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

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

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 constante progredire della frontiera tra teologia e scienza. Parte 2º: Metafisica

On constant movement of frontiers between Science and Theology. Part 2: Metaphysics In the first part (Karwasz, Scientia et Fides, 3(1) 2015) entitled “Physics” we showed how discoveries of modern sciences do not contradict Bible: neither in the subject of the beginning of the word nor in the subjects of the homogeneity of Homo Sapiens and the common origin of Euroasiatic languages. In this part we show that numerous “explanations” of natural phenomena like Pauli’s exclusion principle governing the chemistry, like space-time of Einstein, like apparent paradoxes of quantum mechanics, in reality move the border of our knowledge towards metaphysics: writings of philosophers from Aristotle, S. Augustine, S. Thomas to Kant are not in contrast with ontological conclusions of modern physics. In this way, the explanations based on philosophical principles find their place in natural sciences

Constructivistic didactics in physics: implementations

Cognitive strategies in teaching physics in Poland were first introduced in late 90’s. The first exhibition in the interactive form, was devoted to interactive physics - "Physics and Toys" in 1998 and "Contemporary Physics" in 2003 (founded at the University of Pomerania in Slupsk). Later, more comprehensive, interdisciplinary exhibitions were created at the Nicolaus Copernicus University. The success of this teaching method exceeded our expectations. We discuss the principles and practical methods of innovative didactics based on constructivist and cognitive theories. The two main paradigms of this teaching method are based on constructing the knowledge and competences of students (listeners, students) in interactive narrative and using real teaching subjects that can be pulled out of pocket. We call these concepts hyper-constructivism and neo-realism

Hyper-konstruktywizm w nauczaniu fizyki. Tożsamość indywidualna i kompetencje społeczne

This paper demonstrates how hyper-constructivist methodology used in interactive lectures and workshops in physics for children and young people develops both the individual identity of young people and their social competence. These activities are also examples of the practical implementation of the long-proposed pedagogical contents knowledge

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

Characterization of sputtered W–Si–N thin films by a monoenergetic positron beam

A monoenergetic positron beam was employed to characterize the uniformity and the microstructural variation of thermally treated W–Si–N thin film. As the annealing temperature is increased, positrons are found to be progressively trapped in sites rich in silicon. This behavior is explained by the formation of W clusters from which positrons are favorably trapped into the Si–N amorphous matrix. Positron results are discussed together with information obtained on similar samples by Rutheford backscattering, infrared spectroscopy and transmission electron microscopy measurements