Table of contents

It is shown, with particular reference to the decay μ⁺ → e⁺+λ, how the study of rare decays of pions and muons, by means of counter techniques, has contributed to our understanding of the weak interactions.

The scattering from carbon nuclei of photons in the energy range 50-130 MeV has been measured by the use of a total absorption Cerenkov spectrometer in conjunction with a counter telescope. The angular range investigated was 90° to 135°. The results have been analysed by means of a simple model of nuclear charge distribution with nucleon polarizability and indicate the presence of some magnetic dipole scattering. A dispersion relation is applied to check the validity of this simple model.

The rate of energy loss for ²⁰Ne and ¹⁴N ions in the energy region of 0.4 to about 6 MeV has been measured in C, Al, Ni, Ag and Au. The ranges of the ions in the above elements were calculated by integrating the differential energy loss taking into account scattering and energy losses due to nuclear collisions. The rate of energy loss for ⁴He ions up to 2 MeV kinetic energy is reported and range curves in Al, Ni, Ag and Au up to 3 MeV are presented. Results on the energy loss of deuterons in Ag are used to extend the data at present available for protons to lower energies. The relative accuracy of the stopping power data is to about 1% and the absolute accuracy to better than 5%.

A measurement of the polarization retained by negative muons in light elements is described. For elements with spin 0 the muon is found to retain about 17% of its initial polarization.

Measurements are reported on the capture rates of negative muons in certain light elements. Agreement with other experimental data is found, but a discrepancy between the calculated and experimental values of the capture rate in fluorine is noted.

A value of (59±9) μbn has been obtained for the total cross section for the production of π°-mesons in proton-proton collisions at 383 MeV.

Neutron-deuteron scattering phases are evaluated at five energies below 8 MeV for two ranges of a central Yukawa interaction. The dependence of the phases on the range is found to be very slight. Considerable differences are found between these results and those given by Haas and Robertson in 1959 who used the same form of interaction with the shorter of the two ranges considered here. The results and subsequent discussion resolve some previously inexplicable differences between the scattering lengths obtained with various potential shapes.

Cross sections for the following reactions with 36 MeV ¹⁶O ions have been measured:

Neutron transfer	27Al(16O, 15O)28Al	less-than-or-eq, slant7 μbn
Proton transfer	27Al(16O, 17F)26Mg	210±50 μbn
Neutron-proton exchange transfer	27Al(16O, 16F)27Mg	0.7±0.4 μbn

The mechanism of the exchange transfer reactions is discussed in terms of the single transfer reactions. There is some evidence to suggest that an exchange reaction is not composed of two single transfer reactions.

The variational methods of Kohn and Hulthén are employed to calculate the scattering lengths for elastic collisions between positrons and hydrogen and helium atoms. Allowance is made for the dipole polarizability of the target atom by using a trial function which includes a term corresponding to the first-order perturbation of the atom due to the electric field of the positron.

The effect of allowing for the dipole polarizability of the atom is to change the sign of the scattering lengths for both hydrogen and helium in agreement with the variational calculations of Spruch and Rosenberg for hydrogen. In the case of hydrogen the total elastic cross section at zero impact energy is increased when allowance is made for polarization, but in the case of helium it is decreased from 0.72πa₀² to 0.10πa₀². The experimental cross section derived by Teutsch and Hughes for 18 ev positrons in helium is still smaller, being only 0.023 ±0.006πa₀².

Calculations have been made of the electron spin resonance line shapes for polycrystalline substances showing uniaxial g-value anisotropy. The calculations have been made for the Lorentzian and Gaussian line shapes of various line widths. Empirical rules are given for determining g_parallel, g_{perpendicular} and the line width from the experimental line shapes. Line shapes calculated to fit experimental curves from irradiated deuterium peroxide are given.

The characteristic electron energy loss spectra of the elements Zr, Pd, Ag, Au, Zn and Cd have been obtained using the reflection technique and primary electron energies of 1500 and 800 ev. It is observed that in the second group of transition metals, the relation between the observed plasma losses and the theoretical values is not quite the same as that found previously for the first group of transition metals, in that the observed values are here greater than the theoretical near the beginning of the series. The spectra of the noble metals are complex and show few similarities to one another. The two elements Zn and Cd, which follow noble metals in the periodic table, have very similar spectra and it is obvious that plasma oscillations involving their two valence electrons are still influenced by the recently filled d band.

The luminescent efficiencies and decay times of CsBr(T1) and CsI(T1) have been studied as a function of temperature in the range - 150°C to 150°C. Protons of energy 14 MeV, and alpha particles of energy 5.3 MeV were used as the exciting radiation. In general, at any one temperature, the luminescence appears to consist of the sum of a fast and a slow exponential component. It is shown that for optimum particle discrimination by pulse shape analysis, there is no advantage to be obtained by maintaining the crystal of CsI(T1) or CsBr(T1) at temperatures other than room temperature.

Activation energies for the electron traps in the crystal corresponding to the decay time components τi have been obtained.

The electronic band structures of a simple cubic and a face-centred cubic array of square potential wells were calculated by a plane wave method for various depths of the potential wells. Certain features of the band structure depend only on the symmetry of the crystal and not on the details of the potential: in a simple cubic monatomic substance an s-type band has its minimum at k=0 and its maximum at k=(1, 1, 1); a p-band has its minimum at k=(1, 0, 0) and almost certainly its maximum at k=(1, 1, 0). In a face-centred monatomic crystal an s-band has its minimum at k=0, while its maximum may be at any of several positions, such as k=(2, 1, 0), k=(1, 0, 0), or intermediately. A p-band has its minimum at k=(1, 1, 1) with a secondary minimum at k=(1, 0, 0), and its maximum at k=0. Various methods of band structure calculation were compared on the example of the lowest level at k=0 for any depth of the potential wells for the face-centred structure. Plane wave methods gave reliable results with least labour.

A simple theoretical expression is proposed for K quanta production in directions at large angles to the surface of a thick target, neglecting absorption. Direct and indirect production are calculated and the ratio of indirect to total production is shown to be in agreement with experimental results both in magnitude and in independence of over-voltage U₀. Total production is expressed as a function of atomic number Z and over-voltage U₀, and is found to vary as (U₀ - 1)^{1 67}. Values for total production are in fair agreement with experimental values.

The dissociation cross section on interaction with hydrogen gas was measured for H₂⁺ ions with energies between 280 and 670 kev and with both high and low vibrational excitation. An increase of 7 ± 4% was found for the cross section for simple dissociation in the case of the more highly vibrationally excited ions. For dissociation into two protons the difference between the cross sections was certainly less.

The critical supersaturation for the precipitation of water droplets or ice crystals from the vapour was measured between 0°C and -75°C by an expansion-chamber technique. Nitrogen was used as the carrier gas, and measurements were made both in the presence and in the absence of an electric field. The temperature dependence of critical supersaturation was found to be the same in both situations. Thus existing critical supersaturation data for nucleation of water droplets from the vapour in the presence of an electric field probably represent heterogeneous nucleation on ions. Comparison of the data taken in the presence of a field with the Becker-Doring equation for homogeneous nucleation shows fair agreement at the higher temperatures but marked negative deviation at lower temperatures. The precipitate particles appeared to be spherical above -65°C, while at lower temperatures precipitation was in the form of ideomorphic ice crystals.

The high temperature plasma (kT_e similar, equals 20 eV) produced in ZETA is a copious source of spectral lines emitted by highly ionized atoms in the vacuum ultra-violet. Spectroscopic investigations in the wavelength range 400-1000 Å have revealed several new lines due to the multiply ionized inert gases Ne, A, Kr and Xe. The method of identification is based on the successive appearance of the ionization states of each element, supplemented by isoelectronic calculations which also allowed transitions to be assigned to most lines.

The decay of a magnetic resonance absorption in the nitrogen after glow has been followed and compared with the decay of the afterglow itself. Afterglow was never, in any case, obtained without the presence of this absorption and vice versa. Simultaneous records of the two quantities showed that in all cases the absorption disappeared logarithmically at a rate which did not increase with nitrogen pressure while the afterglow intensity decayed according to an I^-½ law in a somewhat longer time. The rates of both processes are increased by addition of oxygen. The processes involved seem quite independent.

A magnetic field is `frozen' into a moving conducting fluid when certain conditions are fulfilled, as for example, when the frequency of the fluid disturbance is small compared with the cyclotron frequencies of the fluid particles. If the fluid contains streams of moving particles, parallel to the magnetic field, the magnetic field is also `frozen' into the streams when there are transverse perturbations. The condition now is that the Doppler shifted frequency of the disturbance must be small compared with the cyclotron frequency of the stream particles. It follows that the phase velocity of transverse hydromagnetic waves is modified if such streams are present. In effect, the momentum flux of the streams reduces the `tension' of the magnetic flux lines. When the kinetic energy density relative to the centre-of-mass system exceeds the magnetic energy density, the phase velocity in an infinite medium has complex conjugate values and the hydromagnetic wave grows in amplitude. In the case of a stream of finite radius the phase velocity shows dispersion for wavelengths greater than the stream radius and there is an increase in the domain of stability.

In aluminium-rich transition-metal intermetallic compounds the behaviour of transition-metal atoms in an electron-rich environment can be studied. Electron-density maps, prepared from x-ray data, and considerations of Brillouin zones for these compounds have not, up to the moment, yielded accurate information on the state of the transition-metal atoms. The results of the measurements of the magnetic susceptibilities of some such compounds are given: from these measurements information on the 3d state of the transition-metal atoms is derived.

A value of 930 ± 70 mbn has been obtained for the proton total reaction cross section for copper at 9.3 ± 0.3 MeV by a poor geometry transmission method not involving counter coincidence techniques. This result, which is in good agreement with values obtained by indirect methods, is appreciably higher than values predicted by published optical model analyses using a volume absorption term. Differential elastic cross sections are presented for the angular range 30°-155° (centre of mass). These were obtained using the same target as in the reaction cross section measurement. Good agreement with both the differential cross sections and the reaction cross section can be obtained using an optical model potential with an absorptive term peaked at the nuclear surface.

An optical model analysis is given of the experimental data of Hintz at 9.75 MeV and of Greenless et al. at 9.30 and 9.47 MeV on the scattering of protons by natural copper. A sufficiently general form factor for the imaginary part W of the optical potential is used such that W can have a maximum value lying in any desired region of the nucleus. It is found that the absorption must be peaked at the surface of the nucleus in order to fit not only the polarization and differential elastic cross section, but at the same time to give the correct magnitude of the total reaction cross section. The available experimental data do not at present allow the determination of how much absorption occurs at the centre of the nucleus or whether the maximum of W should lie slightly beyond the half-way radius of the real part of the optical potential.

The reaction Pt(n, α)Os has been investigated by a nuclear emulsion technique, using the thermal neutron flux of the Pennsylvania State University reactor. A semi-empirical range-energy relationship has been developed for α-particles in platinum and has been used for the evaluation of data. Two groups of alpha particles have been observed with certainty, corresponding to Q-values 6.9±0.3 MeV, and 8.5±0.3 MeV and have been identified with reactions ¹⁹⁴Pt(n, α)¹⁹¹Os and ¹⁹⁵Pt(n, α)¹⁹²Os respectively. A probable group of alpha particles corresponding to Q-value 12.1±0.3 has been associated with the reaction ¹⁹³Pt(n, α)¹⁹⁰Os.

Ilford G5, 400μ thick nuclear emulsion plates were bombarded by a hardened x-ray beam of energy 5-90 MeV. Altogether 54 433 fields of view were examined, the volume of each field of view being 120μ×150μ×220μ. A total of 21 887 pairs, 1935 triplets, 106 quartets, 10 quintets and one sextet have been observed. Frequency of occurrence of multiplets, (quartets, quintet and sextet), together with the energy distribution of the small energy partners of the multiplets have been presented. Possible explanations of the origin of multiplets have been discussed.

The isotope shifts in the singlet resonance line of CdI have been observed. The line was excited by electron bombardment of an atomic beam and the high resolution was obtained with a Fabry-Pérot interferometer. The shifts measured in this line (λ2288 Å) are compared with those previously measured in the intercombination resonance line (λ3261) to show that the specific mass effect is small. Comparisons are made with similar measurements in magnesium, zinc, and strontium.

The rotational analysis of twenty bands of the E-X system of SiS has been carried out. The system arises from a transition ¹Σ⁺ - ¹Σ⁺, and, unexpectedly, no perturbations have been detected in E¹Σ⁺. Constants (in cm^-1) for the state E¹Σ⁺, valid for 0 less-than-or-eq, slant ν less-than-or-eq, slant 7 are as follows: T₀ = 41743.8₆, G_ν = 406.8₃ (ν+½) - 1.95₂ (ν+½)², B_ν = 0.2213₇ - 0.0013₉ (ν+½) - 1·₇₅×10^-5 (ν+½)².

It seems probable that the state E is the ¹Σ⁺ state arising from the configuration...π³ σ² π^*, analogous to the state B¹Σ⁺u of the isoelectronic molecule P₂.

An alternative method for calculating the atom-atom, atom-bond, bond-bond and other polarizabilities in π-electron molecules, originally due to R. D. Brown, is extended to deal with orbital degeneracy. It is then applied to a new discussion of the bond lengths in certain aromatic hydrocarbons. A simple and partly self-consistent method of calculation is developed, which yields results in satisfactory agreement with recent accurate experimental measurements.

The theory of the magnetic properties of iron put forward by Mott and Stevens made a number of assumptions about the band structures of the body-centred cubic 3d transition metals. The purpose of the present paper is to give an account of a theoretical study which has been made to see what could reasonably be expected on fairly general grounds about the band structures. It then becomes possible to see more clearly what innovations are required for the Mott and Stevens theory. The method used is essentially a tight binding method, with the feature that the functions used are not located at lattice sites but are on the links joining nearest neighbour lattice points. It leads to an 8 × 8 matrix for the lattice potential for each value of K. A discussion of the diagonalization of this 8 × 8 matrix is given for a number of symmetry points and directions in K-space, and it is shown that a good deal of valuable information can be obtained from relatively simple ideas. It is also shown that the band structure so obtained is incomplete because two of the d-functions are omitted, and these are then included by perturbation methods. The Mott and Stevens model of iron is shown to follow from assumptions about the results of this perturbation treatment. A discussion is given of the ground state determinantal functions for vanadium, chromium and iron which it is hoped will be of use in interpreting the physical properties of these elements. Apart from the value the theory may have in its application to the above metals, the algebraic treatment provides an elegant example of the effects of symmetry on band structures, previously thoroughly discussed in terms of groups by Bouckaert, Smoluchowski and Wigner.

The electron spin resonance spectra of Gd³⁺ have been measured in gadolinium hexa-antipyrene iodide (HAPI), lanthanum HAPI, and cadmium fluoride. In CdF₂ the Gd³⁺ ions are sometimes in sites of cubic and sometimes in sites of tetragonal symmetry. In the latter the zero field splitting is remarkably small, being about 0.05 cm^-1. In the HAPI there is a large zero field splitting, about 0.98 cm^-1 overall, and even in the undiluted salt the line width is only about 230 gauss, so that it may be suitable for a zero field maser. An Appendix gives a discussion of the general problem of rotation of the frame of reference in which the crystal field is described so that the spin Hamiltonian may be written in a form diagonal in the applied magnetic field. The coefficients have been tabulated for the polynomials involved in the general rotation matrix for the operator equivalents. The polynomials have been plotted as a function of angle. There is also a table of factors to relate some of the untabulated matrix elements of the operator equivalents to the Wigner 3-j symbols.

Electron spin resonance measurements have been made on lanthanon ions in the hexa-antipyrene iodide (HAPI) salts and also in lanthanum trifluoride. At room temperature the HAPI have trigonal symmetry with one lanthanon ion per unit cell but at low temperatures there is a change of crystal structure. For all ions except Ce³⁺ and Gd³⁺ electron spin resonance is observed only at temperatures below the transition. The lanthanon ion in the HAPI at low temperatures and in the trifluoride have rhombohedral point symmetry and there are several ions in the unit cell. Not all ions with Kramers degeneracy exhibited resonance in both salts, and the few non-Kramers cases investigated also exhibited no resonance. In both salts the most extensive measurements were made on Ce³⁺. In the HAPI Ce³⁺ has a remarkably long relaxation time and the spectrum is visible at 90°K. The measurements on Ce³⁺ in LaF₃ are correlated with the theoretical discussion given by Van Vleck and Hebb in 1934.

Thermal conductivity data at liquid helium temperatures, on poly-crystalline rods of three dilute silver alloys (containing respectively 0.55, 0.32 and 0.14 at.% of manganese in solid solution) in magnetic fields ranging from 0 to 25 kilogauss, have been analysed afresh. The electronic and lattice components of the thermal conductivity are separated by the method of Gruneisen and de Haas. It is inferred that the electronic Lorenz parameter L_e (i) is independent of the magnetic field but varies with the temperature in the liquid helium region, (ii) exhibits a minimum at a temperature which increases with the increase in manganese content, and (iii) is much smaller than the normal ` Sommerfeld ' value, but seems to extrapolate to that value at about 1°K.

This behaviour of L_e is explained on the basis of inelastic scattering of the conduction electrons by the magnetic impurity centres having closely spaced energy states, for such an inelastic scattering would contribute considerably to the electronic thermal resistivity while making only a small contribution to the electrical resistivity. Further, since such a scattering cannot occur at 0°K, L_e should approach the normal value at the lowest temperatures.

The general macroscopic description of the electromagnetic behaviour of superconductors and normal conductors is developed and dispersion relations for the frequency dependent material functions are rigorously established. From these dispersion relations expressions similar to the usual sum rules of electromagnetic theory are derived. Using these, Ferrell's proof that the Meissner effect is a consequence of the energy gap is shown to be unsound. Using the complex surface impedance it is shown macroscopically that as a consequence of the Meissner effect the area under the absorptivity curve for a superconductor is less than for the normal state.

The Boltzmann equation for polar semiconductors is solved formally as a series expansion. The form of the collision operator used is that derived by Howarth and Sondheimer. The method of solution is based on an iteration procedure analogous to Neumann's series solution for an integral equation. The solution has been computed numerically as a function of electron-energy-phonon-energy for certain typical combinations of values of the temperature and degeneracy parameters. Guided by these `control solutions' algebraic equations are derived which approximate to the Boltzmann equation in important limiting cases. From these algebraic equations the conductivity and the thermoelectric power are deduced.

Measurements of the infra-red Faraday effect have been made in n-type, p-type and intrinsic germanium. The Faraday rotations observed are interpreted as being due to free electrons in n-type germanium, valence to conduction band transitions in intrinsic germanium, and light and heavy holes and intervalence band transitions in p-type germanium. The rotations obtained for variously doped n-type specimens are used in conjunction with Hall effect measurements on the same specimens to evaluate the Hall scattering constant as a function of the impurity content. In p-type material the rotations obtained are used to estimate the relative population of the light and heavy hole states.

The original theory of thermally stimulated emission is extended to include the effect of a temperature dependent trapping cross section. A method is proposed whereby the ionization energy and temperature dependent capture cross section of a set of identical trapping states may be determined from the half-width and shape of a thermally stimulated emission peak obtained from a single experiment. The method is also applicable to thermally stimulated current peaks if the free electron lifetime varies only slowly with temperature.

Observations are made of the time variation of the intensities of spectral lines emitted by small quantities of impurity ions in a deuterium discharge in ZETA. A vacuum ultra-violet monochromator which covers the wave-length range 500-2000 Å is used. The observations are interpreted in terms of temporal ionization distributions determined for a partially contained plasma model. The observations are consistent with the model and it is shown that plasma containment in ZETA is violated by two processes: an escape of plasma to the wall represented by a loss rate coefficient λ(sec^-1), and an injection of atoms in a neutral or low state of ionization represented by an injection coefficient Λ(sec^-1). The value of λ is effectively independent of the stabilizing magnetic field strength B_z, whereas the injection coefficient varies considerably with this parameter. Both λ and A are closely correlated with , the energy input per unit mass of gas, and over the range of conditions investigated they show a linear increase with . The ion containment time 1/λ is about 100 microseconds at = 3 keV/m_p and at this condition most of the energy input is carried to the walls by the escaping plasma. The net effect of the processes of loss and injection controls the variation of plasma line density, and in general this shows a decrease with time or `pump-out'. This is measured and related to other discharge phenomena.

The first results are reported of experiments new to plasma research, namely time-resolved interferometry in the optical region. It is shown how the electron density distribution of a fast cylindrical pinched discharge may be measured and how the physical conditions in the discharge may be deduced from such measurements.

An adiabatic calorimeter has been constructed for the study of properties of condensed substances in the temperature range 2° to 300°K. Two resistance thermometers were used, one of platinum for T>11°K and one of carbon for T<11°K. The carbon thermometer was calibrated on the thermodynamic temperature scale by using the calorimeter vessel as a gas thermometer; subsequent absolute shifts of its resistance on cycling between room temperature and liquid helium temperatures were taken into account by calibrations against the platinum thermometer.

The heat capacities of solid and liquid argon have been measured between 2° and 86°K with estimated accuracies to ±2% at the lowest temperatures, increasing to ±0.2% for T>20°K but decreasing to ±0.5% at the highest temperatures. In conjunction with these measurements, vapour pressures were measured in the temperature range 66° to 86°K.

The heat of fusion was found to be 284.5±0.4 cal mole^-1, the triple point temperature 83.810°K and the triple point pressure 516.86±0.02 mm Hg. The amount of impurity in the specimen of argon was estimated to be 3 parts per million from a study of the melting range.

Direct measurement of the heat of vaporization of the liquid gave the result 1563.6±4.6 cal mole^-1 at 85.67°K, which corresponds to 1555.0±4.6 cal mole^-1 at the normal boiling point.

The calorimetric methods described in the preceding paper have been used to measure thermodynamic properties of solid and liquid krypton. Besides heat capacities and vapour pressures over a range of temperatures, the following were obtained: heat of fusion = 392.0 ± 2.3 cal mole^-1, T (tr. pt.) = 115.77₆ °K, p(tr.pt.) = 548.7 ± 0.1 mm, heat of vaporization at 116.85 °K = 2179.2±0.9 cal mole^-1 and at the normal boiling point = 2162 ± 1 cal mole^-1.

A number of properties of solid argon and solid krypton has been derived, in particular, the apparent Debye characteristic temperatures at 0°K and as a function of temperature, the heats of sublimation at 0°K, the static lattice energies and the zero point energies. The results of the thermal measurements on the solids have been correlated with expansivity and compressibility results and certain inconsistencies resolved. The calorimetric results are shown to be internally consistent.

The shapes of curves of Θ_D (T) against temperature indicate that anharmonic contributions to the vibrational properties of solid argon and solid krypton are appreciable, particularly in the region T > Θ₀/10.

In the region below the melting points, C_p for both argon and krypton increases rather rapidly with temperature. This is interpreted as an effect of formation of vacancies in the solids. Enthalpies of formation are found to be 1280 ± 130 cal mole^-1 for argon and 1770 ± 200 cal mole^-1 for krypton. These are about two-thirds of values estimated from theory. An effect of vacancy formation may also be seen in the vapour pressures.

The specific heats of cadmium and magnesium have been measured in the temperature range 0.4° to 1.5°K. For cadmium the electronic specific heat coefficient γ is 163.6±2.6 μcal deg^-2 (gat.)^-1, the Debye temperature θ is 204±3°K, and the superconducting transition temperature is 0.52±0.01°K. For magnesium γ is 292.7±2.5 μcal deg^-2 (gat.)^-1. These results show that a previously reported discrepancy between the elastic and thermal values of θ for the hexagonal metals was due to incorrect interpretation of specific heat data.

Aluminium-manganese alloys do not show the resistance-minimum phenomena often found in dilute alloys containing transition metals, but anomalous thermoelectric powers are observed. Alloy systems which do show the resistance minimum also have large specific heat anomalies at low temperatures. It was therefore of interest to see whether specific heat anomalies occurred in the aluminium-manganese system.

Measurements of the specific heat of pure aluminium and of an alloy containing 0.045 atomic% manganese were therefore made in the temperature range 0.4° to 1.5°K. In the normal state the specific heats of the two samples are the same. Thus a specific heat anomaly of the type found in systems showing the resistance minimum does not occur. The superconducting transition temperature of the alloy is about 0.84°K (compared with 1.174±0.002°K for pure aluminium) but the transition remains sharp (width less than 0.001 deg K) and of the second order. The reduced electronic specific heats in the superconducting state C_es/γT_c, when given in terms of reduced temperature T_c/T, are identical.

The vibration spectrum and the specific heats of gold have been studied by two models in order to test whether the electrons participate in the complete vibration spectrum of a crystal. The two models represent the extreme cases given by de Launay, one of which ignores the effect of electrons on the lattice vibration while the other assumes its full participation for all the frequencies. Frequencies have been calculated for the 1000 points of the Brillouin zone and the specific heats have been evaluated by the sampling technique. The choice of this metal for calculation was dictated by the fact that, on account of the large discrepancy in the Cauchy relation, the difference between the lattice frequencies of the two models is expected to be very high. It is found that the central force model does not predict the value of the C_v of the metal at all correctly, while de Launay's model is in qualitative agreement with experiment above 15°K. De Launay's idea that electrons participate only in the non-dispersive region of the spectrum thus appears to be wrong.

Sound absorption and velocity were measured in ethylene at 500 kc/s and 700 kc/s in the ranges 0.07 to 2 atm and -10 to 80°C. All the vibrational modes relaxed out at approximately 1 Mc/s atm, but the assumption of two relaxation times, for the transfer of energy between translational and vibrational motion, fitted the measurements better than the assumption of a single relaxation time. Assuming that the average relaxation time found by fitting single relaxation curves to the measured points was approximately that of the lowest frequency mode, the value of the force constant β in the exponential intermolecular potential was found to be 6.71 x 10⁸ cm^-1. This agrees well with the value 4.72 x 10⁸ cm^-1 calculated from the Lennard-Jones potential.

An exact solution is given for scattering by the potential ρ^-1 in two dimensions. This is compared with the results of the first and second Born approximations for the same potential in an analysis similar to that of Dalitz for the Coulomb potential r^-1 in three dimensions. Seeger and Bross have shown that, in the scattering of conduction electrons by an edge dislocation, the second-order terms diverge logarithmically with increase of the radius of the cylinder in which the potential of the dislocation is assumed to act. Similar logarithmic terms appear in the second Born approximations for the potentials r^-1 and ρ^-1, and, following Dalitz, reasons are given for believing that they represent a phase shift produced by the refraction of the incident and scattered waves, and that they do not contribute to the scattered amplitude. The cross sections for scattering by a dislocation are probably never much greater than those given by the first Born approximation, and may even be smaller. It is not possible to deduce the large values suggested by some experimental observations.

Internal friction measurements have been carried out on specimens of high purity iron from which carbon and nitrogen have been removed. A relaxation peak, observed at about 500°C for a frequency of vibration about 1c/s is associated with the presence of grain boundaries in the specimens. The activation energy Q associated with this damping process is 46 kcal mol^-1. The damping appears to be governed by a term, frequency × (grain size)² exp (Q/RT). The variation of peak damping and background damping is similar to that observed in other pure metals.

Internal friction measurements of the grain boundary relaxation peak have been carried out on alloys of high purity iron containing carbon or nitrogen. The influence of these impurities on peak height, peak temperature and on the activation energy for the mechanism giving rise to the damping has been determined. The results differ from those reported on the influence of substitutional impurities. The explanation of these effects is discussed qualitatively in terms of the boundary sliding and boundary migration mechanisms.

A microwave cavity method has been used to measure the electron loss rate following a pulsed discharge in oxygen-nitrogen mixtures. Preliminary results indicate that, when suitable pressures of oxygen and nitrogen are chosen, the main mechanism of electron removal in the later afterglow is a three-body attachment process. The three-body coefficient K=2.4 × 10^-30 cm⁶ sec^-1 is in good agreement with the drift tube measurements, for thermal electrons, of Chanin, Phelps and Biondi.

In a previous paper by Flynn and Seymour a technique was developed whereby a type of distortion produced by linear apparatus could be corrected rapidly and efficiently to obtain a `true' output signal. The distortion considered was not the most general linear distortion, and several cases of practical importance were therefore excluded.

In the present paper, the general linear distortion is examined and equations are developed which permit the rapid correction of distorted output signals into those to be anticipated from the use of ideal apparatus. The procedure is illustrated by means of an example. The accuracy of the corrected signals is then discussed, and it is shown that in some apparatus, as for instance, the magnetic resonance spectrometer, predictable optimum conditions occur under which the form of the true output signal may best be determined.