Table of contents

A review lecture on the possible application of Regge poles to the analysis of high energy elementary particle diffraction scattering.

A review lecture on the theoretical interpretation of elementary particle resonances. The generalization of isotopic spin to invariance under the group U₃ is discussed and a number of predictions of the Sakata model and `eightfold way' are illustrated. Various dynamical models of the resonances are described and some suggestions made about the implications of the mass splitting within particle multiplets.

This paper contains no new results, but aims at expressing the new notion of unitary symmetry in terms of familiar concepts.

The physical restrictions imposed by U₃ invariance are expressed in terms of isotopic spin and generalized charge symmetry operations. The simple multiplets are developed. As examples, meson-Sakaton scattering is expressed in terms of three invariant amplitudes, and relations are found for the decay of a Sakaton-antiSakaton pair into two bosons.

Tables are presented of decay probabilities for ρ, ω and K* particles for various spin and parity assignments.

The present state of the experimental evidence for elementary particle resonances, other than the pion-nucleon resonances, is presented. The properties of the four pion-hyperon resonances, as well as those of the K*, ρ, ω, and η mesons, are discussed. Emphasis is placed on the experimental determination of the spin, parity and G parity of the ω and η particles.

A review of high-energy proton-proton and pion-proton elastic scattering experiments and inelastic scattering with small inelasticity.

The fracture strength of diamond can be measured by the critical average stress required to produce a ring crack on a diamond surface with a spherical impacter. By using impacters of different sizes and materials, an inverse strengtharea relationship has been established for diamond.

This relationship and the similarity between it and that found for glass add to the indications, already reported, of a possible flaw distribution in diamond. Evidence is given that, if such a distribution does exist, it is likely to consist of flaws bigger than point defects.

The energies of the 1s2s ³S and ¹S excited states of an atom of nuclear charge Z are calculated in the form of a series in ascending powers of 1/Z. The first four terms in the series for these non-relativistic, but otherwise exact, energies are obtained numerically; the corresponding zero-order and first-order wave functions are calculated - the zero-order function exactly, and the first-order function by a variational method, up to twelve variable parameters being taken. The energies of these same states are also calculated within the Hartree-Fock scheme. A common misunderstanding in the Hartree-Fock equations for the excited singlet state is corrected, and then the zero-order and first-order wave functions are calculated exactly. Formulae are obtained from which, by numerical integration, these Hartree-Fock energies may be computed in a power series similar to that for the exact energy. Electron correlation is very small for the triplet, but larger for the singlet. But both values are much less than for the 1s² ground state.

An attempt is made to determine with high accuracy the effect of configuration interaction in the second-order term in the expansion of the energy of the ground state of the two-electron systems in inverse powers of the nuclear charge. The equations for the separate angular harmonics of the first-order wave function are solved variationally using expansions in terms of one-electron orbitals, with the object of examining the rate of convergence as the number of orbitals in the trial solution is increased. The convergence of the harmonic expansion is found to be slow, the contributions falling off as 0.35 l^-4. The radial expansion is also slowly convergent particularly in the case of the high-order harmonic contributions, l >or= 5.

Comparison with the similar calculation carried out by Schwartz in 1962 using an expansion in terms of Hylleraas coordinates indicates that the interelectron separation is a basis function which gives accurately the contributions of the high-order harmonics to the second-order correlation energy.

The calculations show that the contributions to the second-order energy from radial and angular correlation are -0.0286 and -0.0647 rydberg respectively compared to the Hartree-Fock contribution, -0.2220 rydberg.

The rate at which helium atoms are exchanged between liquid helium II and its vapour is discussed and compared with the rate at which momentum is exchanged between liquid and vapour. Evidence is drawn from existing experiments on evaporation, second sound, and film flow, and it is concluded that the vapour exchanges momentum with the normal fluid only.

The variational approach to a many boson system suggested by Edwards and Naqvi is carried through by the explicit evaluation and variation of the energy using a simple choice of variational function. The trial function is very crude in comparison with that required for an adequate discussion of liquid helium but still a true many-body function, and the comparison of the result with the experimental constants of liquid helium is adequate considering this crudity.

The average work functions of vacuum-deposited uranium films and of uranium foil have been measured by the Kelvin contact potential difference method, under ultra-high vacuum conditions. The reference surface was that of well-aged polycrystalline tungsten. A reproducible value of 3.203 ± 0.013 ev was found for the work function of the vacuum-deposited films. In the case of the foil, the work function increased continuously and monotonically with the duration of electron bombardment, eventually reaching a limiting value of 3.080 ± 0.005 ev after about thirty-three hours' bombardment. Reasons are put forward for believing that the surface of the foil may not be that of clean uranium, but of a patchwork of uranium and uranium monoxide.

The average work functions of vacuum-deposited thorium films and of thorium foil have been measured by the Kelvin contact potential difference method, under ultra-high vacuum conditions. A reproducible value of 3.455 ± 0.012 ev was found for the work function of the vacuum-deposited films. In the case of the foil, the work function increased continuously with the duration of electron bombardment, eventually reaching a limiting value of 3.728 ± 0.010 ev after ninety-seven hours of bombardment. Reasons are discussed for identifying this value with the average work function of well-aged, polycrystalline thorium.

Experimental equipment has been developed for the measurement of spin-spin (T₂) and spin-lattice (T₁) relaxation times in electron resonance by the transient method at 3.21 cm wavelength. T₂ values down to approximately 1 μsec can be measured. The values of T₂ and T₁ for solutions of lithium, sodium, potassium and calcium in ammonia have been measured over a range of concentrations at 23° c. T₁ and T₂ are equal within the experimental error except for potassium over a limited range. They both increase from about 1.0 μsec to about 3.5 μsec with falling metal concentration, and agree with measurements at lower frequencies where these are available. The approximate equality of T₁ and T₂ at this high frequency, which compares with previous measurements in the region of 30 Mc/s, puts an important limit on the correlation time for the electron relaxation mechanism and supports the theory that the electron interaction is a scalar coupling with the nitrogen nuclei.

An attempt was also made to measure the electron self-diffusion constant from the echo decay in a high field gradient. It is concluded that this is not greater than 10^-2 cm² sec^-1 but is probably faster than the diffusion of the ammonia molecules.

The work reported here was initiated following some preliminary measurements on ultra-violet irradiated lithium hydride when it was found by Doyle et al. in 1959 that the formation of ultrafine colloidal particles of lithium could be followed by electron resonance techniques.

The electron spin resonance measurements on powdered and melted samples of silver bromide irradiated with x-ray, ultra-violet or optical light also showed that the irradiation products were colloidal particles of silver metal less than 10^-4 cm in diameter. The results are discussed in relation to the similar experiments on irradiated lithium hydride where the size of the colloidal particles of lithium metal can be calculated, and the potentiality of such measurements as a method of studying the initial stages of latent image formation is considered.

It has been suggested that, in addition to the usual secondary ionization processes due to the action on the cathode of positive ions and undelayed radiation, a number of other secondary and collisional processes must be taken into account in the rare gases. These processes include the conversion of atomic ions into molecular ions, metastable atoms into metastable molecules, and the transition of atoms from metastable and resonant states with production of undelayed photons. Moreover, it has been suggested that the transfer of resonant photons through the gas takes place in accordance with the Holstein-Biberman theory, and also that delayed radiation (that is, radiation from excited states which have a long lifetime) may be of importance. On the assumption that all these processes are acting, formulae are derived in the present paper for the current growth, between parallel plates, due to specified causes of experimental interest, such as an externally generated cathode electron current of given strength, maintained since time zero, or the liberation of a single electron at time zero. The procedure by which these formulae are derived is general, and is not confined to the particular processes enumerated above.

The growth of pre-breakdown currents in uniform field conditions in sulphur hexafluoride at different pressures for values of E/p in the range of 90 to 160 v cm^-1 mmHg^-1 (5-200 mmHg pressure) indicates very large electron attachment. It is assumed that the mechanism of negative ion formation is due to dissociative attachment; therefore values of α and the dimensionally equivalent attachment coefficient η have been computed from the semi-logarithmic plots of current against electrode separation by employing the modified Townsend equation for the growth of current. Further, static breakdown potentials have been measured up to a value of pd (pressure × gap length) similar 400 mmHg cm, and a comparison with the data for dry air gives the relative dielectric strength of SF₆ as about 2.8 at 380 mmHg cm.

The segregation coefficients and electrical behaviour of the group IVB elements in aluminium antimonide have been determined. Crystals were grown by the Czochralski technique using pulling rates of 0.5-1 in. hr^-1 and a rotation rate of 15 rev/min. Values found for the effective segregation coefficients are: silicon, 0.04₅; germanium, 0.02₆; tin, 2-8 × 10^-4; lead was abnormal and cannot be specified by a single coefficient, the results corresponded to values of 10^-4 to 10^-3. With the exception of tin all the elements were acceptors. Tin appeared to occupy both aluminium and antimony sites.

The diffusion constant of zinc in n- and p-type aluminium antimonide has been measured in the temperature range 660-860 °C by a radio-tracer technique. At high donor concentrations the diffusion constant is found to decrease. The diffusion constant is given by

D = 0.33 exp(-1.93/kT)cm²sec^-1

when it is independent of doping level. A model is proposed for the diffusion mechanism.

A detailed study of the isolated modes due to a variety of defects in one-dimensional two-component vibrating systems is made. A version of an analytic method outlined by Montroll and Potts in 1955 is used to deal with the localized modes associated with the simpler types of defect. More complicated defects can be treated in the same way, but the analysis becomes inconveniently complex, and a numerical approach already extensively used in a similar connection by Dean in 1959 and 1960 is preferred. It is found that a relatively few general rules describe all the results; these rules may be used to obtain much information on the spectra of a wide variety of one-dimensional systems.

A Schlieren optical system has been used to measure the pressure Δp (by its effect on the refractive index) induced in non-polar isotropic liquid dielectrics by the application of an electric field E. All the results agree with the equation which is derived from the theory due to Helmholtz, Δp = E²(-1)(+2)/24π where is the permittivity of the liquid, and not with the equation based on the theory of Livens.

A calculation has been made of the electric fields at the ionic sites in the lattice of rutile (TiO₂, tetragonal) due to induced dipoles at all the other sites. Following Lorentz, we divide the field at any site into two parts, one due to the distant dipoles outside a large cavity and the other due to the dipoles inside the cavity. A careful analysis has been made of the influence of the shape of the cavity. For accurate calculations in non-cubic crystals, a sphere (chosen by Lorentz) is not suitable but a rectangular cavity similar to the unit cell offers an excellent means of obtaining the accurate values for the fields. Rutile has a large refractivity and a large positive birefringence, both being dominated by the oxygen ion polarizability. The refractive indices cannot be explained if the oxygen ion polarizability is isotropic, but they can be explained if we introduce an anisotropic polarizability. The anisotropy is linked to the crystal structure.

The magnesium hydride bands at 2172, 2100 and 2088 Å (in absorption) and the magnesium deuteride bands at 2172, 2358 and 2364 Å (in emission) have been observed and analysed. Their rotational constants are calculated and a correlation of the molecular states of MgH to the atomic states of Mg is made. The predissociation of some of the molecular states is discussed and it is proposed that this is caused by a ⁴Σ term and not by a ²Σ term as proposed by earlier workers.

A direct determination of the metrical thickness of mono- and multi-molecular films of barium stearate has been carried out with the use of multiple beam interferometry. The thickness of the unimolecular film, as obtained from measurements on a four-layer film, is 25.7 ± 0.3 Å which is in excellent agreement with the length of the molecular chain of barium stearate (=25.75 ± 0.25 Å) as obtained from Fankuchen's X-ray data. The technique employed eliminates differential phase change effects and does not involve the refractive index of the films. The result confirms the monomolecular spreading of stearic acid on a water surface.

The Boltzmann equation for the distribution of conduction electrons in the presence of a temperature gradient, given by McIrvine, is derived by the method of successive approximation to the equations of motion of the density matrix. Some additional `intercell' scattering terms appear.

The Schottky specific heat anomaly of gadolinium sulphate octohydrate is calculated from the recent microwave measurements of the ground-state splittings. The results are tabulated for a number of temperatures between 0.05° and 4.0 °K, together with values of the partition function and entropy. The agreement with measurements of specific heat is good provided that the S_z = ±½ state of the multiplet is lowest in energy, or in other words that the coefficient of S_z² in the spin Hamiltonian is positive.

The magnetic transformation in natural crystals of haematite at low temperatures has been studied in relation to the titanium content, using the electron shadow method. Spectrochemical analyses show that 0.2% titanium is sufficient to depress the transition to -85 °C. In those cases where no transformation was detected on cooling to -180 °C. it was found that the titanium content was at most 1%. These results differ considerably from those obtained by previous workers using synthesized specimens.

An anisotropic absorption edge observed at low temperatures in the electron spin resonance spectrum of Fe²⁺ in zinc fluosilicate is attributed to a `forbidden' (ΔM = 2) transition within an excited doublet. The measured value, g_|| = 2.38, is interpreted in terms of a trigonal crystalline field component some four times smaller than that deduced from susceptibility measurements on the undiluted ferrous salt. Confirmation is obtained from measurements made in the perpendicular plane where the doublet is split by a second-order Zeeman effect. The results of experiments on mixed Fe-Zn crystals point tentatively to a gradual variation of trigonal field strength with Fe²⁺ concentration.

The magnetic properties of FeCl₂, in which neutron diffraction experiments show that the metal atoms form ferromagnetic layers with alternate layers aligned antiparallel, are calculated using the Bethe-Peierls method. Account is taken of a ferromagnetic interaction of strength J_F between nearest neighbours in a layer and an antiferromagnetic interaction of strength J_A between next nearest neighbours in adjacent layers. Expressions are obtained for the usual thermodynamic functions as well as the critical scattering cross sections and are compared with experimental observations. The magnitudes of the interactions are found to be J_F = 8.53K, J_A = 0.69K, and with these values reasonable agreement is found between theory and experiment.

A general theory is given of the modes of operation and performance limits of semiconductor conduction counters. The magnitude and shape of the current pulses in an external circuit are derived for a number of different sets of circuit and semiconductor parameters. The various factors limiting energy resolution are discussed in turn, the effects of thermal and current noise being compared with the linewidth due to incomplete charge collection. For radiation absorbed at random in the volume of a counter, such as occurs with gamma rays, incomplete charge collection is likely to be the principal limitation on resolution.

The best methods of approximating to the ideal counter assumed in Part I are discussed with particular reference to electrode systems. The construction of silicon counters to operate at 78 °K is then described, followed by performance data for α-particles, β-particles, protons and γ-rays. The best resolutions defined as the standard deviation divided by the mean signal are 2.6% for 30 MeV protons, 5.2% for 620 kev β-particles and 5.8% for 1 MeV γ-rays, which, when compared with the predictions of Part I, lead us to believe that short range inhomogeneities in our counter material make the greatest contribution to line broadening. The measurements described enable direct determinations of carrier drift lengths in silicon and of the field dependence of mobility for `hot' electrons to be made. They also provide information about the results of heat treatment of high resistivity silicon.

The mean-square breadth of a deliberately truncated portion of a diffraction line has been suggested as a measure of particle size by Tournarie. Tournarie's theory is generalized to include other causes of line broadening. For small particle size it is shown that the mean-square breadth in 2θ can be expressed in the form

W₂₆ = (Kλδ(2θ)/2π²p cosθ) - (Lλ²/4π²p²cos²θ)

where p is the cube root of the particle volume, Δ(2θ) is the range of 2θ used in evaluating W_2θ, K is a quantity analogous to the Scherrer constant, and L is a quantity, for which the name taper parameter. is proposed, depending on the rate of decrease of the area of cross section of the crystallites in the hkl direction. For non-spherical crystals both K and L are functions of hkl; they are evaluated in terms of hkl for certain simple crystal shapes and Tournarie's numerical values of K are confirmed.

Correction to Proc. Phys. Soc.77 1175.