[PDF]    http://dx.doi.org/10.3952/physics.v54i4.3009

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 54, 205–216 (2014)


ADDITIONAL SYMMETRY PROPERTIES OF ATOMIC STATES WITH ONE AND TWO OPEN SHELLS
Romualdas Karazija
Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108, Vilnius, Lithuania
E-mail: romualdas.karazija@tfai.vu.lt

Received 12 September 2014; revised 2 October 2014; accepted 10 December 2014

Additional symmetry properties of the ground state of atom and quantities related with it, of the configuration with two open shells with the same orbital quantum number, and of the maximal Auger amplitudes are considered. Algebraic energy expressions for terms of the highest multiplicity and terms related with them as well as for the ground and highest levels are presented. Classification of states for n1lN1n2lN2 configuration according to their parentage in the isoelectronic sequence of configurations and the properties of such a basis are considered. Reformulation of this basis using the isospin formalism is discussed. Existence of selection rules for the maximal Auger amplitudes is indicated.
Keywords: ground state of atom, symmetry with respect to a quarter of shell, binding energy, interval rule, isospin basis
PACS: 31.10.+z, 32.10.Hq

 ATOMŲ SU VIENU IR DVIEM ATVIRAIS SLUOKSNIAIS PAPILDOMOS SIMETRIJOS SAVYBĖS

Romualdas Karazija
Vilniaus universiteto Teorinės fizikos ir astronomijos institutas, Vilnius, Lietuva

Darbe nagrinėjamos atomo pagrindinės būsenos ir su ja susijusių dydžių, taip pat konfigūracijų, turinčių du atvirus elektronų sluoksnius su tuo pačiu orbitiniu kvantiniu skaičiumi, bei Ožė šuolių maksimalių amplitudžių papildomos simetrijos savybės. Pateiktos aukščiausio multipletiškumo termų, pagrindinio ir aukščiausiojo lygmenų energijos išraiškos esant vienam atviram sluoksniui. Nagrinėjama konfigūracijos n1lN1n2lN2 būsenų klasifikacija, naudojantis jų kilme izoelektronėje konfigūracijų sekoje, ir tokios banginių funkcijų bazės savybės. Aptariamas atrankos taisyklių egzistavimas maksimalioms Ožė šuolių amplitudėms.

References / Nuorodos

[1] A.P. Jucys, I.B. Levinson, and V.V. Vanagas, Mathematical Apparatus of the Angular Momentum Theory (Gordon and Breach, New York, 1964),
http://www.amazon.co.uk/Mathematical-Apparatus-Theory-Angular-Momentum/dp/B000KADEOE/
[2] E.U. Condon and G.H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935),
http://www.amazon.co.uk/Theory-Atomic-Spectra-E-Condon/dp/0521047137/
[3] A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957),
http://www.amazon.co.uk/Angular-Momentum-Quantum-Mechanics-Investigations/dp/0691025894/
[4a] G. Racah, Theory of complex spectra, I. Phys. Rev. 61(3–4), 186–197 (1941),
http://dx.doi.org/10.1103/PhysRev.61.186
[4b] G. Racah, Theory of complex spectra, II. Phys. Rev. 62(3–4), 438–462 (1942),
http://dx.doi.org/10.1103/PhysRev.62.438
[4c] G. Racah, Theory of complex spectra, III. Phys. Rev. 63(3–4), 367–382 (1943),
http://dx.doi.org/10.1103/PhysRev.63.367
[5] G. Racah, Theory of complex spectra. IV Phys. Rev. 76(9), 1352–1365 (1949),
http://dx.doi.org/10.1103/PhysRev.76.1352
[6] R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, CA, 1981),
http://www.amazon.co.uk/Theory-Structure-Spectra-Applied-Sciences/dp/0520038215/
[7] Z.B. Rudzikas, Theoretical Atomic Spectroscopy (Cambridge University, 2007),
http://www.cambridge.org/lt/academic/subjects/physics/atomic-physics-molecular-physics-and-chemical-physics/theoretical-atomic-spectroscopy
[8] B. R. Judd, Second Quantization and Atomic Spectroscopy (The Johns Hopkins University Press, Baltimore, 1967),
http://www.amazon.co.uk/Second-Quantization-Spectroscopy-Memorial-Lectures/dp/0801803225/
[9] L.N. Labzovskiy, Theory of Atomic Structure of Electronic Shells (Nauka, Moscow, 1986) [in Russian]
[10] B.R. Judd, Lie groups for atomic shells, Phys. Rept. 285(1), 1–76 (1997),
http://dx.doi.org/10.1016/S0370-1573(96)00039-7
[11] B.G. Wybourne, Symmetry Principles and Atomic Spectroscopy (Wiley, New York, 1970),
http://www.amazon.co.uk/Symmetry-Principles-Atomic-Spectroscopy-Wybourne/dp/0471965081/
[12] P. Bogdanovich, R. Karazija, and J. Boruta, The orthogonality of wave functions to the functions of configurations lower-lying energetically and the validity of Brillouin's theorem in the case of electronic configuration n1lN1n2lN2, Litov. Fiz. Sb. – Liet. fiz. rink. 20(2), 16–24 (1980) [in Russian]
[13] J. Kaniauskas and R. Karazija, Algebraic expressions of energy for terms of the highest multiplicity and related ones, as well as for ground and highest energy levels, Litov. Fiz. Sb. – Liet. fiz. rink. 25(2), 31–41 (1985) [in Russian]
[14] R.I. Karazija and L.S. Rudzikaitė, Symmetry of electronic shell in its lowest state and the interval rules for binding energines, Opt. Spektrosk. 68(3), 487–492 (1990) [in Russian]
[15] R. Karazija, A. Udris, A. Kynienė, and S. Kučas, On the symmetry with respect to a quarter of the electronic shell for the intensities of the strongest lines in lanthanide spectra, J. Phys. B 29(11), L405–L409 (1996),
http://dx.doi.org/10.1088/0953-4075/29/11/003
[16] R. Karazija and A. Kynienė, Symmetry of some properties of lanthanides and actinides with respect to a quarter of the fN shell, J. Phys. Chem. A 102(6), 897–903 (1998),
http://dx.doi.org/10.1021/jp9727409
[17] P. Bogdanovich, A. Kynienė, R. Karazija, R. Karpuškienė, and G. Gaigalas, Additional symmetry for the electronic shell in its ground state and many-electron effects, Eur. Phys. J. D 11(2), 175–183 (2000),
http://dx.doi.org/10.1007/s100530070081
[18] A. Kynienė and R. Karazija, Maximal values of the Auger amplitudes and propensity rules for their quantum numbers, Phys. Scr. 70(5), 288–294 (2004),
http://dx.doi.org/10.1088/0031-8949/70/5/005
[19] J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 4: The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974),
http://www.amazon.co.uk/Quantum-Theory-Molecules-Solids-Applied/dp/0070580383/
[20] B.R. Judd, Atomic shell theory recast, Phys. Rev. 162(1), 28–37 (1967),
http://dx.doi.org/10.1103/PhysRev.162.28
[21] Z.B. Rudzikas and J.M. Kaniauskas, Quasispin and Isospin in the Theory of Atom (Mokslas Publishers, Vilnius, 1984) [in Russian]
[22] W.C. Martin, Some aspects of the energy-level structures of lanthanide atoms and ions, Opt. Pura Appl. 5, 181–191 (1972)
[23] G.V. Ionova, V.G. Vokhmin, and V.I. Spicyn, Regularities in Properties of the Lanthanides and Actinides (Nauka, Moscow, 1990) [in Russian]
[24] A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team (2013), NIST Atomic Spectra Database (ver. 5.1) [online]. Available: http://physics.nist.gov/asd [2014, March 23]. National Institute of Standards and Technology, Gaithersburg, MD
[25] J.F. Wyart, Analysis of lanthanide atomic spectra: Present state and trends, J. Opt. Soc. Am. 68(2), 197–205 (1978),
http://dx.doi.org/10.1364/JOSA.68.000197
[26] G.V. Ionova, Periodicity in the variation of properties for series of d and f elements, Uspekhi Khimii 59(1), 66–85 (1990) [in Russian],
http://dx.doi.org/10.1070/RC1990v059n01ABEH003508
[27] V.I. Spicyn, V.G. Vokhmin, and G.V. Ionova, Interval rules for ionization energies and oxidation potentials of f-elements, Doklady AN SSSR 294(3), 650–653 (1987) [in Russian]
[28] Ch. Froese Fisher, Hartree-Fock calculations for atoms with inner-shell vacancies, Phys. Rev. Lett. 38(19), 1075–1076 (1977),
http://dx.doi.org/10.1103/PhysRevLett.38.1075
[29] Ch. Froese Fisher, Brillouin's theorem for excited nlqnlq' configurations. J. Phys. B: At. Mol. Opt. Phys. 6(10), 1933–1941 (1973),
http://dx.doi.org/10.1088/0022-3700/6/10/009
[30] V. Šimonis, J. Kaniauskas, and Z. Rudzikas, Isospin basis for electronic configurations n1lN1n2lN2, Litov. Fiz. Sb. – Liet. fiz. rink. 22(4), 3–15 (1982) [in Russian]
[31] R. Karazija, Sums of Atomic Quantities and Mean Characteristics of Spectra (Mokslas, Vilnius, 1991) [in Russian]