Majorana and the quasi-stationary states in Nuclear Physics

A complete theoretical model describing artificial disintegration of nuclei by bombardment with alpha-particles, developed by Majorana as early as in 1930, is discussed in detail alongside the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear process, which is the direct measurable quantity of interest in the experiments. Though this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana's work anticipates by several years the related seminal paper by Fano on Atomic Physics.Comment: latex, amsart, 13 page

From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors

The Ettore Majorana paper - Theory of incomplete P triplets- published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels. This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels. The Feshbach resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high Tc superconductivity.Comment: 13 pages, 7 figures. Journal of Superconductivity and Novel Magnetism to be publishe

Magnetotransport near a quantum critical point in a simple metal

We use geometric considerations to study transport properties, such as the conductivity and Hall coefficient, near the onset of a nesting-driven spin density wave in a simple metal. In particular, motivated by recent experiments on vanadium-doped chromium, we study the variation of transport coefficients with the onset of magnetism within a mean-field treatment of a model that contains nearly nested electron and hole Fermi surfaces. We show that most transport coefficients display a leading dependence that is linear in the energy gap. The coefficient of the linear term, though, can be small. In particular, we find that the Hall conductivity $\sigma_{xy}$ is essentially unchanged, due to electron-hole compensation, as the system goes through the quantum critical point. This conclusion extends a similar observation we made earlier for the case of completely flat Fermi surfaces to the immediate vicinity of the quantum critical point where nesting is present but not perfect.Comment: 11 pages revtex, 4 figure

From nodal liquid to nodal Mottness in a frustrated Hubbard model

We investigate the physics of frustrated 3-leg Hubbard ladders in the band limit, when hopping across the ladder's rungs (t$_{\perp}$) is of the same order as hopping along them (t) much greater than the onsite Coulomb repulsion (U). We show that this model exhibits a striking electron-hole asymmetry close to half-filling: the hole-doped system at low temperatures develops a Resonating Valence Bond (RVB)-like d-wave gap (pseudogap close to ($\pi$,0)) coinciding with gapless nodal excitations (nodal liquid); in contrast, the electron-doped system is seen to develop a Mott gap at the nodes, whilst retaining a metallic character of its majority Fermi surface. At lower temperatures in the electron-doped case, d-wave superconducting correlations -- here, coexisting with gapped nodal excitations -- are already seen to arise. Upon further doping the hole-doped case, the RVB-like state yields to d-wave superconductivity. Such physics is reminiscent of that exhibited by the high temperature cuprate superconductors--notably electron-hole asymmetry as noted by Angle Resolved PhotoEmission Spectroscopy (ARPES) and the resistivity exponents observed. This toy model also reinforces the importance of a more thorough experimental investigation of the known 3-leg ladder cuprate systems, and may have some bearing on low dimensional organic superconductors.Comment: 26 pages, 16 figure

In vitro evaluation of Mucuna pruriens (L.) DC. antioxidant activity

Mucuna pruriens (L). Dc is a plant of the Fabaceae family, commonly known as velvet bean, itchy bean, chiporro bean, mucuna, among others. This plant has several medicinal properties, including its potential to treat Parkinson's disease (PD). International studies have shown that this plant surpasses the benefits of the substance levodopa in the treatment of PD. Taking into account that nerve cells are highly sensitive to oxidative substances, this study evaluated the antioxidant activity of mucuna and compared it to that of levodopa. The plant seeds' phenolic concentration was quantified by using the Folin-Denis reagent and the antioxidant activity assays were performed by using three different methods: the reduction of the phosphomolybdenium complex, the reduction of radical 1,1-diphenyl-2-picrylhydrazyl (DPPH•) and the formation of radical monocation ABTS•+, from the acid [2-2'-azinobis (3-ethylbenzothiazoline-6-sulfonate)]. Results showed that M. pruriens presents high antioxidant capacity, although not superior to isolated levodopa antioxidant capacity. Therefore, further studies should be performed to elucidate the activity of this plant in humans.A Mucuna pruriens (L). Dc é uma planta da família Fabaceae, conhecida popularmente como feijão-veludo, fava-coceira, feijão chiporro, mucuna, entre outros. Possui diversas propriedades medicinais, entre elas, o tratamento da doença de Parkinson (DP). Estudos internacionais vêm demonstrando que essa planta possui atividade superior à do fármaco levodopa para o tratamento da DP. O presente estudo avaliou a possibilidade da atividade antioxidante dessa planta auxiliar nesses resultados, uma vez que as células nervosas são altamente sensíveis às substâncias oxidativas. Para isto foi quantificada a concentração fenólica da semente da mucuna e os testes empregados para a avaliação da atividade antioxidante foram o teste de redução do complexo fosfomolibdênio, redução do radical 1,1-difenil-2-picril-hidrazil (DPPH•) e a formação do radical monocatiônico ABTS•+, proveniente do ácido [2-2'-azino-bis(3-etil-benzolina-6-sulfonado)]. Essa análise demonstrou que M. pruriens possui alta capacidade antioxidante, no entanto, não superior à levodopa isolada e, portanto, novos estudos devem ser realizados para a elucidação da atividade dessa planta em seres humanos