value 5/2 for the nuclear spin has been confirmed by measurements in weak fields. The magnetic dipole interval factor is A(⁶S_5/2)=72.422±0.002 Mc/s. There is no departure from the interval rule outside experimental error.

The oscillator strengths of the 1sσ-2pπ, 2pπ-2sσ and 2pπ-3dσ transitions of HeH²⁺ are calculated from the exact two-centre wave functions. A comparison is made with results obtained from the LCAO approximation with and without mixing, both the dipole length and dipole velocity formulae being used in each case.

The paper presents a variational method for calculating elastic s-wave scattering phases for short-range potentials, based on the Rayleigh-Ritz method for discrete energy levels, in which the approximate phase approaches the exact phase from below. The method is applied to scattering of electrons by the static field of the hydrogen atom.

The magnetic dipole oscillator strengths of the 1sσ_g-3dπ_g transition of H₂⁺ are computed over a wide range of nuclear separations from the exact two-centre wave functions. A brief discussion is given of some related quantities and reasons are presented for supposing that the average values of the energy separations in second order expressions involving magnetic quantities are larger than for the analogous electric quantities.

Approximate wave functions for the 2pσ state of the HeH²⁺ molecular ion are obtained by the variational method. The values of the electronic total energies and potential energies computed using the approximate wave functions are compared with the exact values of these quantities.

Exact values of the dipole moment are also obtained.

The device of cutting off the potential at a point where the asymptotic form of the wave function is valid permits the use of a simple trial wave function in the form of a polynomial in which some of the coefficients are variation parameters. The variation-iteration method is thereby simplified. As an illustration the bound-state deuteron problem is solved for a central Yukawa interaction and the results compared with those obtained by other authors.

A formalism is developed to relate the total cross section for low-energy nucleon-nucleus scattering to the cross section due to a potential well. By introducing the intermediate model of Lane, Thomas and Wigner for the compound nucleus states, a simple relation between these two cross sections is obtained. The method of extracting a potential well to replace the hard sphere scattering and the scattering from `far distant' levels is given and then extended to find the well which describes the average total cross section.

Corrections to 1957 Proc. Phys. Soc. A 70 388.