Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

[PDF] http://dx.doi.org/10.3952/lithjphys.44202

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 44, 91–120 (2004)

JUCYS GRAPHS OF ANGULAR MOMENTUM THEORY
G. Merkelis
Vilnius University Research Institute of Theoretical Physics and Astronomy, A. Goštauto 12, LT-01108 Vilnius, Lithuania
E-mail: merkelis@itpa.lt

Received 14 May 2004

Dedicated to the 100th anniversary of Professor A. Jucys

A brief review of the results obtained in Vilnius while developing the graphical methods of quantum angular momentum theory is presented. Numerous modifications and extensions of the original method proposed by A. Jucys, J. Levinson, and V. Vanagas are discussed. The application of the graphical method to the study of one-, two-electron as well as the effective operators and their matrix elements in the coordinate and second quantization representation is surveyed.

Keywords: atomic spectroscopy, graphical methods, angular momentum
PACS: 31.15.Md, 31.15.–p, 35.15.Ar

JUDĖJIMO KIEKIO MOMENTO TEORIJOS JUCIO DIAGRAMOS
G. Merkelis
VU Teorinės fizikos ir astronomijos institutas, Vilnius, Lietuva

Darbas skirtas prof. A. Jucio 100-osioms gimimo metinėms paminėti ir apžvelgia judėjimo kiekio momento teorijos grafinio metodo pagrindinių principų, plėtros bei taikymo darbų, atliktų Vilniuje, rezultatus. Supažindinama su pagrindiniais A. Jucio, J. Levinsono ir V. Vanago grafinio metodo elementais, teoremomis bei taisyklėmis. Aptariami A. Jucio ir A. Bandzaičio išplėtoto grafinio metodo privalumai ir trūkumai. Nurodomos kitų autorių pasiūlytos šių metodų atmainos, įgalinančios išplėsti grafiškai vaizduojamų dydžių ir veiksmų ratą. Žymi darbo dalis skirta grafinei technikai antrinio kvantavimo metodu aprašyti. Ji remiasi A. Jucio ir A. Bandzaičio grafiniu metodu. Jos diagramos atspindi tiek judėjimo kiekio momento teorijos savybes, tiek ir fermionų dalelių sistemos antisimetriškumo savybes, todėl tai ypač efektyvus būdas teoriškai tirti įvairius daugiaelektronių atomų ir jonų su neužpildytais sluoksniais dydžius. Aptariami grafiniai būdai atomo sąveikas nusakančių operatorių N-elektronių matricinių elementų išraiškoms koordinatinio ir antrinio kvantavimo vaizdavimais gauti.

References / Nuorodos

[1] A.P. Jucys, J. Levinson, and V.V. Vanagas, Judėjimo kiekio momento teorijos matematinis aparatas (Lietuvos TSR valstybinės politinės ir mokslinės literatūros leidykla, Vilnius, 1960) [in Russian]; Mathematical Apparatus of the Theory of Angular Momentum (Israel Program for Scientific Translation, Jerusalem, 1962) [English translation]; Mathematical Apparatus of the Theory of Angular Momentum (Gordon and Breach, New York, 1964) [English translation],
http://archive.org/details/nasa_techdoc_19630001624/page/n1/mode/2up
[2] E.U. Condon and G.H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1935),
http://www.cambridge.org/lt/universitypress/subjects/physics/atomic-physics-molecular-physics-and-chemical-physics/theory-atomic-spectra
[3] E. Wigner, Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren (Braunschweig, 1931),
http://dx.doi.org/10.1007/978-3-663-02555-9
[4] E.P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, New York, 1959)
[5] G. Racah, Phys. Rev. 61, 186 (1941),
http://dx.doi.org/10.1103/PhysRev.61.186
[6] G. Racah, Phys. Rev. 62, 438 (1942),
http://dx.doi.org/10.1103/PhysRev.62.438
[7] G. Racah, Phys. Rev. 63, 367 (1943),
http://dx.doi.org/10.1103/PhysRev.63.367
[8] G. Racah, Phys. Rev. 76, 1352 (1949),
http://dx.doi.org/10.1103/PhysRev.76.1352
[9] A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1960),
http://press.princeton.edu/books/paperback/9780691025896/angular-momentum-in-quantum-mechanics
[10] B.R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963),
http://openlibrary.org/books/OL5857229M/Operator_techniques_in_atomic_spectroscopy.
[11] U. Fano and G. Racah, Irreducible Tensorial Sets (Academic Press, New York, 1959),
http://dx.doi.org/10.1063/1.3057072
[12] A.P. Jucys and A.J. Savukynas, Mathematical Foundations of the Atomic Theory (Mokslas, Vilnius, 1973) [in Russian]
[13] A.P. Jucys, Selected Papers (Mokslas, Vilnius, 1978) [in Russian]
[14] B.R. Judd, Second Quantization in Atomic Spectroscopy (Johns Hopkins, Baltimore, 1967),
http://archive.org/details/secondquantizati0000judd
[15] L. Armstrong, Jr., Phys. Rev. 172, 18 (1968),
http://dx.doi.org/10.1103/PhysRev.172.18
[16] Z. Rudzikas and J. Kaniauskas, Quasispin and Isospin in the Theory of Atom (Mokslas, Vilnius, 1984) [in Russian]
[17] Z. Rudzikas, Theoretical Atomic Spectroscopy (Cambridge University Press, Cambridge, 1997),
http://dx.doi.org/10.1017/CBO9780511524554
[18] I.B. Levinson, FTI Darbai 2, 17 (1956) [in Russian]
[19] I.B. Levinson, FTI Darbai 2, 31 (1956) [in Russian]
[20] I.B. Levinson, Lietuvos MA Darbai, Ser. B 4, 3 (1957) [in Russian]
[21] I.B. Levinson and V.V. Vanagas, Opt. Spektrosk. (USSR) 2, 3 (1957) [in Russian]
[22] V.V. Vanagas and J. Čiplys, Lietuvos MA Darbai, Ser. B 3, 15 (1958) [in Russian]
[23] A.M. Gutman and S. Budrytė, Lietuvos MA Darbai, Ser. B 4, 3 (1959) [in Russian]
[24] J. Čiplys, S. Budrytė, and A.P. Jucys, Liet. Fiz. Rink. 1(3–4), 263 (1961) [in Russian]
[25] S. Budrytė and A.P. Jucys, Liet. Fiz. Rink. 1, 281 (1961) [in Russian]
[26] A. Bandzaitis, J. Vizbaraitė, and A. Jucys, Liet. Fiz. Rink. 2, 61 (1962) [in Russian]
[27] A. Bandzaitis, J. Vizbaraitė, and A. Jucys, Liet. Fiz. Rink. 2, 73 (1962) [in Russian]
[28] A. Bandzaitis, J. Vizbaraitė, and A. Jucys, Liet. Fiz. Rink. 2, 91 (1962) [in Russian]
[29] A. Bandzaitis, J. Vizbaraitė, and A. Jucys, Liet. Fiz. Rink. 2, 109 (1962) [in Russian]
[30] A.P. Jucys and A.A. Bandzaitis, Theory of Angular Momentum in Quantum Mechanics, 1st edn. (Mokslas, Vilnius, 1965) [in Russian]
[31] A.P. Jucys and A.A. Bandzaitis, Theory of Angular Momentum in Quantum Mechanics, 2nd edn. (Mokslas, Vilnius, 1977) [in Russian]
[32] A.P. Jucys, Z.B. Rudzikas, and A.A. Bandzaitis, Liet. Fiz. Rink. 5, 1 (1965) [in Russian]
[33] A. Bolotin, I. Levinson, and V. Tolmachev, Liet. Fiz. Rink. 4, 25 (1964) [in Russian]
[34] J. Goldstone, Proc. Roy. Soc. London Ser. A 239, 267 (1957)
http://dx.doi.org/10.1098/rspa.1957.0037
[35] A. Matulis, E. Našlėnas, and A. Bandzaitis, Liet. Fiz. Rink. 5, 453 (1965) [in Russian]
[36] A. Matulis and A. Bandzaitis, Liet. Fiz. Rink. 5, 289 (1965) [in Russian]
[37] G. Kamuntavičius, Liet. Fiz. Rink. 7, 553 (1967) [in Russian]
[38] I.B. Levinson, Lietuvos MA Darbai, Ser. B 4, 17 (1957) [in Russian]
[39] V. Tutlys, Automatization of calculations of the atomic theory by using the nonorthogonal orbitals, Thesis (Vilnius, 1972) [in Russian]
[40] Z.I. Kupljauskis, A.V. Kupljauskiene, and V. Tutlis, Izv. Vuzov Ser. Fiz. (3), 7–11 (1981) [Sov. Phys. Tr. (3), 203 (1981)]
[41] J.S. Briggs, Rev. Mod. Phys. 41, 189 (1971),
http://dx.doi.org/10.1111/j.0954-6820.1971.tb01577.x
[42] K.-N. Huang, Rev. Mod. Phys. 51, 216 (1979),
http://dx.doi.org/10.1103/RevModPhys.51.215
[43] D.M. Brink and G.R. Satchler, Angular Momentum, 2nd edn. (Clarendon Press, Oxford, 1968),
http://archive.org/details/angularmomentum0000brin_a9n6
[44] E. El Baz and B. Castel, Graphical Methods of Spin Algebras in Atomic, Nuclear, and Particle Physics (Marcel Dekker, New York, 1972),
http://archive.org/details/graphicalmethods0002elba
[45] P.G.H. Sandars, La structure hyperfine magnetique des atoms et des molecules (Editions du Centre National de la Récherche Scientifique, Paris, 1967)
[46] P.G.H. Sandars, Adv. Chem. Phys. 14, 365 (1969),
http://dx.doi.org/10.1002/9780470143599.ch11
[47] V. Tolmachev, Adv. Chem. Phys. 14, 421 (1969),
http://dx.doi.org/10.1002/9780470143599.ch12
[48] I. Lindgren and M. Morrison, Atomic Many-Body Theory, Springer Series in Chemical Physics, Vol. 13, 2nd edn. (Springer-Verlag, Berlin, 1982),
http://dx.doi.org/10.1007/978-3-642-96614-9
[49] D.A. Varshalovich, A.N. Moskalev, and V.K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988),
http://dx.doi.org/10.1142/0270
[50] G. Merkelis, J. Kaniauskas, and Z. Rudzikas, Liet. Fiz. Rink. 25, 21 (1985) [in Russian]
[51] G. Merkelis and G. Gaigalas, Irreducible tensorial form of effective operator in the perturbation theory of open-shell atoms, in: Abstracts of the Conference “Theory of Atoms and Atomic Spectra” (Minsk, Byelorussia, 1983) [in Russian]
[52] G. Merkelis, G. Gaigalas, and Z. Rudzikas, Liet. Fiz. Rink. 25, 14 (1985)
[53] G. Gaigalas, J. Kaniauskas, and Z. Rudzikas, Liet. Fiz. Rink. 25, 3 (1985) [in Russian]
[54] G. Merkelis, G. Gaigalas, J. Kaniauskas, and Z. Rudzikas, Izv. Vuzov Ser. Fiz. 50, 1403 (1986)
[55] G. Gaigalas and G. Merkelis, Acta Phys. Hung. 61, 111 (1987),
http://dx.doi.org/10.1007/BF03053831
[56] G. Merkelis and G. Gaigalas, The graphical method of construction and the calculation of spin-angular parts of operator's expansion for many-body perturbation theory for atoms with several open shells, in: Energy Levels and Transition Probabilities in Atoms and Ions (Scientific Council of Spectroscopy, Moscow, 1985) p. 20 [in Russian]
[57] G. Merkelis, Physica Scripta 61, 662 (2000),
http://dx.doi.org/10.1238/Physica.Regular.061a00662
[58] G. Merkelis, Lithuanian J. Phys. 38, 247 (1998)
[59] G. Merkelis, Physica Scripta 63, 289 (2001),
http://dx.doi.org/10.1238/Physica.Regular.063a00289
[60] G. Merkelis, Lithuanian J. Phys. 41, 63 (2001)
[61] G. Merkelis and R. Karazija, J. Electron Spectr. Relat. Phenom. 133, 123 (2003),
http://dx.doi.org/10.1016/j.elspec.2003.09.004
[62] G. Gaigalas and Z. Rudzikas, J. Phys. B 29, 3303 (1996),
http://dx.doi.org/10.1088/0953-4075/29/15/007
[63] G. Gaigalas, Z. Rudzikas, and Ch. Froese Fischer, J. Phys. B 30, 3747 (1996),
http://dx.doi.org/10.1088/0953-4075/30/17/006
[64] G. Gaigalas, Lithuanian J. Phys. 39, 79 (1998)
[65] I.P. Grant, in: Methods in Computational Chemistry, Vol. 2, ed. S. Wilson (Plenum Press, New York, 1988) p. 1,
http://dx.doi.org/10.1007/978-1-4613-0711-2_1
[66] P.H.M. Uylings, J. Phys. B 25, 4391 (1992),
http://dx.doi.org/10.1088/0953-4075/25/21/008
[67] R. Karazija, Sums of Atomic Quantities and Mean Characteristics of Spectra (Mokslas, Vilnius, 1991) [in Russian]
[68] L. Rudzikaitė and R. Karazija, Liet. Fiz. Rink. 29, 143 (1989) [in Russian]
[69] A.P. Jucys and J. Vizbaraitė, Lietuvos MA Darbai, Ser. B 4(27), 45 (1961)
[70] U. Fano, Phys. Rev. 140, A67 (1965),
http://dx.doi.org/10.1103/PhysRev.140.A67
[71] V. Tutlys and A. Kupliauskiene, Lithuanian J. Phys. 41, 31 (2001)
[72] A. Kupliauskienė, N. Rakštikas, and V. Tutlys, J. Phys. B 34, 1783 (2001),
http://dx.doi.org/10.1088/0953-4075/34/9/314
[73] P. Rumšas, V. Matulis, and A. Jucys, Liet. Fiz. Rink. 4, 447 (1964) [in Russian]
[74] P. Rumšas, A. Bandzaitis, and A. Jucys, Liet. Fiz. Rink. 2, 197 (1965) [in Russian]
[75] A. Bandzaitis and D. Stulpinas, Liet. Fiz. Rink. 7, 27 (1967) [in Russian]
[76] P.G. Burke, Comput. Phys. Commun. 1, 241 (1970),
http://dx.doi.org/10.1016/0010-4655(70)90040-8
[77] A. Bar-Shalom and M. Klapisch, Comput. Phys. Commun. 50, 375 (1988),
http://dx.doi.org/10.1016/0010-4655(88)90192-0
[78] P.M. Lima, Comput. Phys. Commun. 66, 89 (1991),
http://dx.doi.org/10.1016/0010-4655(91)90010-I
[79] V. Fack, S.N. Piter, and J. Van der Jeugt, Comput. Phys. Commun. 101, 155 (1997),
http://dx.doi.org/10.1016/S0010-4655(96)00170-1
[80] S. Fritzsche, T. Inghoff, T. Bastug, and M. Tomaselli, Comput. Phys. Commun. 39, 314 (2001),
http://dx.doi.org/10.1016/S0010-4655(01)00219-3
[81] D. Van Dyck and V. Fack, Comput. Phys. Commun. 154, 219 (2003),
http://dx.doi.org/10.1016/S0010-4655(03)00280-7
[82] V. Tutlys, A program to calculate the matrix elements in multiconfigurational approximation, in: Collection of Programs for Mathematical Methods of Atomic Calculations, Vol. 4 (Vilnius, 1980) [in Russian]
[83] P.M. Lima, Comput. Phys. Commun. 66, 99 (1991),
http://dx.doi.org/10.1016/0010-4655(91)90011-9
[84] G. Gaigalas, M.J. Vilkas, A. Bernotas, and G. Merkelis, Program to calculate energy spectra of open-shell atoms by using MBPT, in: Abstracts of EGAS-23, eds. S. Legovski and Z. Rudzikas (Torun, Poland, 1991)