Table of contents

In a discussion of the quantum dynamics of a non-relativistic many-particle system it is shown how a two-body interaction, quartic in the field operators, may be replaced by an interaction with an auxliary density-like field. An extension of the procedure of Edwards and Sherrington for expanding in terms of correlations about the state of maximal quantum randomness is applied to the coupled system to give the density correltions and excitations as well as the corresponding single-particle quantities.

As an example, an explicit expression for the density excitations is obtained in terms of the quasi-particle energies, for the case in which quasi-particles exist as well-defined modes of single-particle excitation.

A calculation is reported of the momentum distribution in liquid helium at absolute zero using a pair wave function and a modified superposition approximation. A value of 0 13 for the fraction of particles in the zero-momentum state is obtained. The approximations obtained for the momentum distribution function for small values of k is shown to be inaccurate. The use of an exact result for n_k for small k leads to a modified distribution function which gives 0 25 for the fraction of particles in the zero-momentum state.

A general study has been made of the bound states of a charged particle in a static field which behaves as the dipole form asymptotically. When the field is that of either a point dipole plus a sufficiently repulsive spherical core, or a finite dipole, the existence of bound states of the charged particle depends only on the value of the reduced dipole moment K (equation (5)). It is shown that each symmetry class of states has its own threshold value of K such that states of that symmetry exist if, and only if, K exceeds the critical minimum. There is an infinite number of states of given symmetry when there are any. Critical values of K < 100 are calculated. When the potential has an arbitrary form at short range (but still has the dipole form at long range), the situation remains much the same as above, with the exception that sufficient attraction at short range will allow some states to exist for any value of the dipole moment.

Close-coupling calculations of the positions and widths of the lowest-lying autoionizing D states of He converging on the n = 2 level of He⁺ are presented. Good agreement is found with experiment and with other calculations in almost all cases.

With attention confined to decaying H-H⁺-e and He-He⁺-e plasmas which are optically thick towards lines ending on the ground level, the quasi-equilibrium number density of atoms in the first excited level n_Q'(2) is computed using collisional deactivation coefficients K(2, 1) based on experiment and taking Penning ionization into account. This last is discussed in some detail. Quantal calculations are carried out on the rate at which the electronic transitions involved in 2H(2s-p) -> H(1s) + H⁺ + e occur. It is concluded that the rate is probably fast enough for almost all close collisions to lead to ionization. This also seems to be the case for 2He(2 ³S) -> He(1 ¹S) + He⁺ + e provided collisions which can yield ionization only by violation of Wigner's spin conservation rule are excluded from consideration. Penning ionization is of little importance in hydrogen plasmas, but it can be significant in helium plasmas where it tends to reduce n_Q'(2) and the apparent recombination coefficient.

The perturbed stationary-state approximation is used to calculate the cross section for electron detachment and charge transfer in H-H^- collisions. The problem of the absence of bound states of H₂^- is overcome by the introduction of resonant states. For incident energies between 50 eV and 10 000 eV the electron-detachment cross section decreases monotonically from 18 × 10^-16 cm² to 6 × 10^-16 cm², and the charge-transfer cross section decreases from 70 × 10^-16 cm² to 0 2 × 10^-16 cm².

The process of electron loss in single collisions during the passage of fast hydrogen atoms through hydrogen has been studied in the energy range 40-220 kev.

The ratio Q₀₁(H)/Q₀₁(H₂) of the electron-loss cross sections in atomic and molecular hydrogen has been determined by using a tungsten tube furnace to provide a target composed of highly dissociated hydrogen. At energies above about 120 kev, cross sections Q₀₁(H) estimated by the use of well-established values of Q₀₁(H₂) are found to be in good agreement with theoretical values calculated by Bates and Griffing using Born's approximation.

The odd parity levels of ⁴³Sc are calculated allowing the three extra-core particles to occupy the complete 1f2p shell. It is found that the energy levels are fairly insensitive to changes in the two-body interaction, and that, although agreement is obtained with some of the experimental data, several features of the empirical spectrum are not accounted for this way. These results, and stripping data from the ⁴²Ca(³He, d)⁴³Sc reaction, suggest that there are low-lying states arising mainly from two-particle excitations of the ⁴⁰Ca core.

The magnetic moment of the impurity atoms in dilute ferromagnetic transition alloys is calculated from the scattering of d electrons by spin-dependent Hartree-Fock potentials. The spin-dependent potentials are determined self-consistently by imposing Friedel's screening condition and the Hartree-Fock relation between up and down spin potentials. It turns out from this calculation that the impurity negative magnetic moments are due to the repulsion of a bound state above the Fermi level.

The antiferromagnetic structure of Mn₅Si₃ at low temperatures (Néel point 68 °K) has been determined by neutron diffraction using single crystals. The magnetic structure is complicated, and the model proposed consists of a modulated non-collinear spin structure propagated through the crystal in three hexagonally related directions. This model gives good agreement with the observed intensities of 50 independent magnetic reflections. The mean moments at the two manganese sites are Mn_I 0 4 ± 0 1 μ_B, Mn_II 1 2 ± 0 1 μ_B. In addition, the spin densities of the two mutually perpendicular spin components have been calculated separately. A considerable deviation from spherical symmetry at the Mn_II site is shown by the larger component.

Schrodinger's spin one exchange interaction, P_ij = (S_i S_j)² + (S_i S_j) -1, is introduced to form a Hamiltonian for a nearest-neighbour lattice model of ferromagnetism. The physical relevance of this Hamiltonian is discussed. Group theoretical methods for obtaining the high-temperature partition function and initial susceptibility series are introduced. The first eight terms of the susceptibility series are obtained for the face-centred cubic lattice. Analysis by the ratio and Padé approximate methods yields the critical temperature and the critical index γ which is found to be very nearly 5/4 and thus certainly different from the spin one Heisenberg model index.

A computer model of a Heisenberg paramagnet is constructed from a thousand classical spin vectors situated on a simple cubic lattice and interacting through nearest-neighbour exchange forces. The motion of an initial random set of spins is calculated explicitly and used to evaluate the correlations <S₀(0).S_R(t)> as a function of time for various neighbours. The neutron scattering from a polycrystalline paramagnet is predicted from the correlations and compared with experimental data on RbMnF₃.

The results of nuclear magnetic resonance of Cr³⁺ in antiferromagnetic LaCrO₃ and ENDOR experiments in Cr:LaAlO₃ are reported. From the ENDOR experiments rt is possible to estimate the size of the Cr-Cr transferred hyperfine interaction in LaCrO₃ and thus, by using the result of the Cr³⁺ nuclear resonance, a zero-point spin deviation of 2 6 ± 1.0% is estimated in LaCrO₃. Theory predicts 5 2% or 4 2%. A similar calculation from previously published data yields a zero-point spin deviation of about 4 9% in Cr₂O₃ with, however, a larger uncertainty.

A calculation of the direct process relaxation time for a Cu²⁺ ion in a tetragonally distorted tetrahedral crystal field has been made. The effect of including hybridization of 4p with 3d orbitals is to increase T₁ by a factor somewhere in the region of 1 5 to 3 0 depending upon the direction of the applied steady magnetic field.

The spin-wave impurity states and scattering due to a substituted impurity in body-centred and face-centred cubic ferromagnets are studied by a Green function method. The scattering amplitude is expanded in terms of group-theoretical partial waves. The conditions for the existence of the localized spin-wave states above the spin-wave band and resonant states inside the band are investigated in detail. The low-temperature spin-wave thermal conductivity due to the impurities, giving rise to low-lying resonant levels in the band, is calculated.

A two-neighbour Born-von Kármán model is applied to the diamond crystal. The nearest neighbours are assumed to interact with general forces and central, angular and torsional forces are considered in the second-neighbour interactions. One of the five force constants that occur in this model is taken as a free parameter and is fitted to the experimental frequencies at the zone boundaries in the (100) and (111) directions. A good qualitative fit, substantially better than the corresponding fit in the case of germanium and silicon, is obtained. The phonon spectrum is calculated using the Fourier series expansion method. The specific heat of diamond is evaluated in the temperature range 0-300 °k and is found to agree quite well with the experimental results. Finally, the analysis of the dependence of the frequency and amplitude of the localized mode due to an isotopic impurity on its mass is made.

Interferometric measurements of the linear thermal expansion coefficients α of CaF₂, SrF₂ and BaF₂ between 20 and 273 °K are reported. The results are believed to be accurate to within 2% down to 50 °K, falling to 15% at 25 °K.

The Gruneisen parameters γ = βV/C_Vχ_T, calculated from the volume expansion coefficients β and earlier heat capacity and elasticity measurements, fall with diminishing temperature. The quasi-harmonic approximation has been applied to calculate the maximum frequencies ν_D(n) of the Debye distributions having the same nth moments as the actual crystals, which display minima at n [similar, equals] -1 5, -2.0 and -2.5 for CaF₂, SrF₂ and BaF₂, respectively, and ν_D(n) has been found to fall with increasing mass of the alkaline earth ion. The volume dependence of the moments γ(n) = -d ln γ_D(n)/d ln V for -3 <or= n <or= 4 falls quite rapidly as n becomes increasingly negative, and γ(n) diminishes with increasing mass of the alkaline earth ion.

Observations are reported of the rate at which flux enters or leaves various specimens of type II superconductors when the applied magnetic field is suddenly changed, and the results are used to deduce values of the flux flow resistivity. It is shown that Kim's empirical relation for this resistivity is obeyed both in NbTa alloys (l < ξ) and in pure niobium (l > ξ). Some account of the observed magnetization curves in the specimens is also included.

Existing theories of flux flow resistivity in type II superconductors are reviewed, and an extension of the work of Nozières and Vinen is introduced, in which the motion of a flux line is related to certain relaxation times governing the rate of change of the superconducting order parameter. The various experimental results that we now have on flux line motion are compared with this extended theory.

We discuss a `third Ginzburg-Landau equation' which describes the electric-field distribution inside a local superconductor carrying a steady current. and obtain solutions in two simple cases.

Hot carrier galvanomagnetic characteristics of n-type germanium of intermediate carrier concentration are studied theoretically. The range of carrier concentration considered ensures that the intercarrier collisions enforce a Maxwellian distribution on the carriers, and the momentum loss of the carriers occurs mainly through scattering by the lattice vibrations. Numerical values of Hall mobility obtained from the present analysis are found to be in agreement with the earlier published results for low and high carrier concentrations. Values of magnetoresistance, however, while agreeing with the low concentration case, are found to be different from those for the case of high carrier concentration. The physical origin of this difference is discussed and a comparison between the available experimental data and the values calculated in this paper is also made

The intensity of polarized light reflected from an absorbing vapour has been calculated for optical radio-frequency double resonance and level-crossing. The reflection coefficient was obtained from the refractive index of the vapour, using the equations of classical electromagnetism. The result obtained by integration over a range of frequencies corresponding to broad-band illumination shows that all the familiar magnetic resonance effects are to be expected in the reflected light, except that the resonance curves should be Doppler- and pressure-broadened. A study of the zero-field level-crossing curve, as a function of vapour pressure, should enable one to follow the gradual transition from diffuse to coherent scattering, and to test whether the simple theory of selective reflection is adequate.

Fluorescence has been observed from the v₃ vibration of CO₂ at 2349 cm^-1. By using a modulated source and observing the phase change between the incident radiation and the fluorescent signal the relaxation time for deactivation by collision of the v₃ vibration has been measured. For CO₂-CO₂ collisions at 290 °K and 1 atm pressure it is 7 ± 1 μsec. The relative efficiency of CO₂-Ar collisions to CO₂-CO₂ collisions is 0 09 ± 0 03. The magnitude of the fluorescent signal fits in well with that expected from theoretical calculation on the assumption of pressure-broadened absorption by lines for which the strong approximation is the most applicable.

The relative contributions of diffusion (D = 4 1 × 10^-5 cm² sec^-1) and solvent excitation migration (Λ = 4.9 × 10^-5 cm² sec^-1) to energy transfer and quenching in p-xylene solutions at 20 °C were evaluated experimentally, using the Einstein-Smoluchowski-Voltz theory. Measurements were made of the quenching of the fluorescence of 10^-2 M PPO in p-xylene by carbon tetrachloride, with indirect (via p-xylene) and direct ultra-violet excitation. Similar observations were made of 10^-2 M PPO solutions in p-xylene, diluted up to 20 times by cyclohexane. With indirect excitation and the diluted solvents, there is an important correction (neglected by previous workers) to be made for direct solute excitation, and the data are shown to be consistent with a relation derived to allow for this effect.

The diffuse X-ray scattering from sodium chloride single crystals has been measured in non-symmetry directions over a range of scattering angles from 20° to 110°. The measured intensities show that no need exists to consider defect diffuse scattering and that excellent agreement is obtained with the calculated intensities, comprising theoretical values of Compton scattering and computed values of thermal diffuse scattering. The first-order, second-order and total values of thermal diffuse scattering have been computed from the eigenvectors and eigenfrequencies of Karo and Hardy. Another approximate method of calculating the higher orders of thermal diffuse scattering intensity, involving only the Debye-Waller factors, is given.

The x-ray Bragg reflection data for fluorite of Togawa, of Weiss, Witte and Wolfel, and of Warren have been compared with the theoretical predictions of three models, all of which assume spherically symmetric electron distributions for the component atoms or ions. Using the Hartree-Fock approximation a lattice of free ions gives good agreement with the experimental data, while a lattice of neutral atoms leads to discord for reflection 200, and a lattice of `crystal ions', which take account of the electrostatic potential of the crystal in the way described by Petrashen', Abarenkov and Kristofel', shows general disagreement. The experimental data seem to be too imprecise to show signs of departures, either radial or angular, from a lattice of free ions.

On the basis of a model of free ions an area of confidence has been determined for the values of the crystallographic B factors.

The optical absorption spectrum of MoS₂ shows two series of exciton absorption bands associated with direct optical transitions from a split valence band. The diamagnetic shifts of the exciton absorption bands (H[parallel]c, H[perpendicular]c) have been measured and values obtained for the exciton effective mass and anisotropy parameter (ellipsoidal model).

In thin crystals the exciton absorption bands occur to the high-energy side of their positions in thick crystals and there is an associated diminution in the diamagnetic shifts.

Rotational structure in the 0-0, 1-0 and 0-1 bands of the A-X system and in the 0-0 and 1-1 bands of the B-X and C-X systems of MgF has been analysed. A-type doubling is observed in the one component of the A ²II-X ²Σ⁺ system to be analysed and the variation of this with J suggests that the ²II state is inverted. State C ²Σ⁺ appears to be a Rydberg state... (σ4s) and the ionization potential is estimated to be 7 6₈ eV. The internuclear distance in the ground state r_e" is 1.750 Å.

The character of the electronic states and transitions between them of the astrophysically important molecule ZrO are reviewed. Franck-Condon factors and r centroids, calculated on the basis of a Morse model, are displayed, with wavelengths of known bands, for the α, β, γ, A and B band systems.

A partial (v' + v" [less-than-or-eq, slant] 8) array of Franck-Condon factors and r centroids is reported for some bands of the A³ ϕ -> X³ Δ band system of the zirconium oxide molecule which is of astrophysical interest and which is found in S-type stars.

A simple method to treat consistently the zero-frequency pole in the spectral representation of the correlation functions in equilibrium statistical mechanics is presented.

A new test of the superposition approximation for the triplet distribution function in a classical fluid is reported. This test is based on an exact equation between the pair and triplet distribution functions. The results confirm that the superposition approximation is poor at moderate density.

The leading terms in the asymptotic energy expansion of the forward elastic scattering amplitude of electrons incident on the ground state of the hydrogen atom are investigated using the first Born approximation to the cross section together with a dispersion relation, and compared with the expansion based on the Born series.

We have made a hemispherical electron monochromator and measured the optical excitation functions of the 4 ¹S and 4 ³S states of helium close to threshold. Both excitation functions reach a significant value within 30 mV of threshold and show two narrow maxima. The second maxima coincide in energy (between 23.77 and 23.80 eV) and are identified with a resonance having the configuration (1s5s²)²S_1/2.