[PDF]    http://dx.doi.org/10.3952/lithjphys.51303

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 51, 194–198 (2011)


A NOTE ON RECURSIVE CALCULATIONS OF PARTICULAR 9j COEFFICIENTS
J.-C. Pain
Commissariat à l’énergie atomique et aux énergies alternatives, DAM, DIF, F-91297 Arpajon, France
E-mail: jean-christophe.pain@cea.fr

Received 24 May 2011; revised 27 June 2011; accepted 21 September 2011

The calculation of angular-momentum coupling transformation matrices can be very time consuming and alternative methods, even if they apply only in special cases, are helpful. We present a recursion relation for the calculation of particular 9j symbols used in the quantum theory of angular momentum.
Keywords: angular momentum, 9j coefficient, recursion relation
PACS: 02.70.-c, 31.15.-p, 03.65.Fd, 23.40.-s


DĖL KAI KURIŲ 9j KOEFICIENTŲ REKURENTINIO SKAIČIAVIMO
J.-C. Pain
Atominės energijos ir alternatyviųjų energijų komisariatas, Arpajon, Prancūzija

Judėjimo kiekio momentų perrišimo matricų skaičiavimas gali būti labai ilgas ir čia naudingi alternatyvūs metodai, netgi jei jie tinka tik ypatingais atvejais. Pateikiamas rekurentinis sąryšis skaičiuoti tam tikrus 9j koeficientus, naudojamus judėjimo kiekio momento kvantinėje teorijoje.

References / Nuorodos

[1] Z.B. Rudzikas, Theoretical Atomic Spectroscopy (Cambridge University Press, Cambridge, 1997),
http://dx.doi.org/10.2277/052144425X
[2] B.R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963),
http://www.amazon.co.uk/Techniques-Spectroscopy-Princeton-Landmarks-Mathematics/dp/0691059012/
[3] A.P. Jucys and A.A. Bandzaitis, Teoriya Momenta Kolichestva Dvizheniya v Kvantovoi Mekhanike (Angular Momentum Theory in Quantum Mechanics) [in Russian] (1st ed.: Mintis, Vilnius, 1965, 2nd ed.: Mokslas, Vilnius, 1977)
[4] S.J. Ališauskas and A. Jucys, J. Math. Phys. 12, 594–605 (1971),
http://dx.doi.org/10.1063/1.1665626
Erratum: J. Math. Phys. 13, 575 (1972),
http://dx.doi.org/10.1063/1.1666016
[5] A.C.T. Wu, J. Math. Phys. 14, 1222–1223 (1973),
http://dx.doi.org/10.1063/1.1666469
[6] L.C. Biedenharn and J.D. Louck, Angular Momentum in Quantum Physics (Addison-Wesley, Reading, MA, 1981),
http://www.amazon.co.uk/Angular-Momentum-Quantum-Physics-Encyclopedia/dp/0521102448/
[7] D. Zhao and R.N. Zare, Mol. Phys. 65, 1263–1268 (1988),
http://dx.doi.org/10.1080/00268978800101761
[8] K.S. Rao, V. Rajeshwari, and C.B. Chiu, Comput. Phys. Commun. 56, 231–248 (1989),
http://dx.doi.org/10.1016/0010-4655(89)90021-0
[9] L. Wei, Comput. Phys. 12, 632–634 (1998),
http://dx.doi.org/10.1063/1.168745
[10] L. Wei, Comput. Phys. Commun. 120, 222–230 (1999),
http://dx.doi.org/10.1016/S0010-4655(99)00232-5
[11] G. Gaigalas, T. Žalandauskas, and Z. Rudzikas, Lith. J. Phys. 41, 226–231 (2001)
[12] A.V. Karosienė, S.J. Ališauskas, and A.A. Bandzaitis, Lietuvos Fiz. Rinkinys 5, 13–21 (1965) [in Russian]
[13] 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
[14] A. de-Shalit and I. Talmi, Nuclear Shell Theory (Academic, New York, 1963),
http://www.amazon.co.uk/Nuclear-Shell-Theory-Amos--Shalit/dp/1483253872/
[15] L. Szybisz and V. Seshagiri Rao, Lett. Nuovo Cimento 14, 237–240 (1975)
[16] D.M. Brink and G.R. Satchler, Angular Momentum (Clarendon Press, Oxford, 1968),
http://www.amazon.co.uk/Angular-Momentum-Library-Physical-Science/dp/0198514190/
[17] R.T. Sharp, Nucl. Phys. A 95, 222–228 (1967),
http://dx.doi.org/10.1016/0375-9474(67)90163-7
[18] S. Jang, J. Math. Phys. 9, 397–402 (1968),
http://dx.doi.org/10.1063/1.1664592
[19] L.C. Biedenharn, J.M. Blatt, and M.E. Rose, Rev. Mod. Phys. 24, 249–257 (1952),
http://dx.doi.org/10.1103/RevModPhys.24.249
[20] T. Regge, Nuovo Cimento 10, 544–545 (1958),
http://dx.doi.org/10.1007/BF02859841
[21] M. Nomura, J. Phys. Soc. Jpn. 58, 2677–2686 (1989),
http://dx.doi.org/10.1143/JPSJ.58.2677
[22] M. Rotenberg, R. Bivins, N. Metropolis, and J.K. Wooten, Jr., The 3-j and 6-j symbols (The Technology Press, M. I. T., Cambridge, MA, 1959)
http://www.amazon.co.uk/3-j-6-j-symbols-Manuel-Rotenberg/dp/B0000EGNPF/
[23] K. Schulten and R.G. Gordon, J. Math. Phys. 16, 1961–1970 (1975),
http://dx.doi.org/10.1063/1.522426
[24] J.H. Luscombe and M. Luban, Phys. Rev. E 57, 7274–7277 (1998),
http://dx.doi.org/10.1103/PhysRevE.57.7274