Table of contents

²⁰⁸Pb has a double closed shell of 82 protons and 126 neutrons The classification of the lowest excited states of ²⁰⁷Pb, ²⁰⁷Tl, ²⁰⁹Pb, ²⁰⁹Bi, which differ by one nucleon, should thus follow the single-particle model closely. The attempt is made to classify the lowest excited states of ²⁰⁶Pb, ²⁰⁶Tl, ²⁰⁶Hg, ²¹⁰Pb, ²¹⁰Bi and ²¹⁰Po, which differ by two particles, in terms of the one-particle model, taking the interaction of the two particles as a perturbation Considerable uncertainties in the order of the energy levels remain, but some definite conclusions are possible The existence of an isomeric state of ²¹⁰Bi (RaE) with very high spin (I=8?) is predicted. This fits in with known facts about the alphaparticle emitting isomeric state.

The method can also be applied to ²⁰⁸Tl, ²⁰⁸Bi and the excited states of ²⁰⁸Pb which arise by lifting one nucleon into the next shell, leaving a hole. It meets with considerable success for ²⁰⁸Tl Discrepancies with known facts in the case of ²⁰⁸Pb suggest a more complex picture, according to which the first excited state would have I=0 and even parity. Such a state has never been observed, but its existence is not completely excluded by observation.

The angular distribution of γ-radiation from nuclei aligned at low temperature is given as a series of Legendre polynomials, I(θ) = 1 + σ_KA_K(T) P_K (cos θ) the A_K being temperature dependent. The formulation is applicable to cascade processes of arbitrary multipole orders and nuclear spins. An approximation valid for low degrees of alignment is given, as is the angular distribution from completely aligned nuclei. Application is made to ⁶⁰Co.

The matrix elements of beta-decay theory are expressed in a way which not only gives the beta-spectra and angular distributions for arbitrary degree of forbiddenness, but also yields very simply the selection rules appropriate to any type of interaction.

Results for the energy spectra confirm those found by Greuling by inspection; angular distributions and electron-neutrino correlations are considered in a subsequent paper

The method of a previous paper is used to derive general formulae (valid for arbitrary Z) for the angular distributions of beta-emissions.

The Bloch (tight-binding) approximation is applied to a study of graphite The Mean energy per atom and the internuclear distance are calculated in good agreement with experiment. Previous accounts are extended by including certain overlap imegrals and by dealing with a set of parallel layer planes instead of only one plane. The shape of the band due to the π-electrons is calculated, and the experimental x-ray emission spectrum of graphite is interpreted It is concluded that the role of σ-electrons is greater than is often supposed

The space wave functions for the π-electrons in a graphite layer, as found in Part I, are transformed into momentum coordinates, and the radial distribution function, including σ-electrons, and π-electrons, is calculated. Using the theory of Jauncey and DuMond the shape of the Compton profile in x-ray scattering is predicted. Both this, and the momentum distribution, are in excellent agreement with experimentally determined values. The introduction of a plausible scale factor in the atomic wave functions would make the agreement almost perfect

An analysis is made of the distribution of π-electrons in the crystal of boron nitride. The insulating character of this substance is shown by the fact that these electrons completely occupy one band, of width approximately 2.4 eV, separated from the next higher band by a gap of about 4.6 eV. The density of states in the band is calculated, accurately for a single layer plane, and approximately for the three-dimensional crystal. Until the energies of the σ-electrons are better known, further progress in understanding this substance will be difficult

The π-electron diamagnetic susceptibilities of polyacenes of up to ten rings are calculated by a method introduced in an earlier paper: the method, which involves only a single numerical integration, is simplified. An alternative method of calculation, which has certain attractions and is widely applicable, is sketched in an Appendix.

The relationship between the diamagnetic anisotropy and the number of rings in the molecule is found to be almost linear.

The various approximations which have been used to calculate the probability of excitation of an atom by impact with an electron whose energy is not greatly in excess of the threshold are known to fail under certain conditions This is especially true in the important cases in which the excitation proceeds mainly through electron exchange. In these cases the exchange coupling is too strong for approximate methods, which assume weak coupling, to be valid By using a schematic model exact solutions for strong exchange coupling are obtained and compared with the results of different weak coupling approximations It is found that the Born-Oppenheimer approximation is never reliable at low electron energies but if distortion of the incident and scattered waves by the atomic field is allowed for correctly much better results may be obtained.

A general relation between two fundamental functions appearing in fluctuation problems in cascade theory is derived. This leads to a direct method of solving for the nth moments of the distribution function. It is also shown that the Jánossy G-equations are superfluous for the solution of the fluctuation problem.