Resonance Structure of Cross-Sections of Slow-Electron Scattering by Calcium Atom
DOI:
https://doi.org/10.15407/ujpe67.3.161Keywords:
electron, calcium atom, scattering, excitation, ionization, R-matrix with B-splines method, nonorthogonal orbitals, resonancesAbstract
The extended BSR-version of the R-matrix method has been applied to systematically analyze the electron scattering by neutral calcium atoms at collision energies up to 4.3 eV. The strong coupling method with the sets of term-dependent nonorthogonal orbitals and the spline representation of the basis functions are used to accurately represent the target wave functions. The strong-coupling expansion included 39 bound states of the neutral calcium atom, which cover all its states from the ground one to 4s8s 1S. The complex resonance structure of the angleintegrated total cross-sections of the elastic e+Ca scattering and the electron-impact excitation of the 4s4p 3Po, 3d4s 3De, 3d4s 1De, 4s4p 1Po, and 4s5s 3Se states of a Ca atom are studied in detail. The observed structures are associated with particular autodetachment states of the “incident electron + Ca atom” system. The positions and widths of detected resonances are determined, and their spectroscopic classification is carried out.
References
O. Zatsarinny, H. Parker, K. Bartschat. Electron-impact excitation and ionization of atomic calcium at intermediate energies. Phys. Rev. A 99, 012706 (2019).
https://doi.org/10.1103/PhysRevA.99.012706
J.L. Hall. Nobel lecture: defining and measuring optical frequencies. Rev. Mod. Phys.78, 1279 (2006).
https://doi.org/10.1103/RevModPhys.78.1279
V.E. Fortov, B.Y. Sharkov, H. Stocker. European facility for antiproton and Ion research (FAIR): The new international center for fundamental physics and its research program. Phys.-Usp. 55, 582 (2012).
https://doi.org/10.3367/UFNe.0182.201206c.0621
Applied Atomic Collision Physics. Vol. 2: Plasmas. Edited by C.F. Barnett, M.F.A. Harrison (Academic Press, 1984).
E.Yu. Remeta, O.B. Shpenik, Yu.Yu. Bilak. Elastic scattering of slow electrons by calcium atoms into the angle interval depending on the collision energy. Zh. Tekhn Fiz. 71 (4), 13 (2001) (in Russian).
https://doi.org/10.1134/1.1365458
O. Zatsarinny, K. Bartschat, S. Gedeon, V. Gedeon, V. Lazur. Low-energy electron scattering from Ca atoms and photodetachment of Ca. Phys. Rev. A 74, 052708 (2006).
https://doi.org/10.1103/PhysRevA.74.052708
S. Gedeon, V. Gedeon, V. Lazur, L. Bandurina. Partially integrated differential cross-sections of e + Ca scattering. In Abstracts of the 9th European Conference on Atomic and Molecular Physics (ECAMP), 6-11 May 2007 (Crete, Greece, 2007).
S. Gedeon, V. Lazur. Low-energy electron scattering from calcium. In Abstracts of the 40th Annual Conference of the European Group for Atomic Systems (EGAS), 2-5 July 2008 (Graz, Austria, 2008).
O. Zatsarinny, K. Bartschat, S. Gedeon, V. Gedeon, V. Lazur, E. Nagy. Cross sections for electron scattering from magnesium. Phys. Rev. A 79, 052709 (2009).
https://doi.org/10.1103/PhysRevA.79.052709
O. Zatsarinny, K. Bartschat, S. Gedeon, V. Gedeon, V. Lazur, E. Nagy. Cross sections for electron scattering from magnesium. J. Phys.: Conf. Ser. 194, 042029 (2009).
https://doi.org/10.1088/1742-6596/194/4/042029
V. Gedeon, S. Gedeon, V. Lazur, E. Nagy, O. Zatsarinny, K. Bartschat. Electron scattering from silicon. Phys. Rev. A 85, 022711 (2012).
https://doi.org/10.1103/PhysRevA.85.022711
O. Zatsarinny, K. Bartschat, V. Gedeon, S. Gedeon, V. Lazur, E. Nagy. Electron scattering from silicon. In Abstracts of the 43rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (DAMOP12), 4-8 June 2012 (Orange County, California, 2012).
V. Gedeon, S. Gedeon, V. Lazur, E. Nagy, O. Zatsarinny, K. Bartschat. B-spline R-matrix-with-pseudostates calculations for electron-impact excitation and ionization of fluorine. Phys. Rev. A 89, 052713 (2014).
https://doi.org/10.1103/PhysRevA.89.052713
D.J. Pegg, J.S. Thompson, R.N. Compton, G.D. Alton. Evidence for a stable negative ion of calcium. Phys. Rev. Lett. 59, 2267 (1987).
https://doi.org/10.1103/PhysRevLett.59.2267
C.F. Fischer, J.B. Lagowski, S.H. Vosko. Ground states of Ca− and Sc− from two theoretical points of view. Phys. Rev. Lett. 59, 2263 (1987).
https://doi.org/10.1103/PhysRevLett.59.2263
P.G. Burke, W.D. Robb. The R-matrix theory of atomic processes. Adv. At. Mol. Phys. 11, 143 (1976).
https://doi.org/10.1016/S0065-2199(08)60030-5
P.G. Burke. R-matrix Theory of Atomic Collisions (Springer, 2011).
https://doi.org/10.1007/978-3-642-15931-2
A.R. Johnston, G.A. Gallup, P.D. Burrow. Low-lying negative-ion states of calcium. Phys. Rev. A 40, 4770 (1989).
https://doi.org/10.1103/PhysRevA.40.4770
N.I. Romanyuk, O.B. Shpenik, I.P. Zapesochnyi. Cross sections and characteristics of electron scattering by calcium, strontium, and barium atoms. JETP Lett. 32, 452 (1980).
N.I. Romanyuk, O.B. Shpenik, F.F. Papp, I.V. Chernysheva, I.A. Mandi, V.A. Kelemen, E.P. Sabad, E.Yu. Remeta. Study of low-energy scattering of electrons by Mg and Ca atoms using an optimized trochoidal spectrometer. Ukr. Fiz. Zh. 37, 1639 (1992) (in Russian).
V. Gedeon, S. Gedeon, V. Lazur, E. Nagy, O. Zatsarinny, K. Bartschat. B-spline R-matrix-with-pseudostates calculations for electron collisions with aluminum. Phys. Rev. A 92, 052701 (2015).
https://doi.org/10.1103/PhysRevA.92.052701
O. Zatsarinny, K. Bartschat, E. Nagy, S. Gedeon, V. Gedeon, V. Lazur. Electron scattering from aluminum: B-spline R-matrix calculations. J Phys.: Conf Ser. 635, 052012 (2015).
https://doi.org/10.1088/1742-6596/635/5/052012
O. Zatsarinny, K. Bartschat, E. Nagy, V. Gedeon, V. Lazur. Low-energy outer-shell photodetachment of the negative ion of aluminum. J. Phys.: Conf. Ser. 875, 022003 (2017).
https://doi.org/10.1088/1742-6596/875/3/022003
V. Gedeon, S. Gedeon, V. Lazur, O. Zatsarinny, K. Bartschat. Low-energy outer-shell photo-detachment of the negative ion of aluminum. J. Phys. B 51, 035004 (2018).
https://doi.org/10.1088/1361-6455/aa9c37
E.A Nagy V.F. Gedeon, S.V. Gedeon, V.Yu. Lazur. Electron-impact excitation of 51S − 51Po resonance transition in Sr atom. Ukr. J. Phys. 63, 11 (2018).
https://doi.org/10.15407/ujpe63.01.0011
N.Yu. Kondor, O.V. Yegiazarian, V.Yu. Lazur. Calculations of the energy structure of P, S atoms by the R-matrix method with B-splines. Nauk. Visn. Uzhgorod. Nats. Univ.
Ser. Fiz. 48, 67 (2020) (in Ukrainian).
A. Igarashi, N. Toshima, T. Shirai. Muon transfer and elastic scattering in t + dmu collisions at low energies. Phys. Rev. A 50, 4951 (1994).
https://doi.org/10.1103/PhysRevA.50.4951
A. Igarashi, I. Shimamura. Time-delay matrix analysis of resonances: application to the positronium negative ion. J. Phys. B 37, 4221 (2004).
https://doi.org/10.1088/0953-4075/37/21/001
I. Shimamura, J.F. McCann, A. Igarashi. Eigenvalues of the time-delay matrix in overlapping resonances. J. Phys. B 39, 1847 (2006).
https://doi.org/10.1088/0953-4075/39/8/003
K. Aiba, A. Igarashi, I. Shimamura. Time-delay matrix analysis of several overlapping resonances: applications to the helium atom and the positronium negative ion. J. Phys. B 40, F9 (2007).
https://doi.org/10.1088/0953-4075/40/2/F01
I. Shimamura. Complete separation of resonance and nonresonance channel spaces. J. Phys. B 44, 201002 (2011).
https://doi.org/10.1088/0953-4075/44/20/201002
O. Zatsarinny. BSR: B-spline atomic R-matrix codes. Comput. Phys. Commun. 174, 273 (2006).
https://doi.org/10.1016/j.cpc.2005.10.006
C. Bloch. Une formulation unifi'ee de la th'eorie des r'eactions nucl'eaires. Nucl. Phys. 4, 503 (1957).
https://doi.org/10.1016/0029-5582(87)90058-7
O. Zatsarinny, K. Bartschat. The B-spline R-matrix method for atomic processes: application to atomic structure, electron collisions and photoionization. J. Phys. B 46, 112001 (2013).
https://doi.org/10.1088/0953-4075/46/11/112001
P.J.A. Buttle. Solution of coupled equations by R-matrix techniques. Phys. Rev. 160, 719 (1967).
https://doi.org/10.1103/PhysRev.160.719
S. Gedeon, V. Lazur. The calculations of cross sections of electron scattering on Calcium atom. Nauk. Visn. Uzhgorod. Nats. Univ. Ser. Fiz. 25, 130 (2009).
O. Zatsarinny, C. Fischer. Atomic structure calculations using MCHF and BSR. Comput. Phys. Commun. 180, 2041 (2009).
https://doi.org/10.1016/j.cpc.2009.06.007
C. Froese Fischer, T. Tachiev. Allowed and spin-forbidden electric dipole transitions in Ca I. Phys. Rev. A 68, 012507 (2003).
https://doi.org/10.1103/PhysRevA.68.012507
J. Yuan, L. Fritsche. Electron scattering by Ca atoms and photodetachment of Ca− ions: An R-matrix study. Phys. Rev. A 55, 1020 (1997).
https://doi.org/10.1103/PhysRevA.55.1020
J. Yuan, C.D. Lin. Effect of core-valence electron correlation in low-energy electron scattering with Ca atoms. Phys. Rev. A 58, 2824 (1998).
https://doi.org/10.1103/PhysRevA.58.2824
J. Yuan. Core-valence electron correlation effects in photodetachment of Ca− ions. Phys. Rev. A 61, 012704 (1999).
https://doi.org/10.1103/PhysRevA.61.012704
NIST Atomic Spectra Database.
W.L. Wiese, J.R. Fuhr, T.M. Deters. Atomic transition probabilities of carbon, nitrogen, and oxygen: a critical data compilation. J. Phys. Chem. Ref. Data Monogr. 7, 522 (1996).
J.R. Taylor. Scattering Theory: The Quantum Theory on Nonrelativistic Collisions (John Wiley and Sons, Inc., 1972).
F. Nichitiu. Phase Shift Analysis in Physics of Nuclear Interactions (Mir, 1983) (in Russian).
F.T. Smith. Lifetime matrix in collision theory. Phys. Rev. 118, 349 (1960).
https://doi.org/10.1103/PhysRev.118.349
K. Bartschat, P.G. Burke. Resfit-A multichannel resonance fitting program. Comput. Phys. Commun. 41, 75 (1986).
https://doi.org/10.1016/0010-4655(86)90022-6
K. Bartschat, M.J. Kushner. Electron collisions with atoms, ions, molecules, and surfaces: fundamental science empowering advances in technology. Proc. Natl. Acad. Sci. 113, 7026 (2016).
https://doi.org/10.1073/pnas.1606132113
S.M. Kazakov, O.V. Khristoforov. Resonance scattering of low-energy electrons by calcium atoms. Zh. Tekhn. Fiz. 55, 795 (1985) (in Russian).
V.J. Ehlers, A. Gallagher. Electron excitation of the calcium 4227-˚A resonance line. Phys. Rev. A 7, 1573 (1973).
https://doi.org/10.1103/PhysRevA.7.1573
I.I. Garga, I.S. Aleksakhin, V.P. Starodub, I.P. Zapesochnyi. Excitation of alkaline-earth atoms by the electron impact. Opt. Spektrosk. 37, 843 (1974) (in Russian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.