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Katedra Fizyki Atomowej, Molekularnej i Optycznej
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Year 2018
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Electron-impact dissociation of molecular hydrogen: benchmark cross sections
PublicationWe present a joint experimental and theoretical investigation of a fundamental process in atomic and molecular physics: electron impact excitation of molecular hydrogen’s (H2) most dominant transition (X1Σg+ → b3Σu+). Excitation of this state is by far the main channel that causes the dissociation of H2 into H + H atoms at low energies. The Convergent Close-Coupling (CCC) calculations predicted significant, more than factor of...
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Electron-impact ionization cross section of formic acid
PublicationExperimental electron-impact ionization cross sections of one of the simplest carboxylic acids, formic acid, are presented. The molecular target was studied in two independent experimental setups applying different methods: the total ion collection and the electron–impact mass spectrometry methods. Experimental data were taken at incident electron energies ranging from ionization threshold [11.31 eV; J.C. Traeger, Int. J. Mass...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublicationWe study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...
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Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System
PublicationThis work presents a study of the mechanism of physical crosslinking of hyaluronic acid in the presence of common phospholipids in synovial joint organ systems. Molecular dynamic simulations have been executed to understand the formation of hyaluronan networks at various phospholipid concentrations. The results of the simulations suggest that the mechanisms exhibit subdiffusion characteristics. Transportation quantities derive...
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From unextendible product bases to genuinely entangled subspaces
PublicationUnextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure...
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Hyaluronan-Chondroitin Sulfate Anomalous Crosslinking Due to Temperature Changes
PublicationGlycosaminoglycans are a wide class of biopolymers showing great lubricating properties due to their structure and high affinity to water. Two of them, hyaluronic acid and chondroitin sulfate, play an important role in articular cartilage lubrication. In this work, we present results of the all-atom molecular dynamics simulations of both molecules placed in water-based solution. To mimic changes of the physiological conditions,...
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Influence of the Spectral Quality of Light on Daytime Alertness Levels in Humans
PublicationExposure to light is very important for human health. However, the characteristics of the light stimulus and the appropriate timing of such exposure are essential. Studies that have used monochromatic light exposure have shown no systematic patterns for the effects of blue light compared to longer wavelengths. Previous studies have shown that red light exposure increases objective and subjective measures of alertness at night without...
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Investigations of the optical activity of nonlinear crystals by means of dual-wavelength polarimeter
PublicationA dual-wavelength method in high accuracy polarimetry has been successfully tested and applied to measure optical activity (OA) of nonlinear crystals. In proposed polarimetric scheme two neighboring semiconductor laser wavelengths (635 and 650 nm) are used, which increases number of parameters measured simultaneously and improves the data processing. By neglecting dispersion of eigen wave ellipticity in crystals, more efficient...
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Low energy differential elastic electron scattering from acetonitrile (CH3CN)
PublicationMeasurements of elastic differential cross sections for electron scattering from acetonitrile (CH3CN) have been performed utilizing a crossed electron-molecular beam experiment and with the relative flow method, for the incident electron energy range of 0.7 eV–30 eV and the scattering angle range of 10◦–130◦. These differential cross sections have been used to calculate the elastic integral and momentum- transfer cross sections,...
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Low-energy electron scattering from molecular hydrogen: Excitation of the X1Σg+ to b3Σu+ transition
PublicationWe present time-of-flight differential cross-section measurements and convergent close-coupling calculations of differential cross sections for the electron-impact excitation of the X 1 g + → b 3 u + transition in molecular hydrogen. A part of this work was recently published [M. Zawadzki et al., Phys. Rev. A 97, 050702(R) (2018)]. In this work, agreement between theory and experiment is excellent overall, and marks a transition...
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Nuclear magnetic shielding constants of Dirac one-electron atoms in some low-lying discrete energy eigenstates
PublicationWe present tabulated data for the nuclear magnetic shielding constants (σ) of the Dirac one-electron atoms with a pointlike, motionless and spinless nucleus of charge Ze. Utilizing the exact general analytical formula for σ derived by us (Stefańska, 2016) valid for an arbitrary discrete energy eigenstate, we have computed the numerical values of the magnetic shielding factors for the ground state and for the first and the second...
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Physical crosslinking of hyaluronic acid in the presence of phospholipids in an aqueous nano-environment
PublicationHyaluronic acid and phospholipids are two components in the synovial joint cavity that contribute to joint lubrication synergistically. Molecular dynamics simulations were performed and hydrogen bonds in hyaluronic acid were analyzed to identify specific sites that are responsible for its physical cross-linking. Two molecular masses of hyaluronic acid, 10 kDa and 160 kDa, were considered. We use molecular dynamics simulations and...
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Resonances and Dissociative Electron Attachment in HNCO
PublicationIn a combined experimental and theoretical study, we probe the dissociative electron attachment in isocyanic acid HNCO. The experimental absolute cross section for the NCO− fragment shows a sharp onset and fine structures near the threshold. The autoionizing state responsible for the dissociative attachment is found in both the R-matrix calculation and using analytic continuation in the coupling constant. The involved A' resonance...
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Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state
PublicationThe second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green's function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...
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Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak 2L-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E)...
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The Dynamical Projectors Method Hydro and Electrodynamics
PublicationThe dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book...
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Time-of-flight electron scattering from molecular hydrogen: Benchmark cross sections for excitation of the X1Σ+g→b3Σ+u transition
PublicationThe electron impact X1Σ+g to b3Σ+u transition in molecular hydrogen is one of the most important dissociation pathways to forming atomic hydrogen atoms, and is of great importance in modeling astrophysical and industrial plasmas where molecular hydrogen is a substantial constituent. Recently it has been found that the convergent close-coupling (CCC) cross sections of Zammit et al. [Phys. Rev. A 95, 022708 (2017)] are up to a factor...
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Two-dimensional hydrogen-like atom in a weak magnetic field
PublicationWe consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr¨odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth...
Year 2017
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Anomalous Behavior of Hyaluronan Crosslinking Due to the Presence of Excess Phospholipids in the Articular Cartilage System of Osteoarthritis
PublicationLubrication of articular cartilage is a complex multiscale phenomenon in synovial joint organ systems. In these systems, synovial fluid properties result from synergistic interactions between a variety of molecular constituent. Two molecular classes in particular are of importance in understanding lubrication mechanisms: hyaluronic acid and phospholipids. The purpose of this study is to evaluate interactions between hyaluronic acid...
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Cross sections calculations for electron scattering from dimethylamine, NH(CH3)2, molecule
PublicationThe total cross section for single electron-impact ionization and the integral elastic cross section for electron scattering from dimethylamine have been calculated using the binary-encounter-Bethe model and the independent atom method, respectively.
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Dissociation of 2-oxopropanoic acid by low energy electrons
PublicationElectron attachment to molecular target can lead to a variety of negative fragment ions. We experimentally probe the main dissociative electron attachment (DEA) channels in 2-oxopropanoic acid (CH3 - CO - COOH) - an important trace component in the Earth's atmosphere. In our studies we utilise nearly mono-energetic electrons at electron energies from 0 eV up to 15 eV.
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Dual-wavelength laser polarimeter and its performance capabilities
PublicationA dual-wavelength optical polarimetric approach has been proposed as a means of elimination of the systematic errors and estimation of the optical anisotropy parameters for a single DKDP crystal. Our HAUP-related polarimeter uses two semiconductor lasers with the neighbouring wavelengths of 635 nm and 650 nm. Based on the temperature dependence analysis of small characteristic azimuths of light polarization with respect to the...
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Dual-wavelength polarimeter application in investigations of the optical activity of a langasite crystal
PublicationA method of high accuracy polarimetry, which includes optical activity measurements systematic errors, was realized with dual-wavelength polarimeter for two wavelengths of 635 and 650 nm. Simultaneous measurements with neighboring wavelengths significantly improved the data processing, by increasing the amount of data to eliminate the systematic errors. For langasite crystal La3Ga5SiO14 we measured temperature dependence of the...
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ELECTRON ATTACHMENT TO HETEROGENEOUS MOLECULAR CLUSTERS
PublicationHeterogeneous clusters are unique model species enabling studies of bulk and surface processes by vacuum restricted methods. This is of particular importance for the reactions of low-energy electrons which have extremely short penetration depth in bulk environments. This contribution overviews our recent experiments with low-energy electrons and clusters prepared by different techniques. First, the deposition of molecules on argon...
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Elektryczne i magnetyczne statyczne podatności multipolowe jednoelektronowego atomu Diraca w stanie podstawowym
PublicationW rozprawie rozważono relatywistyczny atom jednoelektronowy w stanie podstawowym umieszczony w statycznym multipolowym polu elektrycznym i magnetycznym. Wykorzystano rachunek zaburzeń, wraz z rozwinięciem sturmowskim uogólnionej funkcji Greena-Diraca-Coulomba [R. Szmytkowski, JPhys. B 30 (1997) 825; errata 30 (1997) 2747], co umożliwiło wyznaczenie analitycznych wyrażeń dla podatności multipolowych pól dalekich i pól bliskich....
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Magnetic-dipole-to-electric-quadrupole cross-susceptibilities for relativistic hydrogenlike atoms in some low-lying discrete energy eigenstates
PublicationIn this paper we present tabulated data for magnetic-dipole-to-electric-quadrupole cross-susceptibilities (χ_{M1→E2}) for Dirac one-electron atoms with a pointlike, spinless and motionless nucleus of charge Ze. Numerical values of this susceptibility for the hydrogen atom (Z = 1) and for hydrogenic ions with 2 \leqslant Z \leqslant 137 are computed from the general analytical formula, recently derived by us (Stefanska, 2016), valid...
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On the derivatives $\partial^{2}P_{\nu}(z)/\partial\nu^{2}$ and $\partial Q_{\nu}(z)/\partial\nu$ of the Legendre functions with respect to their degrees
PublicationWe provide closed-form expressions for the degree-derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$ and $[\partial Q_{\nu}(z)/\partial\nu]_{\nu=n}$, with $z\in\mathbb{C}$ and $n\in\mathbb{N}_{0}$, where $P_{\nu}(z)$ and $Q_{\nu}(z)$ are the Legendre functions of the first and the second kind, respectively. For $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$, we find that % \begin{displaymath} \frac{\partial^{2}P_{\nu}(z)}{\partial\nu^{2}}\bigg|_{\nu=n} =-2P_{n}(z)\Li_{2}\frac{1-z}{2}+B_{n}(z)\ln\frac{z+1}{2}+C_{n}(z), \end{displaymath} % where...
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SKY PG - kolejny sukces na Wydziale Fizyki Technicznej i Matematyki Stosowanej
PublicationSukcesem zakończyła się misja balonu meteorologicznego z sondą pomiarową przygotowaną przez studentów Wydziału Fizyki Technicznej i Matematyki Stosowanej. W lipcu 2016 roku grupa studentów z WFTiMS, we współpracy z Kołem Naukowym Studentów Fizyki PG, wykonała pomiary wybranych wielkości zycznych, posługując się autorskim układem pomiarowym, umieszczonym w sondzie badawczej przyczepionej do balonu meteorologicznego. Podczas około...
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Total cross section for low-energy electron scattering from formic acid, (HCOOH), molecules
PublicationTotal cross section (TCS) for low-energy electron scattering from formic acid molecules has been measured using electrostatic electron spectrometer working in linear transmission mode. Two local maxima centered around 1.7 eV and 7.8 eV have been observed and associated with resonant scattering processes.
Year 2016
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Calculation methods of interaction of electromagnetic waves with objects of complex geometries
PublicationModeling of the electromagnetic interaction with different homogeneous or inhomo-geneous objects is a fundamental and important problem. It is relatively easy to solve Maxwellequations analytically when the scattering object is spherical or cylindrical, for example. How-ever, when it loses these properties all that is left for us is to useapproximation models, to ac-quire the solution we need. Modeling of complex, non-spherical,...
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Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac–Coulomb Green function
PublicationWe present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are...
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Electron scattering from 2-methyl–1,3-butadiene,C5H8, molecules: Role of methylation
PublicationWe report cross-section results from experimental and theoretical investigations into electron collisions with the 2-methyl–1,3-butadiene [C5H8] molecule. The current results are compared with our previous results for the 1,3-butadiene [C4H6] molecule, a structural homologue of 2-methyl–1,3-butadiene, to investigate how the methylation (the substitution of hydrogen atom by a methyl group) affects the shape and/or magnitude of the...
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Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function we derive a closed-form expression for the electric quadrupole moment induced...
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Magnetizabilities of relativistic hydrogenlike atoms in some arbitrary discrete energy eigenstates
PublicationWe present the results of numerical calculations of magnetizability of the relativistic hydrogenlike atoms. Exploiting the analytical formula for $\chi$ we have found the values of the magnetizability for the ground state and for the first and the second set of excited states of the atom. The results for ions with the atomic number $0
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Static electric and magnetic multipole susceptibilities for Dirac one-electron atoms in the ground state
PublicationWe present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range $1\leq Z\leq137$. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities $\alpha_{\mathrm{E}L\to\mathrm{E}L}$ and magnetizabilities (magnetic susceptibilities) $\chi_{\mathrm{M}L\to\mathrm{M}L}$...
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Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$ polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical...
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Zbadaj powietrze, którym oddychasz
PublicationPrzedstawienie dydaktycznego aspektu badania składu powietrza; począwszy od prostych układów, których wykonania może się podjąć niemalże każdy, posiadający trochę zapału, do urządzeń wykorzystywanych naukowo lub komercyjnie.
Year 2015
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Electron collisions with methyl-substituted ethylenes: Cross section measurements and calculations for 2-methyl–2-butene and 2,3-dimethyl–2-butene
PublicationWe report electron-scattering cross sections determined for 2-methyl–2-butene [(H3C)HC==C(CH3)2] and 2,3-dimethyl–2-butene [(H3C)2C=C(CH3)2] molecules. Absolute grand-total cross sections (TCSs) were measured for incident electron energies in the 0.5–300 eV range, using a linear electron-transmission technique. The experimental TCS energy dependences for the both targets appear to be very similar with respect to the shape. In each...
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Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closed-form expression for the magnetizability of an arbitrary discrete state of the relativistic one-electron atom with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...
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Scattering of electrons by a 1,2-butadiene (C4H6) molecule: measurements and calculations
PublicationWe present the results of experimental and theoretical study on electron collisions with a 1,2-butadiene (H2C=C=CHCH3) molecule. Absolute grand-total cross sections (TCSs) were measured using a linear electron-transmission method for collision energies in the 0.5–300 eV range. Two distinct features in the TCS energy curve were detected: a narrow peak located at 2.3 eV and a broad enhancement centered around 9 eV. We attributed...
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Solution of coupled integral equations for quantum scattering in the presence of complex potentials
PublicationIn this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
Year 2014
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublicationThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.
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APPLICATION OF BINARY-ENCOUNTER-BETHE METHOD TO ELECTRON-IMPACT IONIZATION CROSS SECTION CALCULATIONS FOR BIOLOGICALLY RELEVANT MOLECULES
PublicationElectron-impact cross sections for platinum chemotherapeutic compounds, purine and pyrimidine molecules calculated using binary-encounterBethe model are presented as examples of possible applications of that method.
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Electric-field-induced magnetic quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla magnetycznego momentu kwadrupolowego, indukowanego przez zewnętrzne słabe, stałe, jednorodne pole elektryczne w stanie podstawowym relatywistycznego atomujednoelektronowego.
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ELECTRON-IMPACT IONIZATION CROSS SECTIONS CALCULATIONS FOR PURINE AND PYRIMIDINE MOLECULES
PublicationCross sections for electron-impact ionization of purine and pyrimidine molecules have been calculated using binary-encounter-Bethe method for electron energies ranging from the ionization threshold up to 5 keV. Ionization cross section for purine molecules is 1.4 times higher than for pyrimidine molecules. Acceptable agreement between experimental and theoretical ionization data for pyrimidine molecule has been found.
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Electron-impact ionization of fluoromethanes – Review of experiments and binary-encounter models
PublicationExperiments and recommended data on electron-impact ionization of methane and fluoromethanes (CH3F, CH2F2, CHF3, CF4) are reviewed and compared with binary-encounter models (Gryzinski’s, ´ Deutsch and Märk’s, and Kim and Rudd’s). A good agreement between recent experiments and the two latter classical-like models is shown. Kim and Rudd’s model (calculated presently in the restricted HartreeFock 6-31**G orbital basis) predicts well...
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Electron-scattering cross sections for selected alkyne molecules: Measurements and calculations
PublicationWe report cross-section results from experimental and theoretical studies on electron collisions with 1-butyne (HC≡C–CH2CH3) and acetylene (HC≡CH) molecules and from computations for a propyne (HC≡C–CH3) molecule. Absolute grand -total electron-scattering cross sections (TCSs) were measured at impact energies ranging from about 0.5 to 300 eV using the linear electron-transmission method. The TCS energy curve for 1-butyne has a...
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Integrable zero-range potentials in a plane
PublicationWe examine general statements in the Wronskian representation of Darboux transformations for plane zero-range potentials. Such expressions naturally contain scattering problem solution. We also apply Abel theorem to Wronskians for differential equations and link it to chain equations for Darboux transforms to fix conditions for further development of the underlying distribution concept. Moutard transformations give a convenient...
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Jednoelektronowy atom Diraca w słabym polu magnetycznym
PublicationW rozprawie przedstawiono opis wpływu zewnętrznego stałego, słabego, jednorodnego pola magnetycznego na jednoelektronowy atom Diraca. Wykorzystując funkcje gęstości ładunku elektrycznego oraz gęstości prądu elektrycznego, rozważono procesy indukowania się w atomie dodatkowych elektromagnetycznych momentów multipolowych. Dokonano analizy indukowanego momentu dipolowego, w wyniku której uzyskano wyrażenie dla magnetyzowalności atomu....
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KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublicationWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...