Intensities of 4f-4f transitions in glass materials

In this article we review some of the basic aspects of rare earth spectroscopy applied to vitreous materials. The characteristics of the intra-atomic free ion and ligand field interactions, as well as the formalisms of the forced electric dipole and dynamic coupling mechanisms of 4f-4f intensities, are outlined. The contribution of the later mechanism to the 4f-4f intensities is critically discussed, a point that has been commonly overlooked in the literature of rare earth doped glasses. The observed correlation between the empirical intensity parameter W2 and the covalence of the ion first coordination shell is discussed accordingly to the theoretical predictions.

One reason, several logics

Humans have used arguments for defending or refuting statements long before the creation of logic as a specialized discipline. This can be interpreted as the fact that an intuitive notion of "logical consequence" or a psychic disposition to articulate reasoning according to this pattern is present in common sense, and logic simply aims at describing and codifying the features of this spontaneous capacity of human reason. It is well known, however, that several arguments easily accepted by common sense are actually "logical fallacies", and this indicates that logic is not just a descriptive, but also a prescriptive or normative enterprise, in which the notion of logical consequence is defined in a precise way and then certain rules are established in order to maintain the discourse in keeping with this notion. Yet in the justification of the correctness and adequacy of these rules commonsense reasoning must necessarily be used, and in such a way its foundational role is recognized. Moreover, it remains also true that several branches and forms of logic have been elaborated precisely in order to reflect the structural features of correct argument used in different fields of human reasoning and yet insufficiently mirrored by the most familiar logical formalisms.