Modified effective-range theory for low energy e-N2 scattering

We analyze the low-energy e-N2 collisions within the framework of the Modified-Effective Range Theory (MERT) for the long-range potentials, developed by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum \hbar k, but instead we apply the exact analytical solutions of the Schroedinger equation for the long-range polarization potential, as proposed in the original formulation of O'Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross sections in the 0.1 - 1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N2. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross section as well as the presence of resonances in the few eV range.Comment: 9 pages, LaTex, 4 eps figures, EPJ style; extended and upgraded version of arXiv:0708.2991, now considering only e-N2 scatterin

Learning physics. The joy of scientific discovery

Physics, with Kopernik, Galileo and Newton became first science with a modern methodology: observation – analysis – mathematical model. What is the source of the scientific success of physics is the reason for didactical difficulties – pupils must understand the verbal description, translate it to mathematical formalism and relate it to the real world. Humanistic currents from second half of last century – cognitivism, constructivism and pedagogical perspectives – would facilitate teaching physics. We show how apply these concepts, at different ages of pupils, in an interactive teaching, based on real, simple experiments.La fisica, con Copernico, Galileo e Newton divenne la prima scienza con la metodologia moderna: osservazione, analisi, modello matematico. Quello che è la sorgente del successo scientifico è in contemporanea la ragione delle difficoltà didattiche: gli allievi devono capire la descrizione verbale, tradurla al formalismo matematico e mettere in relazione con il mondo reale. Correnti umanistiche della seconda metà del secolo scorso – cognitivismo, costruttivismo e prospettive pedagogiche – dovrebbero supportare e facilitare l’insegnamento di fisica. Mostriamo come applicare questi concetti a diverse età, in un insegnamento interattivo, basato su semplici ma reali (non virtuali) esperimenti

Applicability of Modified Effective-Range Theory to positron-atom and positron-molecule scattering

We analyze low-energy scattering of positrons on Ar atoms and N2 molecules using Modified Effective-Range Theory (MERT) developped by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. We use formulation of MERT based on exact solutions of Schroedinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes well experimental data, provided that effective-range expansion is performed both for s- and p-wave scattering, which dominate in the considered regime of positron energies (0.4 - 2 eV). We estimate the values of the s-wave scattering lenght and the effective range for e+ - Ar and e+ - N2 collisions.Comment: RevTeX, 4 pages, 2 figure

Electron scattering on molecules: search for semi-empirical indications

Reliable cross-sections for electron-molecule collisions are urgently needed for numerical modeling of various processes important from technological point of view. Unfortunately, a significant progress in theory and experiment over the last decade is not usually accompanied by the convergence of cross-sections measured at different laboratories and calculated with different methods. Moreover the most advanced contemporary theories involve such large basis sets and complicated equations that they are not easily applied to each specific molecule for which data are needed. For these reasons the search for semi-empirical indications in angular and energy dependencies of scattering cross-section becomes important. In this paper we make a brief review of the applicability of the Born-dipole approximation for elastic, rotational, vibrational and ionization processes that can occur during electron-molecule collisions. We take into account the most recent experimental findings as the reference points

Il costante progredire della frontiera tra teologia e scienza: “Fisica”

On constant movement of frontiers between Theology and Science: Physics Pope Benedict XVI wrote in 1979 in “Four sermons on the Creation of world” that scientific discoveries cause a kind of retreat of the faith on “defensive” positions, giving an impression that in few centuries there would be no single dogma of faith valid. Discussing progresses of physics in last century (inflation of Universe, non-locality of quantum mechanics), of linguistics (the origin of Indo-European languages) and of genetics (mitochondrial DNA of Homo sapiens) we show that scientific discoveries make the faith retreat only apparently. In fact, the progress of science does not change the principles of Faith, but only illustrates and validates them: remain valid thesis of St. Thomas and St. Augustine. Every science discovery creates new questions, making clear that man has to depend both on reason and Faith. The aim of the article is not to “explain” the Bible according the newest discoveries but to show that these discoveries do not corrode the principles of Faith. In this way the border between natural sciences and theology remains in a constant movement: theology leaves to science obvious facts, entering deeper to the mystery of Revelation.Papa Benedetto XVI nel 1979 scrisse in “Quattro sermoni sulla Creazione” che le scoperte scientifiche fanno in un certo senso ritirare la fede in posizioni sempre “più difensive”, dando l’impressione che tra qualche secolo non rimarranno più i dogmi oggi validi. Discutendo il progresso dell’ultimo secolo della fisica moderna (l’espansione dell’Universo, non-località della meccanica quantistica), della linguistica (origine delle lingue indoeuropee) e della genetica (DNA mitocondriale dell’ Homo sapiens), facciamo notare che le scoperte scientifiche solo apparentemente fanno ripiegarsi la teologia sulle posizioni difensive. In realtà, il progresso della scienza non sposta i principi della Fede, ma soltanto li illustra e li convalida: rimangono valide le frasi non solo di S. Tommaso ma anche di S. Agostino. Ogni scoperta scientifica crea altrettante nuove domande. Lo scopo del presente articolo non è “aggiustare” la Scrittura alle recenti scoperte scientifiche, ma mostrare, che queste scoperte non corrodono la Fede. Così la frontiera tra scienza e teologia è in un movimento perenne, dove la teologia lascia cose ovvie alla scienza, esplorando in cambio sempre di più il mistero della Rivelazione.O bezustannym przesuwaniu się granic między teologią a naukami przyrodniczymi: fizyka Papież Benedykt XVI w 1979 roku w „Czterech kazaniach o Stworzeniu świata” napisał, że odkrycia naukowe powodują swego rodzaju wycofywanie się wiary na pozycje „obronne”, robiąc wrażenie, że za parę stuleci nie pozostanie ważny żaden z dogmatów wiary. Dyskutując postępy fizyki w ostatnim stuleciu (rozszerzanie się Wszechświata, nielokalność mechaniki kwantowej), lingwistyki (pochodzenie języków indoeuropejskich) i genetyki (DNA mitochondrialne Homo sapiens) pokazujemy, że odkrycia naukowe jedynie pozornie powodują wycofywanie się teologii na pozycje obronne. W rzeczywistości, postęp nauki nie zmienia zasad Wiary, ale je tylko ilustruje i potwierdza: pozostają prawdziwe rozważania i św. Tomasza i św. Augustyna. Każde odkrycie naukowe stwarza kolejne pytania, dając do zrozumienia, że człowiek musi opierać się w równej mierze na rozumie i na Wierze. Celem artykułu nie jest „wyjaśnienie” Pisma na podstawie najnowszych odkryć naukowych, lecz pokazanie, że odkrycia te nie naruszają Wiary. Tak więc granica między naukami przyrodniczymi a teologią pozostaje w ciągłym ruchu: teologia pozostawia nauce fakty oczywiste, w zamian za to coraz dokładniej zgłębiając tajemnicę Objawienia

Jordan-Hölder sequences and self-adjoint (a,b)(a, b)-modules

10 pages.Given the lack of uniqueness of the Jordan-Hölder composition series in the theory of $(a,b)$-modules we are interested whether the particularities of certain $(a,b)$-modules can be transmitted to their composition series. This article will focus on the properties of Jordan-Hölder composition series of self-adjoint $(a,b)$-modules. In particular we will prove that a self-adjoint composition series always exists for self-adjoint $(a,b)$-modules

Electron scattering on molecular nitrogen: common gas, uncommon cross sections

We discuss peculiar features of electron scattering on the N2 molecule and the N2+ ion, that are important for modeling plasmas, Earth’s and other planets’ atmospheres. These features are, among others: the resonant enhancement of the vibrational excitation in the region of the shape resonance around 2.4 eV, the resonant character of some of electronic excitation channels (and high values of these cross sections, both for triplet and singlet states), high cross section for the dissociation into neutrals, high cross sections for elastic scattering (and electronic transitions) on metastable states. For the N2+ ion we discuss both dissociation and the dissociative ionization, leading to the formation of atoms in excited states, and dissociative recombination which depends strongly on the initial vibrational state of the ion. We conclude that the theory became an indispensable completion of experiments, predicting many of partial cross sections and their physical features. We hope that the data presented will serve to improve models of nitrogen plasmas and atmospheres. Graphical abstract: [Figure not available: see fulltext.]