The strength functions for single-particle states in 59Ni are calculated in a simple model which couples the p32, f52, p12, g92, d52, s12 and d32 neutron states with various numbers of 2+ and 3− core vibrations. The coupling splits the single-particle strength into many states. The neutron energies are taken from the experiments of Fulmer, McCarthy, Cohen and Middleton, and the properties of the core are determined by the energies of the lowest 2+ and 3− states in 58Ni. The only parameters which appear are the magnitudes of the λ = 2, 3 multipole terms of the particle-core interaction. The general complexity of the strength function is roughly that observed by Fulmer et al.

The cross section for the reaction 12C(α, γ)16O has been measured for a range of c.m. energies extending from 1.41 MeV to 2.94 MeV, by using 12C targets of high isotopic purity, large NaI(T1) crystals, and the time-of-flight technique for the suppression of prompt neutron background and time-independent background. Gamma-ray angular distributions were measured at c.m. energies of 2.18, 2.42, 2.56 and 2.83 MeV. By means of theoretical fits, which include the coherent effects of the 1− states of 16O at 7.12 MeV, 9.60 MeV, and those at higher energies, the electric-dipole portion of the cross section at astrophysically relevant energies has been determined. A three-level R-matrix parametrization of the data yields an S-factor at Ec.m. = 0.3 MeV, S(0.3 MeV) = 0.14+0.14−0.12 MeV · b. A “hybrid” R-matrix optical-m parameterization yields S(0.3 MeV) = 0.08+0.05−0.04 MeV · b. This S-factor is of crucial importance in determining the abundances of 12C and 16O at the end of helium burning in stars.

Whereas one usually assumes that nearly all the single particle strength is in the neighbourhood of the shell-model level, it is pointed out that coupling of the particle with odd-parity vibrations will shift an appreciable part of the strength several MeV away. Schematic calculations are carried out for nuclei neighbouring to O16 and Ca40. It is shown that the approximation used is reliable if and only if the coupling between a particle level and the vibration is weak.

An analysis of p—2p reactions is carried out and it is pointed out that with good energy resolution in detection of the particles, it would be possible to obtain important information about the energies of shell-model levels. Treatment of the direct-interaction part of the process as a surface reaction is justified. Calculations in the direct-interaction formalism show strong correlations in angle of the two emitted protons.

The process by which certain types of collective excitations in nuclei are built up from single-particle excitations through the nucleon-nucleon interaction is described. Analogies in the methods used to those employed in describing other Fermi systems are shown. Among the types of collective excitations are the dipole state and vibrational motion. A schematic model formulated in the language of the many-body theory and designed to handle the main qualitative features of a finite system is described. It was found that taking ground-state correlations meant doubling the order of the matrix in shell- model calculations. The ground-state correlations enhanced the transition probability for vibrational states where E << epsilon and cut it dow. for plasma oscillations. (M.C.G.)

A four-dimensional perturbation theory for bound-state problems is developed here. It is shown that modified S-matrix techniques and graphical methods can be applied to bound-state problems. The correspondence of this theory to the ordinary perturbation theory is discussed, and by way of illustration, the four-dimensional theory is applied to the calculation of energy corrections from the exchange of two transverse photons by the electron and proton in hydrogen. This exchange is found to contribute only to the fine-structure and not to the spin-spin interaction in the first order it enters, $\alpha ^{3}$(m/M) R.

A relativistic wave equation for helium-like systems which gives energy levels correct to within α 2 Ry is derived from quantum electrodynamics, care being taken in the handling of pair-production processes. Calculations made with it agree to this accuracy with Breit’s calculations.