Table of contents

In this paper the approximate validity of the quantum adiabatic theorem is established without the restriction of considering the spectrum of the discrete and non-degenerate Hamiltonian, provided that the assumptions made in a previous paper are fulfilled.

The sensitivity of s- and p-wave positron-hydrogen-atom elastic phase shifts to the presence or absence of various multipole components of the adiabatic polarization potential is discussed. It is concluded that higher multipoles than the quadrupole component are unimportant and support is given to the view of Drachman that in s-wave scattering the monopole component of the adiabatic potential should be suppressed.

The cross-section formulae for transfer of energy and momentum between a pair of free colliding electrons in an arbitrary frame in non-relativistic quantum mechanics have been derived. These formulae are applied in the electron-atom binary encounter collision theory in order to obtain the quantum-mechanical differential and total cross-section formulae for electron-atom collisions. This work represents an advance over the work of Gryzinski in that it includes interference between direct and exchange terms. Moreover, in the application some influence of the nucleus is taken into account since use is made of the symmetrical collision model. The interference term in the application to the binary encounter theory of electron-atom collisions corrects an earlier form of this term.

The classical impulse approximation to the electron and proton impact ionization cross sections is expressed as u²Q(y) = g(y) m₂, where g(y) m₂ is a unique function of y = E₁/u (E₁ being the impact energy and u the ionization potential) for a given incident particle of mass m₂. Results are presented for H and Li, and are compared with the Thomson and the Born approximations.

Extensive calculations are being made of cross sections for electron impact excitation of the metastable states of ions in configurations p², p³ and p⁴. These are of importance for the interpretation of the spectra of gaseous nebulae. The collision problem is formulated using a variational principle and calculations are made using improved forms of the exact resonance and distorted wave approximations. Results are given for ions in 2p² configurations.

The cross section for excitation of the 2 ²S_1/2 state of atomic hydrogen by electron impact has been remeasured in the energy from the threshold (10.2 ev) to 500 ev. The shape of the σ(1s, 2s) cross section curve observed agrees with the earlier measurements. The absolute values of our σ(1s, 2s) cross section disagrees with those of Lichten and Schultz by about a factor of 3. The maximum of the cross section and its total error is σ_max(1s, 2s) = (0 11 ± 0 025)πa₀²; this is somewhat smaller than that of Stebbings et al. which is (0.16 ± 0.01)πa₀². Comparison has been made with theoretical results.

The cross section for the thermal collision-induced radiative de-activation process He(1 ¹S) + He(2 ¹S) -> He(1 ¹S) + He(1 ¹S) + hv is calculated to be 2 × 10^-20 cm², in harmony with the value derived experimentally by Phelps.

Calculations are described for the processes e + H(1s)->e + H(n, l), where the n,l values are 2s, 2p, 3s, 3p and 3d, the approximation used being a modification of earlier work by Rudge who considered the cases of elastic scattering and excitation of the 2s state. By interpolating between our calculations for these values of n,l and partial wave values for the ionization cross section an estimate is made of the excitation cross section to more highly excited states. Using these data, the contribution to the measurements of the 1s-2s and 1s-2p cross sections due to cascade is estimated and our results compared for these cases with experimental measurements. Satisfactory agreement is obtained.

A comparison is also made with the classical theory of Gryzinski. It is observed that the classical theory does not yield close agreement with our theory or experiment and that, over certain ranges of energy, it can be in error by several orders of magnitude.

The penetration of matter by fast charged particles can be characterized by the mean excitation energies I appropriate to stopping and I₁ appropriate to straggling. A semi-empirical procedure is used to obtain I and I₁ for helium, xenon and radon; the results are in satisfactory agreement with available experimental data.

Measurements of the photoabsorption cross section of atomic hydrogen at 840 0 Å and 826 3 Å, using a previously published technique, are described. The experimental results of 2.9 ± 0.5 Mbn (840 0 Å) and 3 8 ± 0.8 Mbn (826.3 Å) are in fair agreement with the theoretical values of 5.0 Mbn and 4 8 Mbn respectively.

A new method, not involving any infinite series, for calculating four-centre electronic repulsion integrals in molecules is presented. The integrals are reduced to three-dimensional form for atomic Slater-type orbitals. For spherically symmetric orbitals the result agrees with the Fourier transform method of Bonham, Peacher and Cox. When angular wave functions are considered, the result is an extension of the latter method.

Certain integrals arising from the analysis of three-body interactions between rare-gas atoms or alkali-halide ions with Gaussian electron wave functions are reduced to computational form. The mathematical technique proceeds via the transformation of inverse powers of the interelectronic distances to Gaussian form, using the Gaussian integral transform.

An analysis is made of the neutron diffraction results of Low and Collins on transition metal impurities in iron. The moment values found are shown to be related to the hyperfine fields on impurity sites and on neighbour sites.

The transverse spin fluctuations in MnF₂ have been studied in the temperature range T_N - 2 6 °K to T_N + 5 4 °K using high resolution neutron inelastic scattering techniques. Distinct spin-wave peaks have been seen up to temperatures within 0 6 °K below T_N. These peaks coalesce to form a single peak with a width above T_N which is similar to the width of the spin-wave peaks below T_N. There is no evidence of spin waves persisting above T_N for small momentum transfer as measured by a shift of the critical scattering peaks away from ω = 0, but small shifts (Δ = 0 1 MeV) were detected for larger momentum transfers (0 1 q_max).

Least-squares fits have been made to the results above T_N to determine the widths of the peaks in both energy and momentum, and the resulting parameters are in qualitative agreement with the theory. Quantitative agreement with the simplest form of the theory is not obtained for the energy parameters, but the inverse correlation length squared has a temperature dependence K₁² [infinity] (T - T_{[perpendicular]})^{1 28 ± 0 37} which is consistent with a 4/3 law as postulated for a cubic ferromagnet, and is also consistent with the results of other experiments on antiferromagnets.

A ferromagnetic Heisenberg system with a random arrangement of two different types of atom with spins s₁ and s₂ and exchange couplings J₁₁(r), J₁₂(r) and J₂₂(r) is studied in the limit of very low energies. The eigenstate with k = 0 is known from the symmetry of the Hamiltonian, and so a set of basic states are used which will reduce to the exact result in this limit. These states are used in a variational calculation to obtain an expansion for the spin-wave energies in the low-energy limit. In the limit of a very low concentration of one type of atom the energy can be evaluated exactly. Approximate results are obtained which can over the entire concentration range except when the spins or exchange constants differ from each other by very large amounts.

The critical concentration for a dilute Heisenberg ferromagnet is determined by finding the concentration for which the ferromagnetic ground state is unstable with respect to the formation of long-wavelength spin waves. An upper bound to the spin-wave energies is determined using a variational procedure and this is used to obtain a lower bound on the critical concentration. This result is considerably higher than the corresponding Ising result.

The spatial distribution of ferromagnetic moment associated with Fe and Co atoms dissolved dilutely in Pd has been examined with long-wavelength neutrons at liquid helium temperature. The moments in 3d orbitals at the impurity sites are (3.5 ± 0.4) μ_B and (2 1 ± 0.3) μ_B for Fe and Co respectively. The distribution of polarization in the surrounding Pd matrix appears to be rather similar for these two solutes and extends out to a distance of almost 10 Å. This is somewhat smaller than, but of the same order of magn tude as, the ferromagnetic interaction range deduced from the lower limiting concentrations for the occurrence of ferromagnetism. The moment induced on individual Pd atoms is quite small, that on the nearest neighbours to a solute atom being approximately 1/20 μ_B; the giant moments associated with Fe and Co additions arise through some 200 Pd atoms being influenced by each impurity.

The basis of the two-fluid model of superconductivity is discussed especially for dirty superconductors. It is shown that for the free-electron model of a metal the superfluid velocity can be defined by v_s = p_s/m where the macroscopic order parameter depends on position through the phase factor p_s · r, and where m is the band mass. With this definition of v_s the energy and current densities have the same form in pure and impure materials. It is shown further that, for consistency with the conservation of energy, the time development of v_s is given by the usual macroscopic equation even in very impure material.

The lattice vibration frequency and eigenvector data of Karo and Hardy have been used to compute the intensity of the thermal diffuse X-ray scattering from a small cube of sodium chloride containing one thousand atoms. The results show that, at small scattering angles, (sin θ) / λ < 0.1 Å^-1, the one-phonon process accounts for at least 90% of the total thermal diffuse intensity but that at high angles, (sin θ) / λ > 1.1 Å^-1, the one-phonon process may account for as little as 20% of the total thermal diffuse intensity.

Measurements have been made of the lifetime and absolute values of the Einstein spontaneous radiation probabilities for the ⁴S_3/2-⁴I_15/2 visible fluorescence of erbium in yttrium gallium garnet. These have allowed an estimate to be made of the fluorescence efficiency of this transition and of the value of the phonon contribution to the transition rate. Evidence to support the theory that the phonon process involves five phonons is given.

Zero-phonon lines at 3628 Å, 4684 Å, 4700 Å, 5248 Å, 5680 Å, 6419 Å, 6490 Å and 7058 Å observed in the optical absorption spectrum of magnesium oxide after fast-neutron irradiation have been examined at 77 °K and 4 °K. The half-widths of all the lines varied markedly according to the particular irradiation temperature, dose and the subsequent heat treatment of the specimen. This behaviour is associated with the presence of strain fields associated with interstitial dislocation loops produced by irradiation. The phonon-assisted structure observed on the high-energy side of the zero-phonon lines has been analysed and compared with the phonon spectrum determined by Peckham using slow-neutron scattering. The splittings of the zero-phonon lines under uniaxial stress show that defects are present in magnesium oxide with the same symmetries as the M, R and N₁ centres observed in the alkali halides. As a result, it is suggested that analogous aggregate defects may be present in magnesium oxide although the situation is probably complicated by the divalent nature of the magnesium oxide lattice.

Two new bands of SrH at 3115 Å and 2718 Å and three new bands of SrD at 3115 Å, 2848 Å and 3001 5 Å have been observed in absorption using a King-type furnace containing strontium metal and hydrogen (deuterium) at a temperature greater than 1300 °C. Whereas the SrH band at 3115 Å is shown to be the (0, 0) band of a new transition which may be called G ²Σ <- X ²Σ, the band at 2718 Å is analysed as the (1, 0) band of the previously known system at 2927 Å. The SrD bands at 3115 Å, 3001 5 Å and 2848 Å are analysed as the (0, 0) band corresponding to the (0, 0) band of SrH at 3113 Å and the (0, 1) and the (1, 0) bands of the previously reported system of SrD at 2928 Å, respectively.

The cross section for electron ionization of the first five excited states of hydrogen are calculated using Gryzinski's classical theory. These cross sections are compared with cross sections calculated using the first Born approximation. The classical cross sections are in good agreement with the quantal cross sections except at very large impact energies where the classical cross sections do not have the correct fall-off. If the correct fall-off is added to the classical cross sections, these cross sections differ only slightly from the Born cross sections at high impact energies.

This letter reports calculations of breakdown field for vacuum gaps using the model previously discussed by Chatterton. In this case the effect of varying the electrode temperature at which primary instability could occur is examined. The results indicate that if comparison is to be made between theory and experiment the instability temperature must be known for the materials and configuration under consideration.

Some wrong deductions in a paper by Singh on the effective collision frequency in the F region are pointed out and corrected.

It is shown that the r centroid of each of the bands on the primary Condon locus of a molecular spectrum is the preferred `Franck-Condon' internuclear separation at which the transition occurs.

Using a curved crystal x-ray spectrograph of the transmission type two new forbidden lines L_IM_Iλ 1476 64 X.U. and L_IIIN_IIIλ 1393 06 X.U. have been found for the element lutetium 71.

Variational calculations by Taylor and Harris for the ground state of H₂^- have been interpreted as showing that the state is not stable. It is pointed out that this conclusion is false since the adiabatic approximation is not valid when one electron is at a large distance from the rest of the system. A five-particle non-adiabatic calculation is required.

The half-life of the 14 4 kev level of ⁵⁷Fe has been measured with scintillation detectors and a digital timer. The value obtained was 97 7 ± 0 2 nsec.