Table of contents

The need for direct measurements of paramagnetic resonance absorption spectra in zero magnetic field is discussed. Two spectrometers have been built which together cover the range of 8 to 18 Gc/s; with one of these a spectrum is recorded over a range of nearly 6 Gc/s in a time of two minutes with a sensitivity sufficient to detect about 10¹⁷ Fe³⁺ ions at 80°K. Polycrystalline samples may be used, and examples are shown of the spectra of a dilute ferric chelate compound. A technique is described for obtaining the absorption line shape free from the effects of the associated anomalous dispersion.

The small heat changes accompanying the magnetization of cobalt ferrite were measured with two rod specimens. One had been heat-treated to destroy uniaxial anisotropy, the other was untreated. A new method of analysis of the results is described, and while its application to these specimens may not have led to conclusive results, it appears to give useful information when applied to materials of less complex magnetic behaviour.

A core of square loop ferrite was examined under pulse magnetization conditions. Starting from remanence the irreversible change of magnetization produced by a series of very short pulses was measured by a ballistic galvanometer method. The results were interpreted on the basis of a domain wall model, which enabled an estimate to be made of the ratio of the time spent by the walls in reversible motion to the time spent in irreversible motion. From this ratio was deduced the average number of times that the domain wall energy passed through a maximum during the course of a magnetization reversal. The result so obtained, twenty-five, agreed well with that obtained by an independent method, due to Néel.

The range-energy relation for μ-mesons with energies up to 1000 Gev has been studied by comparing the sea-level energy spectrum of cosmic rays with the underground depth-intensity curve. No significant divergence from accepted theory has been found.

Total cross sections of gamma rays from sources cobalt 60, scandium 46, caesium 137, chromium 51 and cerium 141 in the elements graphite, aluminium and copper are determined, using a scintillation spectrometer of good figures of merit and modified narrow beam geometry. The values of total scattering cross section are obtained by subtracting the theoretical values of photoelectric and pair cross sections from the total experimental values. For energies greater than 320 kev good agreement is observed between theoretical and experimental values of total scattering cross section, while at the energy 145 kev definite deviations are observed. The deviations are ascribed to the over-estimation of total scattering cross section by the use of atomic charge distribution predicted by the Thomas-Fermi model.

The positions of the lowest lying T=1 levels in the 2p-shell nuclei with T₃=0 are calculated from the experimental positions of the ground states of the nuclei with T₃= +1 and the energy differences between the ground states of the nuclei with T=½. Coulomb forces are considered as a perturbation in the shell model and it is shown that, apart from small terms which depend on symmetry, the method is equivalent to that used by Wilkinson (1956). The corrections due to symmetry are of the same order of magnitude as the significant differences which Wilkinson found between the experimental and the calculated positions of the T=1, T₃=0 levels, and when these corrections are included the differences are no longer significant. The energy shift due to the charge dependence of nuclear forces caused by the pion mass difference is calculated and is shown to be appreciable. There is good agreement between theory and experiment for the isobars with A=14.

The nuclear resonant scattering technique for γ-rays was used to measure the lifetime of the 364 keV level in ¹³¹Xe, and to determine the mixing ratio of the E2 + M1 ground state transition. Doppler broadening of the emission level, which compensates the recoil losses of the 364 keV gamma ray, is provided by the preceding 608 keV β^--transition from ¹³¹I when the source, methyl iodide, is in the gaseous phase, the scatterer being solid xenon.

The measured lifetime of (1.4 ± 0.4) × 10^-11 sec is in agreement with Sunyar's estimated value of 2 × 10^-11 sec. A 0.34% M1 admixture was found for the 364keV transition, and is of the order expected from internal conversion coefficient measurements.

Measurements have been made of total collision cross sections (Brode 1929), of cross sections for 3s-3p excitation (Haft 1933, Christoph 1935) and, at thermal energies, of cross sections for elastic scattering with electron exchange (Dehmelt 1958). In all cases the measured cross sections are very large.

The distinguishing feature of electron-Na collisions is the very strong coupling between the 3s and 3p states. It has been shown previously (Seaton 1955) that the Bethe approximation gives good results for the 3s-3p cross section when allowance is made for effects of strong coupling. The present paper gives results of calculations for energies above the 3p excitation threshold and also for the limit of zero kinetic energy. Further work is being done for energies in the immediate vicinity of the 3p threshold.

For the higher energies the Bethe approximation is used to calculate partial wave integrals and the transmission matrix is then obtained by two different methods, both of which ensure that conservation conditions are satisfied exactly (Percival 1960, Seaton 1961). The only potential considered is V(3s, 3p). For energies not too close to the 3p threshold these calculations give good results for the 3s-3p cross section and fairly good results for the total cross section. This shows that a substantial part of the elastic scattering is due to the process 3s->3p->3s.

At very low energies exchange effects and polarization effects are both large and a much more elaborate theory is required. The coupled integro-differential equations, of Hartree-Fock type, are discussed in detail. It is shown that the coupling between 3s and 3p accounts for 99.4% of the atom polarizability. Solutions of the coupled equations for 3s and 3p are obtained for the case of zero kinetic energy. The calculated zero-energy elastic cross section is 380πa²₀ and the exchange cross section is 440πa₀². These calculated values are consistent with those obtained experimentally.

A new type of approximation is introduced, with the objects of examining further the transition of a fluid of non-attracting rigid molecules, and of improving the lattice model of a liquid by reducing the ratio of mesh size to molecular volume. The approximation is first checked by applying it to some simple two-dimensional lattices, reproducing many known results and predicting some new ones. The probable qualitative behaviour of the isotherm of a two-dimensional fluid of rigid non-attracting molecules is determined, available evidence suggesting the existence of a finite region in which the fluid phase is metastable. Some preliminary results on the effect of reducing the lattice mesh size suggest that simple lattice models of a liquid do give physically sensible results in spite of their crudity.

A linear pinched discharge in fully ionized hydrogen or deuterium is examined theoretically under an idealized steady-state condition, when there is a pressure and an energy balance and no instabilities. Under this condition, the Joule heating caused by the axial current is balanced by bremsstrahlung radiation losses and by axial heat conduction and diffusion to the electrodes. A partial analytical solution is found assuming that the transport coefficients have the usual power dependencies on temperature throughout the plasma. It is shown that all the energy not radiated is carried to the anode, the cathode even having a negative total heat flux at its surface due to thermal effects of diffusion by the current-carrying electrons. The maximum temperature in the discharge is shown to vary directly with the voltage across the tube and only insensitively to other parameters. Further relations are derived involving the dimensions of the discharge, the current and the maximum temperature. The temperature, the line density and the electric field are plotted showing their variation along the axis. The relative importance of heat conduction and radiation losses is seen to depend only on the total axial current which is flowing. A typical example of a discharge shows that temperatures of 10⁶ to 10^7oK are quite feasible in the presence of heat losses to the electrodes.

A study has been made of the L x-radiations emitted after the disintegration of ²⁴²Cm to determine, as accurately as possible, the fluorescence and other yields of the L_II sub-shell in Pu. Observations have been made (i) on the total intensity per disintegration of the L x-rays by observing the L x-ray photons in coincidence with α-particles from ²⁴²Cm, (ii) on the relative intensity of the L x-rays from the L_II and L_III sub-shells. The sensitivity of the curved crystal spectrograph used for the latter observations had previously been determined.

The experimental results are: fluorescence yield ω₂=0.413 ± 0.02, Coster-Kronig yield f₂₃=0.22 ± 0.08, and Auger yield a₂=0.37 ± 0.08. The total fluorescence yield of the L shells is ω=0.486 ± 0.01. The values of ω₂ and ω are independent of previous work on fluorescence yields, but for the distribution of yields between f₂₃ and a₂ it was necessary to use an extrapolated value of ω₃.

The behaviour of the Si I, II, III and IV and F II and III spectral lines in highly condensed discharges, in the range 2900-6000 Å, at pressures varying from 3 mm to 35 cm, is given. The lines originating from the higher energy levels are found to be more sensitive to pressure.

A change of the intensity of resonance fluorescence may take place when Zeeman states of the excited level have the same energy. The fields at which these `level crossings' occur in ¹⁹⁹Hg and ²⁰¹Hg have been measured. Combined with recent determinations of the hyperfine coupling constants, the results yield values for g_J of the ³P₁ states: g_J (199)=1.48634±0.00005, g_J (201)=1.48606±0.00015.

The Hartree perturbation method is used to calculate the dipole polarizability, the electric field at the nucleus, the quadrupole polarizability and the nuclear shielding factor of helium using a twelve-term representation of the unperturbed Hartree wave functions. It is pointed out that the method yields lower bounds for the dipole and quadrupole polarizabilities. The absolute error in the predicted values of any of the quantities is less than 4.3%.

An approximate method has been developed for obtaining the value of Z, the number of collisions required to make a rotational-translational energy transfer in a diatomic gas from the thermal conductivity data, and the geometry of the apparatus employed in the conductivity measurements. The values of Z for H₂ calculated at different temperatures are in fair agreement with the values obtained by other methods. They also show that Z increases with rise of temperature.

In the present investigation targets of natural nickel and isotopically pure ⁶⁰Ni were bombarded by deuterons with energies of 8.9 MeV and 8.6 MeV respectively. From the resulting proton energy spectra a number of angular distribution measurements have been made for the ⁵⁸Ni(d, p)⁵⁹Ni and ⁶⁰Ni(d, p)⁶¹Ni reactions and spin and parity assignments made to states of ⁵⁹Ni and ⁶¹Ni. The results have also been compared with the gross structure peaks in the proton spectra recently reported by Schiffer, Lee and Zeidman.

The magnetic susceptibilities and electrical resistivities of a series of quenched γ body-centred cubic uranium-molybdenum alloys were measured over the temperature ranges 293°-1200°K and 90°-1200°K, respectively. U-15, 20, 25 at.% Mo each possessed a small negative temperature coefficient of resistivity below about 200°C in the metastable γ-state, and a positive coefficient in the stable γ-region.

All samples exhibited a Pauli weak spin paramagnetism which increased with temperature, and in addition possessed an exchange contribution shown to be independent of composition over the range 15-30 at.% Mo. The bearing of the results on our understanding of the electronic structure of the γ-alloys is discussed.

Solid specimens of GaAs-InAs alloys, showing a composition spread of less than 3 mol%, have been prepared by a slow directional freeze technique. These specimens have been used for measurements of Hall effect and conductivity as a function of temperature and for infra-red transmission measurements to determine the optical energy gap E_G. The electrical measurements show that there is mixed conduction in the alloys and hence the values of Hall mobility have no significance. The optical measurements to determine the variation of E_G with composition are in good agreement with values obtained by diffuse reflection methods on single phase powder samples. The values of E_G show a linear variation over most of the composition range.

The calculation of the integrated density of states for positive electron energies of a one-dimensional chain of atoms whose spacing is given by a probability distribution function is reduced to the form of an integral equation. This equation is simplified considerably when the atoms are distributed at random. In this case, an explicit solution for the integrated density of states is found, which is rigorously valid for δ-function atomic potentials, and may be valid generally. It is shown that the solution gives good agreement with the machine results of Lax and Phillips (1958) for the δ-function case.

Starting from Laval's expression for the first-order thermal diffuse scattering (TDS₁), a new expression for the inversion temperature of TDS₁, T_max = mΘ_D²d²_hklk/3h², has been obtained, valid for a crystal of any symmetry. T_max is attained when (u²)bar above^1/2/d_hkl = 16%. Every crystalline substance has a definite range where the above formula holds: the upper limit is T_mp and the lower limit is Θ_D. The melting temperature defines a d_max for which the inversion phenomenon can be observable. The inversion curves of TDS₁ have been calculated for some metallic, ionic and molecular crystals. It is shown that KCl, Pb and Al, for which the inversion phenomenon has been reported, are not special cases. In molecular crystals this effect will be observable mainly at low temperatures. A method is given for determining Debye characteristic temperatures of crystals of any symmetry. This method is tested using Cartz's experimental T_max for lead.

The scattering length for elastic collisions between electrons and helium atoms is calculated with full allowance for distortion and exchange by the exact numerical integration of the appropriate integro-differential equation for the zero-order partial wave. The resulting cross section 26a₀² for electrons of zero impact energy is in good agreement with the available experimental data, so that the effect of polarization which is neglected in the present calculation is probably small.

The expression for the differential cross section obtained from the second Born approximation by including only terms to the third order in the interaction energy is employed to calculate the differential and total cross sections for the elastic scattering of electrons and positrons by hydrogen atoms. Allowance is made for both distortion and polarization by evaluating the terms which correspond to transitions through the 1s, 2s and 2p intermediate states. It is found that for electrons with impact energies below 100eV the effect of distortion and polarization is to increase the total cross section appreciably above the first Born cross section. For positrons, distortion and polarization decrease the total cross section.

The electron resonance hyperfine triplet at 9.5 mm wavelength of the peroxylamine disulphonate ion has been measured in a series of solutions of water and glycerol from 20% to 72% glycerol by weight and over a temperature range from -46° to 65°C. There is a temperature and solution dependent broadening which affects the individuals of the triplet differently. The high field line is broadened first with falling temperature. The effect is thought to be due to the motionally attenuated anisotropic electron-nuclear interaction. The anisotropic interaction is estimated to be comparable with the isotropic one. The anisotropy of the g factor, δg/g, is 2 x 10^-3. These parameters allow the prediction of a static spectrum of the ion in agreement with experiment (Weissmann and Banfill 1953). The effect of thermal motion of the ion is shown by the close relation between the value and temperature dependence of the thermal reorientation correlation frequency and the variation of the electron resonance signal with temperature and nature of the solvent.

Measurements are reported of the proton spin-lattice relaxation time T₁ at 47.5 Mc/s for both the methyl and ring protons in liquid toluene over a wide temperature range by recovery from saturation of the high resolution signal. The two sets of protons relax independently and show a very different dependence on temperature. The ring proton T₁ has a minimum of 1.4sec at - 108°C while the methyl proton T₁ is still falling at the lowest temperature - 131°C to which the liquid could be supercooled. The results are interpreted in terms of a complex thermal motion of the toluene molecules about more than one axis together with internal motions of the methyl group relative to the molecule. Plausible generalizations of current theories of magnetic resonance relaxation are made to facilitate the analysis. It is suggested that very considerably increased information about molecular liquids is obtainable from magnetic resonance measurements by such a study of each chemical type of proton within a molecule, when present.

The theorem is proved that the first order correction to the expectation value of any operator which can be expressed as a sum of one-electron operators vanishes if Hartree-Fock wave functions are used in its evaluation.

New measurements of the decay of the luminescence produced in LiI(Eu), NaI(Tl), KI(Tl), CsBr(Tl) and three CsI crystals of varying thallium concentration have been made for particles with different ionization densities. The decay time of the luminescence is found to depend on the average ionization density ρ. In all cases except LiI(Eu) two components are found in the decay. The dependence of the decay times and efficiency, the relative voltage pulse height per unit energy, on thallium concentration for different particles has been studied in CsI. The ratio ρe'/ρ_α' has been found to increase with the average Z of the crystal where ρe' and ρ_α' are the average decay times for electrons and alpha particles respectively.

The opacity of ice formed from water containing dissolved air is due to the presence of bubbles of air in the ice. Both bubble concentration and sizes were found to depend on the rate of freezing. Bulk water saturated with air at 0°C was found to freeze into ice containing about six bubbles per mm³ when freezing proceeded at 0.5 mm min^-1 and 300 per mm³ at a rate of 5 mm min^-1. Bubbles were formed at the ice-water boundary when the concentration of dissolved air reached a critical value which, for rates of freezing greater than 2 mm min^-1, corresponded to a supersaturation ratio of 30. Agitation of the water could prevent the critical concentration from being attained and clear ice then formed.

Other factors which influenced bubble concentrations and sizes were the amount of dissolved air, pressure, thickness of the layer of water ahead of the growing ice and escape of bubbles by buoyancy.

The magnitude and extent of the air concentration gradient ahead of the ice were estimated from theory.

Bubbles in ice were found to change shape with time particularly when under the influence of a temperature gradient.

An account is given of the design and construction of a microtron having a 20-ton magnet with a pole diameter of 80 inches. Details are given of the major components, phase stability is considered, and the particle dynamics relevant to vertical focusing and to beam extraction are developed.

This accelerator was brought into operation in the summer of 1958, and provides an extracted electron beam of about 10^-8 A mean at an energy of 29 MeV. The microtron is pulsed at a repetition rate of 100 pulses/sec, and has an electron pulse duration of about 2 μsec. By use of a quadrapole lens system the extracted beam can be focused to a spot about 2 mm in diameter, the corresponding angular spread being certainly less than 1°.

The electronic Hamiltonian for a general atom is obtained as far as terms in 1/c² and m/M_A by reducing a relativistic wave equation with four components for each electron and nucleon to an approximately relativistic form with two components per particle. The presence of non-Hermitian terms in the reduced Hamiltonian is explained. Relativistic corrections to the Coulomb and nuclear interactions and the effect of the intrinsic magnetic moments are treated by first-order perturbation theory. The electronic Hamiltonian is obtained in the centre-of-mass system of the atom. The hyperfine structure interaction is obtained by expressing all electron-nucleon terms as multipole expansions, giving the previously known hyperfine structure expansion with recoil corrections. The exact operator for the nuclear field effect in isotope shift is obtained from the Coulomb interaction. The presence of other corrections depending on nuclear structure is indicated. Terms referring only to s electrons are not considered as the reduction procedure used does not cover the contact approach of particles (cf. Ma 1956). The usual calculation of the normal mass effect in isotope shift is investigated for non-s-electron configurations and is shown to be justified if 0.1% of the spin-orbit interaction and the whole of the other relativistic perturbations are negligible in comparison with the term value.

The principal series of magnesium has been photographed, in absorption, in the ultra-violet region between 2400 Å and 1600 Å by means of a 3-metre vacuum spectrograph and a large King furnace. Measurement of twenty-four new members of the series against accurate copper standards leads to a revised value of 61670.6 cm^-1 for the ionization potential of Mg I, an increase of 1.5 cm^-1 on the value previously accepted.

It is shown that in a plasma which is heated by an electric current the direct heating of the positive ions can be increased markedly by the presence of a small concentration of impurity ions. With favourable impurity concentrations, this heating is sufficient to explain the observed ion temperature in zeta and sceptre.

The anomalous behaviour of the heat capacities at the Néel points of copper-manganese alloys containing 80 and 85 at.% Mn is more marked than that observed in other metallic antiferromagnetics. The entropies associated with the anomalies are 0.20 and 0.35 cal mol^-1 deg^-1, respectively, and are significantly less than the value R ln (2S+1) predicted by localized theories of antiferromagnetism. It is concluded that these results indicate that the appropriate model of antiferromagnetism in metals is not one based on completely localized moments.

The cross section for formation of positronium on impact of a positron with a normal helium atom is calculated by Born's approximation for positron energies up to 125 ev. As judged by the size of the maximum cross sections obtained at positron energy of 27 ev, the coupling between elastic scattering and positronium formation is far from weak. This suggests that virtual formation of positronium may play an important part in the elastic scattering of slow positrons by helium atoms. The coupled equations for dealing with this effect are derived.