In continuation of our earlier investigation on the problem of clustering of quenched-in vacancies reported earlier, starting from the discrete model, we derive a second order partial differential equation for the growth of the clusters. The solution of this equation is shown to be in reasonable agreement with the solution of the discrete model proposed earlier. However, the total number of vacancies is not conserved under slightly less stringent conditions than the conditions dictated by the solution of the discrete model, suggesting a slightly modified differential equation for the concentration of the clusters. The solution of this modified differential equation has the required properties. The leading part of the distribution when transferred into the space designating the linear dimension of the cluster has a Gaussian form. This feature is shown to be consistent with writing a Langevin equation with the linear dimension of the cluster taking the role of the random variable. This permits the identification of the smallness of parameter. An alternate formulation is also given where the concentration of the vacancies stored in a cluster of a certain size is considered as the dynamical variable. The solution obtained in this alternate formulation is shown to be consistent with the other formulation.

The continuum model for the growth of clusters developed in the previous paper (paper III) is applied to the formation of stacking fault tetrahedra in quenched gold and the formation of faulted vacancy loops in quenched aluminium. The results of the theory namely the distribution of the clusters as a function of their size and time, and the average size and the total density of the clusters as a function of time and the ageing temperature are shown to be in good agreement with the experimental results.

The thermoluminescence of x-irradiated CaSO₄: Dy phosphors has been studied for diverse activator concentrations. The concentration-dependence of these phosphors on the increase of glow peak intensities has been found to be remarkable. For higher concentration of dysprosium the concentration quenching effect has been observed. This has been attributed to the resonant transfer of energy from one activator atom to another, bringing the possible migration of energy in a solid, which is likely to get dissipated without luminescence, at the quenching site itself. The effect of irradiation time on the glow peak intensities reveals the initial linearity and a subsequent decrease indicating the possible radiation damage. The role of Na₂SO₄ as a charge compensator has been studied in detail. An attempt has been made to unravel the type of kinetics involved in the process, by calculating the activation energies by different methods. It has been concluded that the type of kinetics involved in the process is bimolecular.

The evolution of defects in a material under irradiation is studied at low doses (∼5 dpa or less) using rate equations. It is shown that as a function of temperature at a critical valueT_c a transition occurs in the behaviour of the solutions of the rate equations. BelowT_c the voids show incubation effects. An expression is derived for the critical dislocation density at which the void growth starts. This is related to the trapped vacancy fraction ε in vacancy dislocation loops. AboveT_c the incubation effects are shown to be related to the gas production rate which becomes the rate controlling parameter in determining the evolution of the defects. A gas-bubble to void transition occurs at a critical void radius and expressions are derived for the critical void size and dose at which the transition appears. It is shown that closely related to this is the incubation dose for interstitial loops. Finally, these features are corroborated by actual numerical integration of the rate equations.

Cosmic rays were discovered in 1911 but it is only now that some ideas are beginning to emerge as to their origin. This paper will examine the present evidence concerning the origin question over the whole energy range, from 10⁹ eV to 10²⁰ eV.

At the lowest energies, (10⁹–10¹⁰ eV), the new subject of gamma ray astronomy plays a crucial role and a galactic origin is favoured. At higher energies (10¹²–10¹⁷ eV) recent measurements of the anisotropies in arrival directions also suggest a galactic origin, although the evidence is not as strong.

At the very highest energies it seems likely that some, at least, of the particles come from outside the galaxy although the non-existence of the cut-off at about 6 × 10¹⁹ eV arising from interactions with the cosmological relict radiation provides a paradox. The likely future areas of advance in this fascinating subject will be indicated.

The analogues of the low-lying levels in⁷¹Ge have been observed as resonances in the compound nucleus⁷¹As through proton elastic scattering on⁷⁰Ge in the energy rangeE_p=3.5 to 5.3 MeV. The excitation functions cover the analogue resonances corresponding to states upto 2.3 MeV excitation in⁷¹Ge. The sub-structures in the 5.06 MeV resonance, first observed by Temmer and co-workers have been confirmed in the present experiment. The present investigation reveals similar sub-structures in the 4.13 MeV resonance lending further support to the existence of intermediate structure near an isobaric analogue resonance. The resonance parameters and the spectroscopic factors (for the corresponding parent states) have been extracted. The results are compared with the information available from the⁷⁰Ge(d, p)⁷¹Ge reaction.

Elastic scattering cross-sections of lead, tantalum and molybdenum were determined with the help of a Ge (Li) detector for 1.17 and 1.33 MeV rays between 30° and 115°. Theoretical evaluations of the cross-sections are based on a coherent addition of the well-known nuclear Thomson scattering amplitudes, the Rayleigh amplitudes calculated by Kissel and Pratt and the Delbrück amplitudes given by Papatzacos and Mork. The fairly good agreement between experiment and theory reveals the importance of the real Delbrück amplitudes. However, the experimental results in the 30–60° range tend to lie slightly but systematically below the calculated cross-sections.

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV⁽³⁾ (k_1j1; —k_1j1;o_j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV⁽³⁾ (k_1j1;k_2j2;k_3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.

It is noted that the Heisenberg uncertainty relations set a lower bound on the product of variances of two observablesA, B when they are separately measured on two distinct, but identically prepared ensembles. A new uncertainty relation is derived for the product of the variances of the two observablesA, B when they are measured sequentially on a single ensemble of systems. It is shown that the two uncertainty relations differ significantly wheneverA andB are not compatible.

The 2-0, 1-0 and 0-0 bands of the ultraviolet system of PS have been analysed for their rotational structure. It is shown that they involve the transitionC²Σ -X² Π_r(a). TheC²Σ state shows a significant spin doubling.