Table of contents

Adopting a recent proposal made by Macke, the problem of calculating approximate particle densities and sums of eigenvalues by a variational method is examined thoroughly for the case of particles moving along the x axis in a given potential. An Euler equation is derived, which can, in principle, be solved to obtain the best possible density in the sense of the restricted variational method employed. Connection is made with previous work of von Weizsacker, and it is pointed out that the solution of von Weizsacker's equation may often be used to obtain a good initial approximation to the optimum results of the present treatment.

Illustrative calculations have been carried through for the linear harmonic oscillator with the first ten levels singly occupied, and the results for the particle density are extremely encouraging.

The approximate representation of states whose potential energy curves cross (or nearly cross) is discussed quantitatively, by comparing the energies and transition integrals of the 2sσ and 3dσ states of HeH²⁺ calculated using various approximate molecular orbitals with the exact values. It is concluded that, whilst the usual methods of taking mixing with neighbouring states into account may lead to accurate values of the energies provided orthogonality is imposed, the oscillator strengths may be seriously in error, especially if they are associated with weak transitions.

Dispersion relations are derived for the scattering in the forward direction of spin zero (scalar or pseudo-scalar) particles by a real, extended potential. The contribution from the bound states is expressed in terms of the residues of the bound-state wave functions in momentum space at the resonance energies.

The multiple scattering of electrons and positrons at an energy of 0.4 MeV has been measured with a scintillation counter. The difference between the distribution width for electrons and that for positrons after scattering by aluminium, silver and gold is smaller than previous measurements have indicated, and is given approximately by the calculations of Mohr.

Further work with electrons only, using silver and Ilford G5 emulsion as the scattering foil material shows good agreement with the theory of Molière.

The energies of the protons emitted by ²⁷Al, ⁵⁴Fe, ⁵⁶Fe, ⁵⁸Ni, ⁶⁰Ni, and ⁶³Cu when bombarded by 14 MeV neutrons have been determined using a photographic plate method. In addition, the angular distribution of the protons emitted by ⁶³Cu has been measured. The energy distribution of the protons is consistent with some of them being produced by the (n, np) reaction and others by a direct interaction. Rough cross sections for these processes are given; in the course of the work a cross section of 10±4 mbn has been measured for the reaction ⁵⁴Fe (n, 2n). The results, generally, are in good agreement with the statistical and direct interaction theories.

The cross sections of carbon, aluminium, copper, antimony and lead for 900 MeV protons have been measured. Observations were made with a counter telescope in which the final counter subtended a number of different angles at the absorber. Extrapolation of `poor geometry' results gave the inelastic cross sections. Extrapolations for nuclear cross sections, which require `good geometry' measurements, were possible only for the lighter elements carbon, aluminium, and copper because of Coulomb scattering.

If the nuclear radius R is assumed to follow the form R=r₀A^1/3, the value r₀=(1.26±0.03) × 10^-13 cm is obtained. If the tapered nuclear density distribution of Williams is assumed, a radial parameter of 0.73 × 10^-13 cm is obtained.

Rotational analyses of bands in the far ultra-violet absorption spectrum of nitric oxide have been carried out. The bands studied include the 0,0, 1,0, 2,0, 3,0 and 4,0 bands of the system (D²Σ⁺ - X²Π), the 4,0 and 5,0 bands of the γ system (A²Σ⁺ - X²Π), and the 8,0, 13,0 and 17,0 bands of the β system (B²Π - X²Π), as well as other bands ascribed to new systems. Summaries are given of the constants for the states A²Σ⁺, B²Π and D²Σ⁺. All bands in the absorption spectrum above 1600 Å have now been assigned. Possible Rydberg series are briefly discussed.