×

Symbolic algorithm for generating irreducible rotational-vibrational bases of point groups. (English) Zbl 1453.20002

Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 18th international workshop, CASC 2016, Bucharest, Romania, September 19–23, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9890, 228-242 (2016).
Summary: Symbolic algorithm implemented in computer algebra system for generating irreducible representations of the point symmetry groups in the rotor + shape vibrational space of a nuclear collective model in the intrinsic frame is presented. The method of generalized projection operators is used. The generalized projection operators for the intrinsic group acting in the space \(\mathrm {L}^2(\mathrm{SO(3)})\) and in the space spanned by the eigenfunctions of a multidimensional harmonic oscillator are constructed. The efficiency of the scheme is investigated by calculating the bases of irreducible representations subgroup \(\overline{\mathrm{D}}_{4y}\) of octahedral group in the intrinsic frame of a quadrupole-octupole nuclear collective model.
For the entire collection see [Zbl 1346.68010].

MSC:

20-08 Computational methods for problems pertaining to group theory
20C15 Ordinary representations and characters
68W30 Symbolic computation and algebraic computation
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1965) · Zbl 0171.38503
[2] Barut, A., Rączka, R.: Theory of Group Representations and Applications. PWN, Warszawa (1977)
[3] Chen, J.Q., Ping, J., Wang, F.: Group Representation Theory for Physicists. World Sci., Singapore (2002) · Zbl 1015.20012
[4] Cornwell, J.F.: Group Theory in Physics. Academic Press, New York (1984) · Zbl 0557.20001
[5] Doan, Q.T., et al.: Spectroscopic information about a hypothetical tetrahedral configuration in \[ {}^{156} \] Gd. Phys. Rev. C 82, 067306 (2010)
[6] Dobrowolski, A., Góźdź, A., Szulerecka, A.: Electric transitions within the symmetrized tetrahedral and octahedral states. Phys. Scr. T154, 014024 (2013)
[7] Dudek, J., Góźdź, A., Schunck, N., Miśkiewicz, M.: Nuclear tetrahedral symmetry: possibly present throughout the Periodic Table. Phys. Rev. Lett. 88, 252502 (2002)
[8] Góźdź, A., Dobrowolski, A., Pȩdrak, A., Szulerecka, A., Gusev, A.A., Vinitsky, S.I.: Structure of Bohr type nuclear collective spaces - a few symmetry related problems. Nucl. Theory 32, 108–122 (2013)
[9] Góźdź, A., Pȩdrak, A., Dobrowolski, A., Szulerecka, A., Gusev, A.A., Vinitsky, S.I.: Shapes and symmetries of nuclei. Bulg. J. Phys. 42, 494–502 (2015)
[10] Góźdź, A., Szulerecka, A., Dobrowolski, A., Dudek, J.: Nuclear collective models and partial symmetries. Acta Phys. Pol. B 42, 459–463 (2011)
[11] Gusev, A.A., Gerdt, V.P., Vinitsky, S.I., Derbov, V.L., Góźdź, A.: Symbolic algorithm for irreducible bases of point groups in the space of SO(3) group. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2015. LNCS, pp. 166–181. Springer, Heidelberg (2015) · Zbl 1434.20034
[12] Pogosyan, G.S., Smorodinsky, A.Y., Ter-Antonyan, V.M.: Oscillator Wigner functions. J. Phys. A 14, 769–776 (1981)
[13] Ring, P., Schuck, P.: The Nuclear Many-Body Problem. Springer, New York (1980)
[14] Rojansky, V.: On the theory of the Stark effect in hydrogenic atoms. Phys. Rev. 33, 1–15 (1929) · JFM 55.0541.04
[15] Szulerecka, A., Dobrowolski, A., Góźdź, A.: Generalized projection operators for intrinsic rotation group and nuclear collective model. Phys. Scr. 89, 054033 (2014)
[16] Varshalovich, D.A., Moskalev, A.N., Khersonskii, V.K.: Quantum Theory of Angular Momentum. World Sci., Singapore (1989) · Zbl 0725.00003
[17] Vilenkin, J.A., Klimyk, A.U.: Representation of Lie Group and Special Functions, vol. 2. Kluwer Academic Publ., Dordrecht (1993) · Zbl 0809.22001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.