Table of contents

An estimate of the exchange splitting between the up and down spin bands in ferromagnetic Ni is made on the basis of the `strong intra-atomic interaction' model, account being taken of the major electron correlation effects. A splitting of about 0.4 eV at the top of the d band is obtained. It is shown that in the strong interaction model the exchange interaction between electrons in orthogonal orbitals leads to a negligible correction for Ni.

Recent advances in the theory of the giant dipole resonance in nuclei suggest that systems of a small number of fermions interacting through a repulsive residual force should have collective states. The theory is adapted to small molecules, and applied to ethylene (C₂H₄) with the Coulomb potential replaced by a dipole-dipole interaction. This approximation should reproduce effects due to correlations arising from the long range of the Coulomb potential. The excitation energies of `single-particle-single-hole' triplet states are taken either from experiment or from rough non-empirical values available in the literature. The calculation yields a collective singlet state at about 50 ev, in a region which has not yet been explored experimentally. It suggests also that long range correlations lead to reductions by about a factor 2 in the spacing of the lowest singlet and triplet excited states (as compared with the value for a pure π -> π^* excitation) and for the dipole transition moment from the lowest excited singlet to the ground state. These results arise from co-operative interactions of several electrons. The reduction of the strength of the π-π interaction can be expressed as a dielectric effect due to the other electrons.

A general formalism for the scattering of particles by a complex target is developed. The scattering amplitude is expressed as the sum of the first Born approximation amplitude plus a sum of contributions from resonance terms. The Pauli principle has been taken into account. No joining radius, defining an internal region, occurs in the theory since the resonant states are defined as extending over all space with asymptotic outgoing wave boundary conditions. There is no hard sphere scattering term in the scattering amplitude. These features make the new resonance expansion particularly applicable to the scattering of electrons from atoms and molecules.

A simple derivation is given of the relaxation time for the scattering of phonons by an `isotopic' impurity in a crystal. A method of applying the result to realistic crystal models is given, and this is related to the analytic formulae derived by other workers. The case of scattering by iodine ions substituted in KCl is used as an illustration throughout. Implications for thermal conductivity in this system are discussed and a comparison is made with experiment. It is shown that the method may be easily applied to scattering by more complicated impurity centres.

It is shown, in agreement with Stewart, that in the open-shell (i.e. unrestricted) Hartree-Fock wave function for the ground state ¹S of helium-like atoms, the two orbitals u, v have terms in Z^-1/2, Z^-3/2,... as well as Z^-1, Z^-2,..., when expanded in a perturbation series in powers of Z^-1. But standard perturbation theory methods are not able to fix the orbitals uniquely. Consideration of the appropriate Hartree-Fock equations for u and v show that, in terms of Z, u(r, Z^1/2) = v(r, - Z^1/2). If u is expanded as u(r, Z) = u₀(r) + Z^-1/2u_1/2(r) + Z^-1u₁(r) +... an approximate expression for u_1/2 is {2Zr + 3)/4 [radical]2}u₀.

The coupled equations of the semi-classical two-state approximation (with velocity of relative motion treated as constant) are considered. It is shown that the probability of a transition occurring for given impact parameter may be expressed in terms of the solutions to these equations at the point where the colliding atoms are closest. The formula obtained is rather similar to, but has revealing differences from, the corresponding formula of the Landau-Zener approximation. The significance of the differences is discussed. Detailed calculations are carried out on H + Be²⁺ -> H⁺ + Be⁺ and on H + Mg²⁺ -> H⁺ + Mg⁺. The cross-section-energy curve for the first has a single peak, the magnitude of which is almost twice that given by the Landau-Zener approximation; that for the second has two widely separated peaks.

The cross section for the rearrangement reaction between a bound pair (2, 3) and a third body 1 is calculated on the assumption of a single hard core collision between bodies 1 and 2. Geometrical and dynamical restrictions on the cross section are shown to be insensitive to the impact energy E₁₂ so that the effective cross section varies approximately as E₁₂^-1, vanishing when E₁₂ = D(m₀m₂(m₁+m₃))/(m₃(m₁-m₂)²) and therefore remaining important at high energies provided m₁ [similar, equals] m₂.

The classical experiment of Maier-Leibnitz has been repeated. Corrections have been applied for secondary electron emission from mesh and collector electrodes resulting from the incidence of metastable helium atoms, for the finite permeability of the mesh to electrons and for the value of retarding potential between mesh and collector. Random walk calculations have been used to determine the mean number of elastic collisions made by an electron in traversing the apparatus. The value obtained at the maximum of the 2³S cross section is 2.6 × 10^-18 cm² ± 17%, indicating that the error in the original determination (3.7 × 10^-18 cm² ± 20%) was underestimated.

A straightforward method of measuring lifetimes of He I excited states, by following the decay of excited states, has yielded generally good agreement with other methods and with theory. Additional information about the importance of indirect population processes is provided by the new technique. In the ³D system a fraction ranging from 75% to nearly 100% is contributed indirectly.

An exploratory study is made of the growth of ionization by collision resulting from the application of an oscillatory electric field E_u(100 Mc/s) to hydrogen in the pressure range 3 to 10 mmHg. Hollow parallel-plate electrodes of Rogowski profile are used, one perforated so that initial electrons from a thermionic source may be admitted into the gap. An oscillating ellipsoid field-meter is used to measure the oscillatory field intensity and calibrate indicating meters. A unidirectional field much smaller than the oscillatory field is used to sweep electrons and ions to the electrodes: thus the electrode containing the thermionic source may be called the cathode.

The chief quantity measured is the electron current i to the anode, examined as a function of E_u. Writing i₀ for the value when E_u is zero, the gas amplification A is i/i₀.

It is found that, as E_u increases from zero, A first decreases and then increases, tending towards a very large value at the threshold of breakdown. The initial decrease is interpreted in terms of back diffusion of the electrons and the later increase is attributed to collision ionization. Methods of assessing the electron lifetime t₁ are considered; from A and t₁ it is possible to deduce values of an ionization coefficient which agree fairly closely with values from Townsend's method.

The peak in the alpha particle angular distribution for the reaction ¹²C(p, pα)⁸Be at 150 MeV has been calculated in the impulse approximation, without optical distortions. The result is sensitive to the set of nuclear wave functions used, being four times larger than the experimental value for one set and 140 times too large for the other.

The time spectra of positrons annihilating in pure argon gas are found to be characterized by a pronounced shoulder. The shoulder is associated with a velocity-dependent annihilation rate of positrons which are slowing down within the range 9 to 0 eV. The annihilation rate of positrons has been derived as a function of time, and an attempt has been made to convert the results to a function of velocity by establishing a velocity-time density matrix G(v, t). Corresponding theoretical values of the annihilation rates for argon have been calculated from previously published wave functions over the range 0.68 to 6.8 eV. The theoretical values are three times the experimental values at the higher energies in this range. The need to use polarized atomic wave functions for positron scattering and annihilation calculations is clearly indicated. Below 1 eV there is a marked increase in the observed annihilation rate, which is in no way indicated by the theoretical results; this increase is not currently understood but could arise from the formation of an argon-positron ion at low positron velocities.

The Ginzburg-Landau equations are derived, following the method of Gor'kov, for superconductors with two bands at the Fermi surface which are pure enough to have two energy gaps. The condition for the material to be a type II superconductor is obtained. This condition is considered for transition metals, with reasonable assumptions about the parameters involved, and it is shown that the superconductor becomes more `soft' as the coupling between the bands becomes stronger.

Semiconductors such as the group IV elements with diamond structure and some III-V compounds of zinc blende structure have recently been shown to collapse under pressure to metallic forms analogous to white tin. It is suggested that these phase transitions are brought about by the destabilizing electronic configuration which can occur when the conduction band becomes critically populated.

Simple expressions relating critical pressure and energy gap may be derived and offer encouraging agreement with observations.

It is further suggested that a similar destabilization might cause collapse of the II-IV semiconductors and calculated estimates of the necessary critical pressures are tabulated for Mg₂(Si, Ge, Sn).

The results of calculations of the magnitude and temperature dependence of the electrical resistivity of sodium are reported. The measured dispersion relations for phonons obtained by Woods and co-workers have been used directly in the theory. Good agreement with the experimental results of Dugdale and Gugan is obtained.

The relative secondary electron coefficient γ of 40 keV and 80 keV singly and doubly charged gas ions has been measured by a new method. Values of γ were also obtained for singly charged ions of the alkali metals. Results have been compared with those obtained by previous workers in this field. The applicability of the Ploch correction factor to ion current measurements using a scintillation detector is considered.

The ⁵¹V nuclear spin-lattice relaxation time T₁ has been measured in the body-centred cubic Ti-V alloy system. Some temperature dependence in T₁T is seen between 77 °K and 298 °K which can be roughly correlated with the density of states curve for these alloys. From 0 to 28 at.% Ti, T₁T increases at room temperature by up to 8% over its low temperature value; above 28 at.% Ti it decreases by up to 20%. Low temperature values of T₁T decrease from 0.79 sec degK for 100% V to 0.73 at 10 at.% Ti, and then increase to about 1.11 at 84 at.% Ti. This relaxation behaviour can be related to existing results on low temperature specific heat, susceptibility and Knight shift in the Ti-V-Cr system on the basis of a rigid two-band model, but only if the hyperfine field coupling constants are allowed to vary with composition. This additional complication makes possible at most only a qualitative solution at present.

Rotational analysis shows that triplet bands of ScF observed in absorption arise from a transition ³Φ_r-³Δ_r. Since singlet systems with a common lower state X ¹ Σ⁺ also appear in absorption, the two states σ^{2 1} Σ⁺ and σδ ³Δ lie close together, and it is uncertain which is the lower state. In the case of YF, singlet systems only have so far been observed. Bands of two ¹II-X ¹Σ⁺ systems have been analysed, and σ^{2 1}Σ⁺ is very probably the lowest state of YF.

A study of the Brownian motion of a dipolar molecule surrounded by a dispersive dielectric medium has resulted in the following generalization of Onsager's equation ( - _∞)(2* + _∞)(2 + 1)/3(2* + 1) = (4πNμ²/3kTV)((_∞ + 2)²/9)(1/(1+iωτ_μ')) where τ_μ' is a microscopic relaxation time which includes the effect of dipole-dipole coupling.

A study has been made of dissociation by an electrical field of H₂⁺ ions formed by the break-up of H₃⁺ ions. In the present experiment it is shown that there is a minimum field of 0.96 ± 0.05 × 10⁴ v cm^-1 required to cause this field dissociation.

This is consistent with the available theoretical value of 10⁴ V cm^-1 which is, however, uncertain to within a factor 2.

This communication is an endeavour to clarify certain of our experimental and theoretical conclusions regarding the physics of irregularities in the equatorial electrojet, in view of their apparent misinterpretation in a previous paper.

Static central field exchange approximation phase shifts for the [(2p)²³P]k²0 ²P channel at impact energies k² [less-than-or-eq, slant] 0.1 ryd are reported and used with previous results for the k²0 ⁴P channel to obtain the partial cross section Q₀(k²).