Formalism for Multiphoton Plasmon Excitation in Jellium Clusters

We present a new formalism for the description of multiphoton plasmon excitation processes in jellium clusters. By using our method, we demonstrate that, in addition to dipole plasmon excitations, the multipole plasmons (quadrupole, octupole, etc) can be excited in a cluster by multiphoton absorption processes, which results in a significant difference between plasmon resonance profiles in the cross sections for multiphoton as compared to single-photon absorption. We calculate the cross sections for multiphoton absorption and analyse the balance between the surface and volume plasmon contributions to multipole plasmons.Comment: 29 pages, 1 figur

Enhanced ionization in small rare gas clusters

A detailed theoretical investigation of rare gas atom clusters under intense short laser pulses reveals that the mechanism of energy absorption is akin to {\it enhanced ionization} first discovered for diatomic molecules. The phenomenon is robust under changes of the atomic element (neon, argon, krypton, xenon), the number of atoms in the cluster (16 to 30 atoms have been studied) and the fluency of the laser pulse. In contrast to molecules it does not dissappear for circular polarization. We develop an analytical model relating the pulse length for maximum ionization to characteristic parameters of the cluster

Survey team on : conceptualisations of the role of competencies, knowing and knowledge in mathematics education research

This paper presents the outcomes of the work of the ICME 13 Survey Team on 'Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research'. It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as mathematical competence and competencies, mathematical proficiency, and mathematical practices, amongst others. The paper provides theoretical analyses of these notions-under the generic heading of mathematical competencies-and gives an overview of selected research on and by means of them. Furthermore, an account of the introduction and implementation of competency notions in the curricula in various countries and regions is given, and pertinent issues are reviewed. The paper is concluded with a set of reflections on current trends and challenges concerning mathematical competencie