Table of contents

The expectation value <ρ(x)ρ(y)> of the pair density operator is calculated for a dilute Bose system in which the excitations move with drift velocity u with respect to the free-particle ground state. In general <ρ(x)ρ(y)> - <ρ>² depends on the drift velocity u and the angle ψ between u and r = x - y. For very large r, <ρ(x)ρ(y)> - <ρ>² is found to vanish as r^-4, and to become practically independent of u and ψ.

The radiation emitted by a charged particle moving with uniform speed parallel to an infinite magnetic field in a hot plasma is evaluated when the phase speed of the excited waves is very much greater than the thermal speed. It is found that Cerenkov radiation in the extraordinary mode cannot be excited by particles travelling with speeds less than the geometric mean of the thermal speed and the speed of light in vacuum. The total energy emitted in the form of plasma waves exceeds that excited in the extraordinary wave when the particle moves slower than √2 times the minimum speed capable of exciting the extraordinary wave radiation.

The analysis of photon beams in terms of the time intervals between photon counts is discussed; in particular, the cases of beats and of sinusoidal amplitude modulation are considered.

A Hartree - Fock approximation scheme is developed for the calculation of the efficiencies of multi-photon processes. It is applied to the calculation of the probability of two-photon radiative decay of singlet metastable helium with a resulting lifetime of 1.2 × 10^-2 sec which is within a factor of 2 of the most accurate available estimate, 2 2 × 10^-2 sec.

The methods developed in a previous paper to study the ionization cross sections of H, He, Li and Be in their ground states using the Born approximation have been used to extend these calculations to neutral systems with outer 3s electrons. The results obtained are qualitatively similar to those for lithium and beryllium and, in the case of sodium, good agreement is obtained with the recent calculations of Bates, Boyd and Prasad.

The Born-exchange and Ochkur approximations are used to calculate cross sections for the electron impact ionization of the atoms He, Li, Be, Na and Mg in their ground states. In all cases where there exists comparison data, the inclusion of exchange leads to better agreement with experiment as compared to ordinary Born cross-section calculations. Of the two exchange approximations considered here, the simpler approximation due to Ochkur consistently gives the best results.

The electron impact ionization cross section of H(2s) and H(2p) in the Born A, Born B, Born-Ochkur and classical approximations are reported together with those of H(2s) in the Born exchange approximations. Calculations cover a range of impact energies from 4.87 eV to 300 eV. The Born-Ochkur approximation results in considerable reduction of the cross section in the low energy region. There is close accord between the Born exchange cross section corresponding to maximum interference and the Born-Ochkur cross section for the ionization of H(2s).

At large impact energies E the cross section Q for the electron excitation from the n, l state of hydrogen to the n', l' state may be written in the form QE = A log E+B. The first Born approximation is used to calculate these A's and B's for all transitions with n = 1, 2, 3, 4, 5 and 6 and with n' = n+1. The A's and B's associated with the main optically allowed transitions (i.e. l' = l+1) are largest. However, for small values of l we find that in calculating the B's we must take account of all other transitions, besides the main optically allowed transitions, for the sum total effect of these minor transitions is almost as large as that of the main optically allowed transitions. These minor transitions can be neglected in calculating the A's for the average cross section from one energy level to another but they increase the B's for the average cross sections by about 25%.

All significant partial cross sections for elastic and inelastic scattering of electrons by helium in the singlet and triplet metastable states have been calculated in the close-coupling approximation for collision energies up to 7.5 ev.

In the doublet total spin system cross sections have been obtained both with and without inclusion of coupling to the ground state of helium.

In the quartet total spin system cross sections for the elastic scattering of electrons by triplet metastable helium have been calculated in the static exchange approximation and with inclusion of coupling to He (1S)(3 ³S) above the threshold for this state.

The calculated total cross section for the superelastic process converting the singlet metastable to the triplet state by collision with thermal electrons at 300 °K is less by a factor of 2 than the experimental value given by Phelps. The estimated total cross sections for the scattering of electrons by triplet metastable helium are less by a factor of 3 than the experimental results of Neynaber et al. for 1 eV electrons. However, the first order partial cross sections are found to yield, in general, a dominant contribution to the total cross sections.

It is concluded that the effect of coupling to the nearby 2P helium states, omitted in this calculation, will be important.

Low-energy s-wave electron scattering has been treated which includes two types of polarization potentials. These potentials are obtained in approximating the calculated potential of Reeh. Scattering equations are solved with the help of the variational methods.

Heating of electrons due to additional energy input into the ionosphere has been considered. The electron temperature profiles for various energy inputs into a model ionosphere were calculated. Using temperature profiles thus obtained, the electron collision frequencies were calculated. It was shown that electron-ion collisions are comparable to electron-neutral particle collisions and cannot be ignored in the lower F region. In view of the large positive ion collision cross section and its temperature dependence, the possibility of ionospheric cross modulation of radio cosmic noise was discussed.

The difference between the matrix elements for ¹²B and ¹²N due to Coulomb effects alone is calculated using a spherical Saxon-Woods potential to generate the nuclear wave functions. The result of about 5%, when combined with other effects amounting to -3%, gives a total of 2%. This is substantially less than the experimental value of 11 ± 1%.

The total cross section for all reactions in nitrogen, excluding inelastic scatters and (p, d) reactions, is found to be 182.2 ± 9.4 mbn for protons of 13 MeV by a triggered cloud chamber method. The (p, α) and (p, 2p) processes each contribute about 40% of this total while the (p, ³He) process contributes a further 15%. The (p, n) and (p, pn) contributions are each found to be less than 3%. The results are discussed in terms of the statistical compound nucleus model which is not found to provide an explanation of the large contribution from the (p, α) and (p, ³He) processes.

Results are reported of measurements of charge-exchange scattering of negative pions by protons, and of elastic scattering of negative pions by protons, at a mean energy of 39 MeV. These results, combined with those obtained from an earlier experiment at 35 MeV, reveal an inconsistency between the hypothesis of charge independence and measured values of the s-wave scattering lengths obtained from elastic scattering and from charge-exchange scattering.

The lifetimes of the 105 and 86.5 keV levels of ¹⁵⁵Gd and 129 keV level of ¹⁹¹Ir are measured with a fast time-to-amplitude converter. The values obtained, respectively, are 5 01 ± 0.25 × 10^-10 sec, 5.31 ± 0 16 × 10^-9 sec and 12 53 ± 1.25 × 10^-11 sec. The experimental transition probabilities are compared with the theoretical estimates. In the case of ¹⁵⁵Gd a good agreement of the experimental transition probabilities with the Nilsson's estimate is observed.

This paper discusses the theoretical implications of results reported previously for the complex dielectric constant of copper and gold in the ultra-violet. The measurements allow one to deduce the optical effective mass of the conduction electrons. It is shown that the experimental far ultra-violet absorption spectrum results from excitation of tightly-bound d electrons. Comments are made on the problem of assigning the low-energy structure in the absorption spectrum to particular excitations in k space.

The Knight shift of the ¹¹⁵In resonance has been measured as a function of composition in the liquid alloy systems In-Cd, In-Hg, In-Tl, In-Sn, In-Pb and In-Bi, and of the ²⁰⁹Bi resonance in In-Bi. The changes in shift follow no simple pattern and show no correlation with valency difference or ionic size difference. The results are not explicable by the theory of electron density fluctuations used successfully by Blandin and Daniel to explain changes in shift in silver-base solid solutions. The results for In-Bi point to the existence of intermetallic compounds in the liquid state. Linewidths are consistently larger than expected from the Korringa relation, probably owing to electric quadrupole interactions.

A general method of deriving the dynamical spin Hamiltonian which incorporates all orders of phonon processes and which is valid for any paramagnetic system has been worked out from symmetry principles. In discussing the dynamical spin Hamiltonian, the terms are distinctly grouped as `Zeeman', `quadrupole', `higher-multipole' and `hyperfine'. Variations in the static spin Hamiltonian constants g, D, A, etc. and probable splittings of electron paramagnetic resonance lines due to these terms are discussed. This Hamiltonian has been used to derive the expression for the spin-lattice relaxation rate between any two spin levels of the paramagnetic system. From this expression one can predict the dependence of the relaxation rates and hence of T₁ of any fine or hyperfine line in the electron paramagnetic resonance spectra on the angles made by the crystalline axes with the Zeeman-field direction. This has been illustrated with specific examples of paramagnetic ions in different symmetries. The electron quadrupole relaxation in cubic crystals is found to be isotropic and the anisotropy in T₁ in such crystals has been shown to be mainly due to the Zeeman relaxation. The nuclear quadrupole relaxation has also been discussed as a special case of the electron quadrupole relaxation.

The spin-wave dispersion relations for the simple cubic antiferromagnet RbMnF₃ have been determined at 4.2 °K by inelastic neutron scattering. Spin-wave theory is used to interpret the results in terms of the exchange interactions 2J_ijS_i-S_j between first, second and third neighbours with J₁ = 3 4±0.3 °K J₂ = 0.0±0 2 °K J₃ = 0 00±0.04 °K. The results also confirm that the anisotropy field is less than 400 gauss. The above value of J₁ is compared with other experimental results, and with values calculated from the Néel temperature. Good agreement suggests that RbMnF₃ is one of the simplest magnetic salts.

A spin-wave theory of ferromagnetic crystals containing a low concentration of impurity atoms with different spin and exchange integrals is developed by a Green function method. The Green function of one-magnon excitations is calculated by expanding in a series in powers of the perturbation introduced by the impurity and then averaging the terms of the series over all possible configurations of the impurities. Those diagrams which correspond to the scattering of a spin wave by one impurity atom in all orders of the perturbation are chosen, corresponding to the approximation for the self-energy linear in the concentration. By an investigation of the poles of the Green function it is shown that the dispersion curves of the spin waves have a non-monotonic character near the points corresponding to energies of the resonance modes of s, p or d types, and the damping, as a function of spin-wave energy, shows a resonance near these points. It is shown that the density of states in the impurity bands corresponding to the energy levels of the localized states in the single-impurity problem is a non-analytic function of the concentration in agreement with a general result of Lifshitz.

On the basis of the theory developed by the author in the previous paper the cross section of one-magnon neutron scattering in a crystal containing a low concentration of impurities is calculated. When the energy transfer is less than the widths of the band of the quasi-continuous spectrum of spin excitations the one-magnon scattering consists of two parts, coherent and incoherent, with effective scattering amplitudes depending on the energy transfer. The widths of the peaks in the energy distribution of neutrons coherently scattered by spin waves are calculated and it is shown that the widths have a resonance character near an energy transfer corresponding to the levels of quasi-localized states of s, p or d type. The cross section of the incoherent scattering shows a resonance only near the level of a quasi-localized s state. When the energy transfer is larger than the width of the band, neutrons are scattered by localized modes of s, p and d type. This scattering is incoherent and the amplitudes of scattering by localized modes of different types have a different angular dependence, the observation of which should allow the determination of the degree of localization of the corresponding states in the crystal.

The symmetry of the colour centre giving rise to an absorption line at 8373 Å in the N-band region of irradiated sodium chloride has been determined by the application of uniaxial stress to the crystal. The stress splitting patterns indicate that the centre has monoclinic symmetry, and the results are compared with those obtained previously on similar zero-phonon lines in lithium fluoride and sodium fluoride. The phonon-assisted transitions accompanying the line are compared with recent calculations of the vibrational spectrum of sodium chloride.

The possibility of obtaining population inversion between the 7 ²P_3/2 and 7 ²S_1/2 thallium levels is investigated, mercury being used as the pumping element. The inversion attained in a radio-frequency discharge at 39 Mc/s is estimated to be, under certain conditions, of the same order of magnitude as the laser threshold inversion.

The absorption cross-section curve for indium vapour has been determined in the range 1640-1800 Å. Five autoionization lines were investigated and it is suggested that the transition designation of the 1757.4 Å line should be changed to ²P_1/2⁰-²S_1/2. The f-number contribution from the ground ²P_1/2⁰ state is found to be 0.25 and that from the ²P_3/2⁰ state to be 0 45 for the lines involved.

Polarization has been observed and measured for the banded luminescence emission in single crystals of cadmium sulphide in the wavelength range 1 5-2 2 μm and for the corresponding excitation spectrum. The experimental results lead to an energy level model for the infra-red emission centre in which the complexity of the emission is explained by considering the lifting of degeneracy (by spin-orbit splitting and crystal field splitting) in both the upper valence band and the localized acceptor level which is the excited state of the centre. Polarization of the 1 06 μm emission band can be explained on the same model.

The vibrational constants of the C ²Σ⁺_u and X ²Σ⁺_g states of the C-X system of the N₂⁺ molecule have been determined from the spectrum obtained by passing a condensed discharge through a mixture of ¹⁵N₂ and helium. These constants have been compared with those calculated by using ¹⁴N₂ instead of ¹⁵N₂. The agreement is very good. The isotope shifts for individual bands have also been calculated. A few bands of the (¹⁴N ¹⁵N)⁺ molecule, which appear during the study of ¹⁵N₂⁺, have been analysed.

A new band of CaH at 2883 Å and three new bands of CaD at 2877 Å, 2789 Å and 2720 Å have been observed in absorption using a King furnace containing calcium metal and hydrogen (deuterium) at temperatures greater than 1100 °c. Whereas the bands at 2883 Å and 2877 Å are shown to be the (0, 0) bands of CaH and CaD respectively, belonging to a new transition which may be called G ²Σ<-x ²Σ, the bands at 2720 Å and 2789 Å are analysed as the (0, 0) and the (0, 1) bands of CaD, corresponding to the previously reported system of CaH at 2720 Å.

Experiments have been carried out on the thermal conduction of mixtures of hydrogen and helium with low hydrogen concentrations. The results show that as the hydrogen concentration is increased from 0-13% there is a decrease in thermal conductivity of mixtures.

The one-electron theory of chemisorption on metals is formulated on the basis of the linear combination method used in quantum chemistry. For a description of metal electrons, the functions which obey periodic boundary conditions in the x and y directions and fixed at the metal surface are used. The electronic configurations leading to dispersional, exchange and ionic interactions are considered, and the atomic structure of the metal surface is also taken into account.

Pinnington's explanation of magnetic enhancement is considered and opposed. Some aspects of the problem are reviewed.

Criticisms made by Mucker et al. in 1965 of the paper by Curzon and Pawlowicz published in 1964 on the crystal structure of solid deuterium are discussed and commented on.

Kay's method of deducing the stage of ionization from which atomic spectral lines are emitted is found to be unsatisfactory on several grounds.

The generalized hyper-netted chain approximation of Hurst is extended so as to produce self-consistent virial coefficients to any order.

The second-order perturbation energy of two interacting atoms may be expressed as a power series in the reciprocal internuclear distance. For two normal hydrogen atoms the energy has been calculated as E₂(R) = - (1.300 × 10)R^-6 - (2 488 × 10²)R^-8 - (6 571 × 10³)R^-10 - (2 430 × 10⁵)R^-12 - (1 212 × 10⁷)R^-14 - (7.875 × 10⁸)R^-16 - (6 469 × 10¹⁰)R^-18 - (6.557 × 10¹²)R^-20 -...ryd where the coefficients are believed to be accurate to two units in the fourth significant place.