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A general spin operator, a function of the so-called step-up and step-down operators, is suggested which when operating on the eigenfunctions of the total S_z operator related to maximal, minimal and zero projections of the total spin creates each eigenfunction of the total S² corresponding to its different eigenvalues.

In the first part of this paper a spin operator was introduced which when operating on the eigenfunctions of the total S_z operator related to maximal, minimal and zero projections of total spin creates each eigenfunction of the total S² corresponding to its different eigenvalues. In this second part a brief discussion of the proposed operator technique developed for the problem of six-electron system is presented.

The fusion of hydrogen and deuterium catalysed by muons was observed by Alvarez et al. Events were seen in a bubble chamber in which the muon was re-emitted with the energy released in the fusion process. In the experiments described here the γ-rays from the fusion process were detected and a measurement made of their time distribution. The yield of γ-rays was found to be 0.34±0.06 per muon stopping in liquid hydrogen enriched with 1.8^o_o of deuterium. A comparison with the results of Alvarez et al. gives an internal conversion coefficient of 0.066±0.014. The analysis of the time distribution enables the following limits to be set on the two reaction rates involved: 0.19×10⁶ sec^-1<λ_slow<0.88×10⁶ sec^-1 0.55×10⁶ sec^-1<λ_fast<2×10⁷ sec^-1.

A comparison with theory shows that it is not possible to assign them to particular processes in the chain of events following a muon stopping in the enriched mixture.

Problem of perturbed boundary condition is reduced to an equivalent problem of perturbation potential with the introduction of a deformed coordinate system. The method is applied to determine the energy of a nucleon in a rigid ellipsoidal box.

The theory of angular correlations is reformulated using the algebra of tensor operators. This has important advantages resulting in considerable simplifications: (1) It enables us to deal in a uniform manner with all polarization problems for both particles and photons, leading automatically to expansions in terms of the most natural functions for any particular problem. (2) We expand the intensity directly in terms of spherical harmonics, rather than `squaring' the expanded amplitude. (3) We avoid the quite unnecessary explicit introduction of sums over magnetic quantum numbers of products of Wigner coefficients and their subsequent elimination by means of cumbersome algebra. (4) In this procedure, the reduced matrix elements of certain tensor operators (formed from the polarization tensors) are calculated once and can then be used in all problems, since any angular correlation can be expressed simply in terms of these reduced matrix elements.

The resonance scattering of the ⁴⁸V 990 kev gamma rays in titanium was observed using the recoil of the previous transition to restore the recoil losses. From the measured scattering cross section, the mean life of the 990 kev level was found to be (6 ± 2) × 10^-12 sec, which is rather shorter than the Coulomb excitation value.

Extending the comparison of mean lives as obtained by the two methods to other even-even nuclei, the same discrepancy is found in all available cases.

Measurements have been made of the transmission through aluminium foils of an electron beam of initially monochromatic energy in the range 0.25-0.75 MeV. The current of transmitted electrons was measured directly, with a collecting cup and a galvanometer, this procedure yielding transmission curves of different shape from those obtained using Geiger counters or ionization chambers. The extrapolated range-energy relationship under these conditions also departs considerably from the generally accepted curve.

A simple physical picture is given of plane waves possessing complex angles of propagation, which play an important role in the theory of elastic wave radiation. Their utility is illustrated by studying continuous sinusoidal wave propagation parallel to the unstressed, plane boundary of a semi-infinite, homogeneous and isotropic solid medium, the Rayleigh and head waves being particular features of the investigation. A novel study of the field due to an impulsive force acting at a line in the surface of a semi-infinite medium indicates a general method of solving important transient propagation problems encountered in seismology. The equivalent problem of an impulsive force acting at the edge and in the plane of a semi-infinite thin sheet has been simulated experimentally by detonating small explosive charges at the edge of an aluminium sheet. The displacements detected by a condenser microphone technique are in excellent agreement with the theoretical determinations.

The alloy contained 44.1 atomic per cent chromium, where the pure sigma phase may be precipitated by prolonged annealing.

In the alpha phase the specific heat is almost identical with that of pure iron In the sigma phase however, a larger specific heat appears which is linear with temperature, and this is assumed to be electronic in origin giving for γ, 26.8 × 10^-3 J deg^-2 mole^-1, which is greater than has been observed for any other metal or alloy.

The stress birefringence relation in the alkali halides KBr, KCl and NaCl has been studied employing for the purpose a modified form of Filon's spectrometer method. A linear law is found to hold for stresses ranging from zero to 25kg cm^-2. Curves are given showing the photo-elastic dispersion of these solids.

The usefulness of the geometrical-optical treatment of frequency response is considered. With this treatment calculations have been made, using numerical integration, for several cases of defect of focus, primary and secondary spherical aberration. The results are compared with those obtained from diffraction treatments of the same cases. Provided the wave front aberration exceeds about 1 wavelength, it appears that geometrical optics will give an accuracy in the calculated frequency response of about 5% of its value for zero frequency, over the range of frequencies encountered in many photographic objectives.

A study is made of the ` Gaussian ' model of an imperfect gas used by Ford, which assumes the Mayer function exp(-/kT) - 1 to be a Gaussian function of the interatomic distance and is, at any fixed temperature, practically equivalent to an elastic sphere model though it could not give the temperature variation of the virial coefficients. The problem is shown to be closely related to one of `restricted random-walk ' type, which can be solved almost completely, the combinatorial problems being similar to those of circuit theory. It is concluded that the virial series is analytic for all positive V and that the high-order virial coefficients probably alternate in sign, though this limiting behaviour may well be approached very slowly, because of various ` small number effects ' that influence the early terms. The model is not directly comparable with that of rigid spheres, because it can be compressed to zero volume.

Lifetime measurements indicate that the 55 kev transition in ¹⁰³Rh is mostly dipole in character. Angular correlation measurements involving this transition rule out 5/2⁺ for the spin of the level at 538 kev, but allow 7/2⁺ or 9/2⁺, the former being preferred. The spin of the 650 kev level is not determined by these results.

The ¹⁶O(d, α)¹⁴N reaction has been investigated at bombarding energies of 6.8, 7.1, 7.2 and 8.9 mev. At these energies the intensity of the transition to the 2.31 mev, T=1 state of ¹⁴N has been measured. Angular distributions have been obtained for the alpha particles leading to the ground state and the 3.95 mev level of ¹⁴N for bombarding energies of 6.8 and 8.9 mev.

This paper is concerned with establishing a rigorous reciprocity relation of the Heisenberg type between the coherence time and the bandwidth of polychromatic radiation. Following upon an observation of Gabor (1946) that the usual formulation of the reciprocity inequality which relates the effective duration of a signal and its effective bandwidth is unsatisfactory for signals that are intrinsically real (e.g., an electric signal) a modified version is here presented. Our analysis is closely related to that of Gabor and supplements it in several respects. In particular we show that his formulation, like our own, is restricted to signals with zero mean value. Contrary to general belief, there is no evidence that the inequality holds when this restriction is removed.

A definition of the coherence time of light is then proposed in terms of the (measurable) correlation function that plays a central part in the theory of partial coherence. The coherence time obeys rigorously a reciprocity inequality of the required type and is shown to have a simple interpretation in terms of averages involving the correlations in fluctuations of the instantaneous intensity. It is also shown that the coherence time may be determined experimentally from Michelson's visibility curve of interference fringes.