Table of contents

In this lecture the case is made for the investigation of various beams of heavily ionizing radiations with a view to their eventual use in radiotherapy. Beams of heavy ions and stopping π^- mesons are considered, and the probable oxygen enhancement ratio and distribution of dose with depth are compared with ⁶⁰Co γ rays and other beams in current use. Beams of stopping π^- mesons give an excellent distribution of dose with depth, and a very favourable oxygen enhancement ratio. The feasibility of preliminary experiments with biological material is considered.

The intrinsic resolution of ten activated alkali halide crystals has been measured over an energy range of 30 kev to 1 Mev. After subtracting the contributions to resolution due to non-proportionality of electron response and to delta rays, a residual resolution is left which consists of an energy dependent term and an energy independent term. The existence of the energy dependent term is not in agreement with the work of Prescott and Takhar, and shows that the variance of the photons produced in the scintillation process is greater than normal. The energy dependent term is sensitive to strain and to the surface condition of the crystal.

Employing a 2.5 curie ¹³⁷Cs source, total elastic scattering cross sections in Pb, Pt, Ta, Sn and Zr were determined using a collimator geometry similar to that of Wilson at angles 20°, 30°, 45°, 60°, 75° and 90°. The experimental results were compared with theoretical values obtained from the form-factor formula of Bethe and exact calculations of Brown et al. The experimental values in Pb, Pt and Ta are in conformity with the theoretical values calculated from Brown et al. data. The experimental values in Sn and Zr show good agreement with form-factor values.

The total atomic cross sections are determined in carbon, aluminium and copper at photon energies of 145, 129, 100 and 84 kev by the transmission method in good geometry. The values of bound-electron inelastic scattering cross sections σ_b are extracted by subtracting the theoretical sum of photoelectric and coherent scattering cross sections from the total cross section. The values of σ_b are also calculated theoretically using the S(q, Z) values based on the Thomas-Fermi atomic charge distribution. The free-electron incoherent scattering cross sections σ_f are computed from the Klein-Nishina formula. Good agreement is obtained between theoretical and experimental ratios of σ_b/σ_f for carbon and aluminium at 145 kev and carbon at 129 kev. Deviations from experiment, increasing with atomic number and decreasing energy, are observed in all other cases and are ascribed to the systematic errors inherent in the Thomas-Fermi atomic charge distribution.

Angular distributions and excitation functions for the ¹⁰B(³He, α₀)⁹B and ¹⁰B(³He, α₁)⁹B* (2.34 MeV) reactions have been measured for ³He bombarding energies between 2 0 and 10.0 MeV. Differential cross sections have been determined. The angular distributions vary smoothly with energy and show a tendency for both forward and backward peaking. The α₀ angular distributions and the excitation function measured at 150° (lab.) indicate a strong resonance, with Γ similar 1 MeV, at 5.8 MeV bombarding energy, corresponding to an excitation of 26.1 MeV in the ¹³N system; but the α₁ data do not show a similar resonance. The occurrence of minor structure in the excitation functions with period of approximately 2 MeV may be evidence for compound nucleus fluctuations. The results suggest that the reaction proceeds mainly by direct processes with a competing resonance process at 5 8 MeV.

The 992 kev resonance of the ²⁷Al (p, γ) reaction has been re-examined with particular attention to the decay of the 7.80 Mev level of ²⁸Si.

Cross sections for electron capture from the ground state of atomic hydrogen into final 1s, 2s, 2p_x and 2p_z states of H and He⁺ by protons and alpha particles respectively are calculated in a second Born approximation, for a model problem in which there is no interaction between the heavy particles and the intermediate states are restricted to lie in the continuum.

In a previous paper by the author OBK cross sections were defined and calculated for H ⁺ + A(^2S+1L) → H(1s, 2s) + A ⁺(^2Ś+1Ĺ) using the atomic orbitals calculated by Tubis. In the present paper the atomic orbitals of Roothaan and Kelly are used in a more extensive calculation of these OBK cross sections for impact energies from 15 keV to 10 MeV. The cross sections are evaluated for the following cases: A = O(³P; 2p⁴): A ⁺ = O ⁺(⁴S, ²D, ²P; 2p³), A ⁺ = O ⁺(⁴P, ²P; 2s2p⁴) A = N(⁴S; 2p³): A ⁺ = N ⁺(³P; 2p²), A ⁺ = N ⁺(⁵S, ³S; 2s2p³). In the important cases of p-orbital capture, the new cross sections are less than the former values from 100 keV to 900 keV, and larger elsewhere. The old values do not exceed the new values by more than 30%. A comparison of the cross sections for 2p- and 2s-orbital capture shows that 2s capture is dominant for impact energies in excess of several MeV, and that 2s capture is not negligible at all lower impact energies. The definition of the OBK cross section is extended to include electron capture between single charged, many-electron ions and atoms. The Born prior and post cross sections are evaluated using Tubis orbitals for capture into H(1s) for A = O(³P; 2p⁴), A ⁺ = O ⁺(⁴S; 2p³). Although the energy dependence is not radically different from the Born estimates obtained using the ratios R(H; He) and the author's OBK cross sections, the magnitudes exceed the OBK values for impact energies less than 1 MeV. These Born cross sections are asymptotically equal to 0.592 QBK(⁴S) at high impact energies.

The cross sections for Na(3s) +X → Na⁺ +e +X, in which X is a proton or an electron, are calculated by the first Born approximation. In the proton case the cross section obtained passes through a maximum of 1.9 × 10^-15cm² at an impact energy of 7.6 keV, and in the electron case it passes through a maximum 5.6 × 10^-16 cm² at an impact energy of 14 eV.

It is pointed out that the approximating expressions for the electronic energy levels of the ion as a function of the internuclear separation R, which have been obtained by Dalgarno and Lewis and by Robinson, should be expected to be good for large R but not for small R. By adopting a slightly different point of view new formulae can be obtained for small R.

Numerical one-centre self-consistent field wave functions are computed for S1H₄ for several values of the bond length using both a spherical and a non-spherical approximation. A ground-state energy value of -290.8 A.U., an equilibrium bond length of 2.78 A.U. and a `breathing' force constant of 0.65 A.U. are calculated for the non-spherical approximation; the corresponding experimental values are -292 1 A.U., 2.80 A.U. and 0.73 A.U. respectively. Theoretical values are also determined for the electronic charge density, multipole moments, diamagnetic susceptibility and polarizability. Comparisons are made with other theoretical work and experimental results where available.

Conventionally, the theory of boundary scattering ignores the dependence of the reflection coefficient (p) on the electron wave vector. An alternative possibility, that the reflection coefficient changes abruptly from 1 to 0 when the change of wave vector on specular reflection exceeds a certain value, is explored here. An important consequence is that, as recently observed in bismuth, the effective conductivity does not decrease continuously with thickness of the conductor, but tends to a limit. The problem is considered for both spherical and ellipsoidal Fermi surfaces and the predictions are compared with those of earlier theories.

A method is given of calculating the total dipole moment in a lattice of polarizable dipoles by using the symmetry of the lattice. For helical symmetry a transformation matrix is used to calculate the value of any dipole m_n* in terms of the origin dipole. The resulting expression is then substituted an equation that enables the components of m₀* to be obtained in terms of a series expansion of the coordinates of the dipoles m_n*. The value of m₀* is then used to calculate the lattice energy. A correction is thereby derived for an earlier calculation by Arridge and Cannon for the α helix of poly-L-alanine.

An approximation equivalent to a generalized Kikuchi approximation is used to study antiferromagnetic behaviour on a triangular lattice using the Ising model. A method of solution is obtained for both antiferromagnetic and paramagnetic phases both in zero and non-zero magnetic fields. Various physical properties are computed and compared, where possible, with the only known results which are in zero field. The critical curve dividing antiferromagnetic and paramagnetic regions is obtained and compared with other approximations and its conjectured form.

An approximate method is used to evaluate the properties of a lattice gas with hard sphere repulsions on a triangular lattice. The method produces a first-order transition.

Calculations are presented of the upper critical field H_c2, the surface nucleation field H_c3, the slope of the magnetization curve and the free energy near H_c2 and the lower critical field H_c1. The free energy of the vortex lattice in which the flux penetrates a bulk type II superconductor depends on the orientation of the lattice relative to the principal axes of the Ginzburg effective mass tensor. The explicit form of this orientation effect is given only for a mass tensor with nearly equal principal values. The remaining results can be summarized in the statement that the parameter κ is anisotropic.

Experiments with unpolarized neutrons on random domain single crystals are unable to distinguish between a simple spiral model and a transverse sinusoidal spin arrangement for the chromium magnetic structure above the low temperature transition. The polarization of the diffracted beams from the {100} satellite reflections of a chromium single crystal, which had been cooled through the Néel point in a strong magnetic field, have been analysed on a three-crystal polarized beam diffractometer. The observations are inconsistent with the simple spiral model and require for their interpretation a model in which each domain has orthorhombic symmetry with axes parallel to the ⟨100⟩ directions: in particular they are in agreement with the model in which each domain contains two sinusoidal spin arrangements with unequal populations, each oriented along a ⟨100⟩ direction. These inequalities, however, were far smaller (≃10%) than the inequalities in domain population (2:1) produced by the cooling field. The preferred spin direction within each domain is that ⟨100⟩ direction most nearly perpendicular to the magnetic field direction, whereas the induced domain population appears to be related only to the shape of the specimen.

The concept of the necessity for equal numbers of electrons of opposed spins in the immediate surroundings of each diamagnetic tetrahedral cation, combined with linear super-superexchange interactions between octahedral cations, leads to a theoretical magnetic structure which is identical with that found by neutron diffraction for GeNi₂O₄ by Bertaut et al. in 1964. This equality of spins gives rise to the coupling between the two interleaved antiferromagnetic lattices, the main coupling within each lattice being provided by the super-superexchange interactions.

The variation of the period of the magnetic orderings in the heavy rare earth metals with temperature and over the series of metals and alloys is calculated with the free-electron model and a δ-function type exchange interaction between the conduction electrons and the localized spins. The total energy and then the period are calculated numerically as functions of two parameters which characterize the long-range order and the spin-disorder scattering. The results of the calculation agree qualitatively with the experimental variation. However, the exchange interaction constant, the only adjustable parameter in the theory, cannot be uniquely determined.

Measurement of the spin-wave specific heat of two antiferromagnetic salts CoCl₂6H₂O and NiCl₂6H₂O is reported in the temperature range 0.7 °K to 4.0 °K. The temperature dependence of the specific heat of both salts is that which would be predicted by spin-wave theory were the energy gap in the spin-wave dispersion relation less than or equal to approximately half the value obtained by antiferromagnetic resonance. The presence of states within the spin-wave energy gap is discussed.

The contribution to the interaction free energy of a pair of substitutional impurities in a ferromagnet due to the distortion of the spin-wave spectrum is evaluated by second-order perturbation theory. It is shown that the leading term in this interaction at low temperatures is attractive and leads to a short range force whose form can be evaluated analytically for large distance of separation between the impurities. This interaction vanishes at absolute zero of temperature.

The scattering of phonons from a substitutional impurity in a simple cubic lattice is studied in detail. The scattering amplitude is expressed in terms of partial waves characterized by the irreducible representations of the point group of the lattice, and the total scattering cross section is found by using the optical theorem. The condition for occurrence of resonances in each partial wave amplitude is investigated. In an appendix, a table of the Green's function integrals for a simple cubic lattice is given.

The Woolley effective molecular partition function solved for a Rydberg potential is used to calculate the ideal dimensionless internal and free energies of molecular nitrogen in the temperature range 3000 °K by 1000 degK intervals to 25,000 °K allowing for 24 molecular electronic levels. The results are presented in tabular, graphical and polynomial form.

The significant increase in these calculated ideal properties over those of other workers is demonstrated and discussed.

The velocity of longitudinal ultrasonic waves in solid argon has been measured in the range 54 to 83 °K, using the diffraction of light technique. Extrapolation of the results gave for the longitudinal velocity at 0 °K ν₁(0) = (16.3 ± 0.5) × 10⁴ cm sec^-1, a value about 7% greater than that obtained by Barker and Dobbs in 1955 by a standing wave method. Using the new figure in conjunction with the Debye temperature obtained by Beaumont et al. in 1961 from specific heat measurements, the transverse velocity, compressibility, and Poisson's ratio at 0 °K are found to be, respectively, ν_t(0) = (9.4 ± 0.2) × 10⁴ cm sec^-1, k_T(0) = (3 84 ± 0.21) × 10^-11 cm² dyn^-1 and σ(0) = 0.25 ± 0.03.

Plasma composition calculations in the local thermodynamic equilibrium approximation are carried out for an argon plasma at high densities. These calculations are then applied to the consideration of the radiative transfer in a homogeneous plasma of spectral lines broadened alternatively by the thermal Doppler effect or the Stark effect produced by electron impacts. In particular the results are contrasted for lines emitted by ionized species and it is shown that the nature of impact broadening sets an absolute upper limit to the optical depth which can be achieved for a given path length and transition, regardless of plasma conditions. Under certain conditions this consequence of impact broadening also results in the peak height of an optically thin line emitted by an ion being of interest for determinations of the plasma temperature.

Space- and time-resolved spectroscopic measurements have been made on arcs of 10-30 nsec duration and 30 A peak current in a coaxial-line spark gap of 0.2 mm width, filled with hydrogen or nitrogen of 2 atm pressure. Breakdown in the glow mode led to cathode current densities of the same order as predicted from low-pressure data by the j ∝ p² law. No radiation due to electrode vapour could be seen. Breakdown in the arc mode, with cathode current densities exceeding 10⁶ A cm^-2, was accompanied by (a) plasma continuum radiation and (b) lines due to excited gas particles, both uniformly distributed across the gap, and (c) lines due to excited tungsten cathode material, appearing near the cathode mainly at the (abrupt) end of the current pulse and propagating like a wave across the gap with a velocity of 2 × 10⁶ cm sec^-1. No lines due to the nickel anode could be seen.

These observations strongly indicate the existence of a high-pressure gas and vapour sheath in front of the cathode, compressed by the positive ions drifting in the cathode fall field. The findings should be of some significance for the theories of the cathode processes in metal arcs, and for the construction of pulsed light sources.

The avalanche current resulting from the release of a short (30 nsec) pulse of photoelectrons (5 × 10⁴) at the cathode of a uniform field gap (5 cm) is observed experimentally. By this technique the drift velocities of electrons (v_-) and of positive ions (v₊) are measured. In dry air in the range E/p = 50-100 v cm^-1 torr^-1 at temperature 20 °c, v- = 256 × 10³E/p + 5 × 10⁶ and in water vapour in the range E/p = 55-85 v cm^-1 torr^-1 at 20 °c, v- = 255 × 10³E/p + 8.9 × 10⁶, with units cm sec^-1 and v cm^-1 torr^-1. The values of v- obtained for dry air fit the values calculated by Heylen and are higher than those measured with the magnetic-deflection method by Townsend and Tizard.

The mobility of positive ions in dry air, which is constant in the range E/p = 45-70 v cm^-1 torr^-1 and is equal to 2.2 × 10³ cm² v^-1 sec^-1 (at 1 torr and at 20 °c), gradually decreases at higher E/p values. In water vapour the mobility of positive ions was constant over the measured range E/p = 50-90 v cm^-1 torr^-1 and is equal to 0.61 × 10³ cm² v^-1 sec^-1 (at 20 °c and at 1 torr). In humid air the value of mobility is lower than the value calculated from Blanc's law. This suggests a clustering of ions.

From an analysis of electron pulses in liquid argon produced by α particles the average energy required to form an ion pair is evaluated, assuming Jaffé's theory of columnar recombination is valid. The mean value of 26.0 eV found in this way agrees well with the corresponding value of 26.4 eV for α particles in argon gas. Application of Jaffé's theory to the liquid state is discussed, and from the pulse distributions it is established that the experimental results are in good agreement with this theory.

Attention is drawn to a possible misuse of the Green function in solid state physics and authors are asked to give fuller justifications of certain approximations.

Departures from the known linear dependence of annihilation rates on gas pressures are described. The annihilation rate per unit pressure in argon is increased by the addition of methane, a thermalization effect which confirms the strong velocity dependence of annihilation for very slow positions in argon. In nitric oxide the annihilation rate varies as a₁p + a₁₁p² where p is the pressure and a₁, a₁₁ are constants.

The correct equation for the transport balance in a Trennschaukel or swing-separator is given and solved. The results are applied to Fischer's data on a H₂-CO₂ system for a simultaneous and accurate determination of the thermal diffusion factor and mutual diffusion coefficient of this system. The merits of this new method of diffusion measurement are pointed out.

Analytic Hartree-Fock functions have been used to make ab initio calculations of the fine structure separations of the 1s²np²P, n = 2 and 3, states of the three-electron systems. Satisfactory agreement with experiment is obtained except in the case of the lightest elements.

A generalized perturbation procedure is outlined which allows the interactions, induced by some potential, amongst a set of neighbouring energy levels to be treated exactly whilst the interactions between these levels and other more distant levels can be included as perturbations to any desired order. The procedure gives the usual results of both non-degenerate and degenerate perturbation theory as special cases.

Weinbaum's treatment of the ¹Σ_g⁺ state of H₂ is adapted to calculate the ground state electronic wave function at several internuclear distances.