Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [Phys. Lett.A 244 (1998) 329] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q-commutator (q is a primitive cubic root of unity) and a new set of matrices η µ instead of the original matrices β µ of the DKP algebra are introduced. It is shown that in terms of these η µ matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z → q, where z is some complex deformation parameter entering into the definition of the η-matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function ψ(x; z) is performed and it is shown that the solution is singular in the z → q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is

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Void and interstitial dislocation loop nucleation and growth in a metal irradiated by fast particles are theoretically investigated on the basis of the kinetic equations for cluster size distribution functions. It is assumed that (i) the dislocations and dislocation loops are the preferential sinks for interstitials; (ii) the point defect clusters (voids and dislocation loops) grow by means of absorption and emission of monodefects; (iii) the nucleation of point defect clusters is a homogeneous one. It is shown that the dose and temperature dependences of the void size distribution function are qualitatively described by the theory presented. But the classical theory of the homogeneous nucleation used leads to results being in a serious contradiction to the experiments: 1. void concentrations found by numerical calculation for metal parameters close to those for pure nickel are two or three orders of magnitude higher than the usually observed values; 2. the interstitial loop concentration increases with increasing irradiation temperature; 3. at a low initial dislocation density the dose dependence of swelling is linear in contradiction to a sharper dependence observed in austenitic stainless steels. There is no tendency for swelling saturation up to a dose of 50 dpa in the theoretical model under consideration. The results of the present paper reveal the need for a serious revision of existing dislocation loop nucleation mechanisms.

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