Table of contents

As an example of the application of the K-meson production cross section we have considered the K-meson component in the extensive air-showers. A cascade theory of the cosmic-ray shower has been developed embracing the fact that the heavy mesons and hyperons cascade in the nucleus in a manner analogous to the pions and nucleons. Numerical results for the nucleons, pions, hyperons and the K-meson components in the longitudinal development of the cosmic-ray air shower have been presented and compared with available experimental data.

A method of setting up variational density matrices which satisfy the necessary subsidiary conditions is discussed, and some explicit variational forms are presented. Each variational matrix is defined essentially in terms of the density matrix for a known problem, for example a system of free particles in a box, using either stationary wave or progressive wave solutions. The latter form is shown, by suitable transformation along lines suggested by earlier work of Macke, to lead very directly to a method intimately connected with that proposed by von Weizsäcker, and a completely quantum-mechanical variational basis for this method is thereby provided. One- and three-dimensional cases for particles moving in a common potential are considered explicitly, and ways of achieving greater accuracy than is possible with von Weizsacker's scheme are clear, especially in the three-dimensional case. A simple example is worked out in order to compare the results obtained from the various approximate variational forms with the exact density matrix for a linear harmonic oscillator potential, and the results are encouraging.

The electrical conductivity and Hall effect have been measured over the temperature range 20°K to 500°K on single crystals of silicon with extrinsic carrier concentrations between 2 and 5 × 10¹² cm^-3. The Hall mobility for electrons and holes can be represented between 100° and 300°K by the expression 1.2 × 10⁸T^-2 and 2.9 × 10⁹T^-2.7 respectively. Both these results indicate a higher Hall mobility than has been previously reported, and the result for holes is greater than values reported for the drift mobility. From the results between 350° and 500°K the expression n_i = 3.10 × 10¹⁶T^3/2 exp -0.603/kT was obtained for the intrinsic concentration. Attempts were made to estimate the total impurity concentration in these specimens. The variation of extrinsic carrier concentration with temperature and the effect of impurity scattering at 20°K both indicate that the total concentration of impurities is less than 10¹⁴ cm^-3.

The energy of interaction between two normal helium atoms is calculated to the second order using a perturbation method which employs properly symmetrized unperturbed wave functions. The results obtained are in good agreement with experimentally derived interaction energies for both large and small internuclear separations.

A formula is derived and used to analyse measurements of the change of technical magnetization caused by the application of hydrostatic pressure. Some of the changes can be described by a dependence of the ferromagnetic anisotropy energy on pressure. Values are obtained for this pressure dependence in certain nickel-iron alloys and they are found to agree moderately well with estimates made from volume magnetostriction measurements.

Ranges of solid solution have been investigated in systems composed of two A^IIIB^V compounds, particularly GaSb-InSb, GaAs-InAs and InAs-InSb. It is found that in practically all cases considered complete solid solution throughout the whole range of composition can be obtained, but that this equilibrium condition can only be reached under special conditions of temperature and time of annealing. The work includes the investigation of solidus curves and the possible presence of low temperature miscibility gaps.

In all cases, it is found that if normal annealing methods are used, equilibrium can be attained with a reasonable length of time of anneal only in the case of compressed powder specimens. Consideration is given to the methods available for producing alloys in equilibrium in the solid form.

A description is given of Bitter figure, magneto-thermal and Bark-hausen studies of the behaviour of a polycrystalline manganese zinc ferrite during magnetization, from which it is concluded that the processes of magnetization are entirely rotational.

If a moving domain wall crosses a small illuminated area, the reflection coefficient may change and the plane of polarization of the reflected light may be rotated. If the wall moves in an alternating field, the change can be detected by collecting the light on a photomultiplier cell and amplifying the alternating component of its output signal.

Using a specimen of a magnetically annealed Perminvar-type alloy, the variation of the output signal and of the signal-to-noise ratio with the angle of polarization has been shown to agree closely with that predicted by theory, both for longitudinal and transverse magnetizations. It is unnecessary to use both a polarizer and an analyser; indeed, an effect is observable with neither.

The complex domain structures existing in most ferromagnetic specimens prevent precise information about individual domain processes from being obtained from technical magnetization curves. Experiments on ring specimens of a magnetically annealed Perminvar-type alloy show that reversal of magnetization in such specimens involves only one 180° domain wall. Rings of varying external to internal diameter ratio were used, and the hysteresis loops of all specimens could be explained using a simple theoretical model. All specimens except those whose hysteresis loops were controlled by nucleation processes had the same coercive field, 0.09 oersted. This field gave a direct measure of the impedance to motion of an isolated 180° wall.

The experiments also show that the use of a specimen with large external to internal diameter ratio effectively reduces the slope of the sides of the measured (B, H) loop; a close approach to a rectangular loop is possible only in specimens with small radial width. The effects of nucleation are evident in all of the loops, and in the case of the specimens with the smallest radial width, the loop shapes are controlled entirely by nucleation.

An approximate method is given for calculating the magnetostriction of a random polycrystal as a function of the magnetization in the range over which magnetization occurs by rotation of the domain magnetization vectors. Calculations valid for the cases of cubic and hexagonal symmetry (these only for the case in which the easy axis is the hexagonal axis) are given in parametric form. Using these calculations and earlier calculations of Brown for the range of magnetization where boundary displacements occur it is possible to calculate the magnetostriction as a function of magnetization over the entire range from zero to saturation.

The reaction ¹¹B(γπ^-)¹¹C has been studied using bremsstrahlung having peak energies from 70 Mev to 320 Mev, by measuring the activity of the ¹¹C product of the reaction. The cross section for the reaction is in agreement with theoretical values for surface production. An unexplained activity is detected below the energy threshold for meson production.

Corrections to 1958 Proc. Phys. Soc.71 533