New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.Comment: 12 pages,no figure

Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research

After revisiting some high points of particle physics and QFT of the two decades from 1960 to 1980, I comment on the work by Jorge Andre Swieca. I explain how it fits into the quantum field theory during these two decades and draw attention to its relevance to the ongoing particle physics research. A particular aim of this article is to direct thr readers mindfulness to the relevance of what at the time of Swieca was called "the Schwinger Higgs screening mechanism". which, together with recent ideas which generalize the concept of gauge theories, has all the ingredients to revolutionize the issue of gauge theories and the standard model.Comment: 49 pages, expansion and actualization of text, improvement of formulations and addition of many references to be published in EPJH - Historical Perspectives on Contemporary Physic

Quercus suber and Betula pendula outer barks as renewable sources of oleochemicals: A comparative study

A comparative study on the chemical composition of oak cork (Quercus suber L.) and corresponding industrial residues and birch (Betula pendula L.) outer bark is reported. Cork oak samples have lower extractives contents (6-9%) and higher contents of carbohydrates and lignin (23-27 and 33-38%, respectively) than those found for birch outer bark (40, 6 and 9%, respectively); suberin contents accounted for around 30% of cork, 11% of industrial cork powder and 45% of birch outer bark. Analysis of the suberin monomeric composition revealed that C18 and C22 omega-hydroxyfatty acids (including mid-chain epoxy- and dihydroxy-derivatives), followed by alpha,omega-dicarboxylic acids, are the main components in both suberins, with 9,10-epoxy-18-hydroxyoctadecanoic, 18-hydroxyoctadec-9-enoic, 9,10,18-trihydroxyoctadecanoic and octadec-9-enoic acids as the major components. The differences in the relative amounts of these acids in the suberin samples and the impact on the potential exploitation of the different industrial by-products are discussed. (C) 2008 Elsevier B.V All rights reserved.WaCheUp project - STRP 013896EC/6FP - priority 3, NM