Publication: The Madelung rule, Regge-like sequences and the conformal Lie algebra
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The two main group theoretical models related to the Periodic System of Chemical Elements are reviewed, in connection with the Madelung rule and the construction of orthonormal bases of states for the conformal Lie algebra so (2,4). Basing on discrepancies between the Madelung rule and chemical experience, a new approach to the conformal symmetry, currently in development, is described.
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Symmetries in Science XVI 21–26 July 2013, Bregenz, Austria
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[1]Weyl H 1928 Gruppentheorie und Quantenmechanik (Hirzel Verlag, Leipzig)
[2]Bohr N 1921 Nature 107 104
Hund F 1925 Z. Phys. 33 855
Lenz W 1924 Z. Phys. 34 197
Pauli W 1926 Z. Phys. 36 336
Condon E U, Shortley G H 1935 The Theory of Atomic Spectra (University Press, Cambridge)
Brauer R, Weyl H 1935 Am. J. Math. 57 425
Fock V A 1936 Z. Phys. 98 145
Bargmann V 1936 Z. Phys. 99 576
[3]Racah G 1949 Phys. Rev. 76 1352
Racah G 1951 Group Theory and Spectroscopy (Princeton Univ. Press, New Jersey)
Racah G 1959 Nuovo imento Supplemento 14 75
Wybourne B G 1965 Spectroscopic Properties of Rare Earths (John Wiley, NY)
Bloch F, Cohen S G, de-Shalit A, Sambursky S and Talmi I 1968 Spectroscopic and Group Theoretic Methods in Physics (North-Holland, Amsterdam)
[4]Madelung E 1936 Die mathematischen Hilfsmittel des Physikers (Springer, Berlin)
Bopp F, Haag R 1950 Zeit. Naturforsch. 5a 644
Pauling L 1965 Phys. Rev. Lett. 15 499
Hara O, Goto T 1968 Prog. Theor. Phys. Suppl. 41 56
Weissmantel C, Lenk R, Forker W, Ludloff R, Hoppe J (Hrsg) 1970 Atom. Struktur der Materie (VEB Verlag Enzyklopadie, Leipzig)
Novaro O A, Berrondo M 1972 J. Phys. B: At. Mol. Phys. 5 1104
Novaro O A, Berrondo M 1973 J. Phys. B: At. Mol. Phys. 6 761
Kibler M R, Négadi T 1983 J. Phys. A: Math. Gen. 16 4265
[5]Malkin I A, Man'ko V 1965 Pis'ma V ZhETF 2 230
Barut A O, Kleinert H 1967 Phys. Rev. 156 1541
Malkin I A, Man'ko V I 1969 YaF 9 184
Rumer Yu B 1970 Dokl. Akad. Nauk SSSR 191 64
Fet A I 1975 Teor. Mat. Fiz. 22 323
[6]Bédnar M 1973 Ann. Phys. 108 49
Byakov V M, Kulakov Yu I, Rumer Yu B, Fet A I 1976 ITEF–26/1976 ITEF–90/1976 ITEF–07/1977
Kregar M 1985 Phys. Scripta 29 438
Cizek J, Clay M R, Paldus J 1980 Phys. Rev. A 22 793
Adams B G, Cizek J, Paldus J 1982 Int. J. Quantum Chem. 21 153
Komarov L I, Romanova T S 1985 J. Phys. B: At. Mol. Phys. 18 859
Adams B G, Cizek J, Paldus J 1988 Adv. Quantum Chem. 19 1
Kibler M R 1989 J. Mol. Struct. 187 83
Gurskii' L I, Komarov L I, Solodukhin A M 1998 Int. J. Quantum Chem. 72 499
[7]Kibler M R, Négadi T 1983 Nouvo Cimento 37 225
Kibler M R, Négadi T 1984 Folia Chim. Theor. 12 117
Kibler M R, Négadi T 1991 J. Phys. A: Math. Gen. 24 5283
Chen J L, Zhang H B, Wang X B, Jing H, Zhao X G 2000 Int. J. Theor. Phys. 39 2043
Zeng G J, Su K L, Li M 1994 Phys. Rev. A 50 4373
Efstathiou K, Sadovskii' D A 2010 Rev. Mod. Phys. 82 2099
[8]Fock B A 1935 Akad. Nauk SSSR VII 2 169
Fock V A 1935 Izv. Akad. Nauk SSSR VII Ser. 2 169
[9]Rumer Yu B, Fet A I 1971 Teor. Mat. Fiz. 9 203
Rumer Yu B, Fet A I 1970 Teoriya unitarnoi simetrii (Nauka, M.)
[10]Barut A O, Kleinert H 1967 Phys. Rev. 156 1541
Konopel'chenko B G 1972 Gruppa SO(2,4) + R i tablitsa Mendeleeva 45 802
Fet A I 1975 Teor. Mat. Fiz. 22 323
Fet A I, Romanov L N 1996 Lecture Notes Comput. Sci. 1067 379
[11]Gross L 1964 J. Math. Phys. 5 687
Niederer U 1972 Helv. Phys. Acta 45 802
Niederer U 1974 Helv. Phys. Acta 47 167
Lagu S, Laue H 1974 Nuovo Cimento A 20 217
[12]Lambert D, Kibler R M 1988 J. Phys. A: Math. Gen. 21 308
Barut A O 1972 The Structure of Matter (Proc. Rutherford Centennial Symp., 1971) (Christchurch, New Zealand)
Campoamor-Stursberg R 2008 J. Phys.: Conf Ser. 128 012052
[13]Keller O L, Seaborg G T 1997 Ann. Rev. Nucl. Sci. 25 139
Indelicato P, Bieroń J and Jönsson P 2001 Theor. Chim. Acta 129 495
Pyykkö P 2011 Phys. Chem. Chem. Phys. 13 161
[14]Goudsmit S A, Richards P L 1964 Proc. Natl. Acad. Sci. U.S.A 51 664
Schwarz W H E, Wang S G 2010 Int. J. Quantum Chem. 110 1455
Schwarz W H E 1990 The Concept of the Chemical Bond ed Maksic Z B (ed) (Springer, Berlin)
Wang S G, Schwarz W H E 2009 Angew. Chem. Int. Ed. 48 2
Schwarz W H E, Rich R L 2010 J. Chem. Ed. 87 435
Scerri E R 2007 The Periodic Table. Its History and its Significance (Oxford UP, Oxford)
[15]Oganessian Y T 2007 J. Phys. G: Nucl. Part. Phys. 34 R165
Google Scholar
Hofmann S 2012 Phys. Unserer Zeit 43 30
[16]Judd B R 1963 Operator Techniques in Atomic Spectroscopy (McGraw-Hill, NY)
Wybourne B G, Smentek L 1994 Optical Spectroscopy of Lanthanides (CRC Press, Boca Raton)
Google Scholar
[17]Hefferlin R A, Campbell R, Gimbel D, Kuhlman H and Cayton T 1979 J. Quant. Spectrosc. Radiat. Transfer 21 315
Hefferlin R A, Kuhlman H, Campbell R and Gimbel D 1979 J. Quant. Spectrosc. Radiat. Transfer 21 337
Kong F A 1982 J. Mol. Struct. 90 17
Hefferlin R A 1989 Periodic Systems of Molecules and Their Relation to the Systematic Analysis of Molecular Data (E Mellin Press, NY)
Hefferlin R A, Sepman A V and Zhuvikin G V 1996 J. Chem. Comput. Sci. 36 399
[18]Sharp R T and Pieper S C 1968 J. Math. Phys. 9 663
Sharp R T 1975 J. Math. Phys. 16 2050
Peccia A and Sharp R T 1976 J. Math. Phys. 17 1313
Louck J D 1976 Proceedings of the International Symposium on Mathematical Physics (Mexico City, Mexico)
Campoamor-Stursberg R 2010 Acta Phys. Pol. B 42 53
[19]Abellanas L and Martinez Alonso L 1975 J. Math. Phys. 16 1580
Abellanas L and Martinez Alonso L 1979 J. Math. Phys. 20 437
Couture M, Sharp R T 1989 J. Phys. A: Math. Gen. 22 1525
Campoamor-Stursberg R 2011 Int. J. Theor. Phys. 50 2153
Campoamor-Stursberg R 2011 J. Phys. A: Math. Theor. 44 025204
[20]Kibler M R 2004 The Mathematics of the Periodic Table ed D H Rouvray and R B King (Baldock: Research Studies Press)
[21]Kleinert H 1968 Fortschr. Phys. 6 1
Jaffe R 1971 J. Math. Phys. 12 882
Böhm A 1986 Phys. Rev. D 33 3358
[22]Thyssen P, Binnemans K 2011 Handbook on The Physics and Chemistry of Rare Earths vol 41 (Academic Press, Burlington)
Thyssen P 2013 Symmetry and Symmetry Breaking in the Periodic Table - Towards a Group-Theoretical Classification of the Chemical Elements PhD Thesis KU Leuven
[23]Dixmier J 1974 Algebres enveloppantes (Gauthier-Villard, Paris)
Giroux Y and Sharp R T 1987 J. Math. Phys. 28 1671
Giroux Y 1987 Degenerate Enveloping Algebras of Low-rank Groups PhD Thesis McGill University
Ruan R, Ruan W 1999 Phys. Lett. A 263 78
Crossref
Ni Z 1999 J. Phys. A: Math. Gen. 32 2217
Campoamor-Stursberg R and Low S G 2009 J. Phys. A: Math. Theor. 42 065205
[24]Gruber B and Lorente M 1972 J. Math. Phys. 13 1639
[25]Barut A O 1972 Dynamical Groups and Generalized Symmetries in Quantum Theory (Univ. Canterbury, Christchurch)
Englefield M J 1972 Group Theory and the Coulomb problem (Wiley, NY)
[26]Quesne C 1994 Phys. Lett. A 193 245
Quesne Ch 1995 J. Phys. A: Math. Gen. 28 2847
Ruan D, Ruan W 1999 Phys. Lett. A 263 78
Ruan D, Jia Y and Ruan W 2001 J. Math. Phys. 42 2718
Indelicato P, Bieroń J and Jönsson P 2001 Theor. Chim. Acta 129 495