A heuristic procedure to go from LS to jj expressions in atomic and nuclear spectroscopy
Keywords:LS coupling, jj coupling, energy levels, radiative transitions
The expressions for the energy matrix elements and for the radiative transitions in the jj coupling can be obtained from the respective LS expressions by making a few simple changes. The results shown as examples are compared with other treatments, where the two formulations are deduced in parallel, without making use of these simple rules. We emphasize that the rules were found by heuristic reasoning. In all cases the application of the rules are in accordance with published results. This work completes two previous papers published in this journal (References 19 and 20).
i. In the middle of the year 2021, there have been more than 5500 citations to Cowan’s book and codes, and each year adds about 150 citations to this list.
R. D. Cowan, The Theory of Atomic Structure and Spectra, University of California Press, Berkeley 1981 (Errors and additional references to third and fourth printings, 2001).
J. C. Slater, Quantum Theory of Atomic Structure, (McGrawHill, New York 1960), 2 vols.
B. W. Shore and D. H. Menzel, Principles of Atomic Spectra, (John Wiley, New York, 1968).
M. Mizushima, Quantum Mechanics of Atomic Spectra and Atomic Structure, W. A. Benjamin, New York 1970.
I. I. Sobelman, Introduction to the Theory of Atomic Spectra, Pergamon, Oxford, 1972.
M. Weissbluth, Atoms and Molecules, Academic Press, New York, 1978.
E. U. Condon and H. Odabasi, Atomic Structure, Cambridge University Press, Cambridge, 1980.
A. de-Shalit and I. Talmi, Nuclear Shell Theory, Academic Press, New York, 1963.
W. R. Johnson, Atomic Structure Theory, Springer, Berlin 2007.
I. P. Grant, Relativistic Quantum Theory of Atoms and Molecules, Springer, Berlin 2007.
Z. Rudzikas, Theoretical Atomic Spectroscopy, Cambridge University Press, Cambridge, 1997 (a few misprints corrected in the paperback edition, 2007).
A. K. Pradhan and S. H. Nahar, Atomic Astrophysics and Spectroscopy, Cambridge University Press, Cambridge 2011.
N. Hell, Master Thesis, Universitat Erlangen-N ¨ urnberg, 2012.
I. I. Sobelman, L. A. Vainshtein and E. A. Yukov, Excitation of Atoms and Broadening of Spectral Lines (2nd edition), Springer-Verlag, Berlin, 1995.
J. C. Aguiar, M. Raineri and H. O. Di Rocco, The study of the 4s4p configuration of the Zn isoelectronic sequence using the
relativistic jj-coupling approach, Eur. Phys. J. D 67 (2013) 158. DOI: 10.1140/epjd/e2013-30714-5.
J. C. Aguiar and H. O. Di Rocco, An examination of the consistency of the published levels of the p2, p3 and p4 isoelectronic
sequences using jj-relativistic expressions, J. Quant. Spectroscop. Radiat. Transfer 149 (2014) 1. http://dx.doi.org/10.1016/j.jqsrt.2014.07.021.
H. O. Di Rocco, M. Raineri and J. G. Reyna-Almandos, Study of the 4p2, 5p2 and 5s5f excited configurations of the Zn and Cd
isoelectronic sequences, using relativistic and non-relativistic semiempirical approaches, Eur. Phys. J. D 70 (2016) 239, DOI:10.1140/epjd/e2016-70297-y.
G. K. Woodgate, Elementary Atomic Structure (2nd ed) Clarendon Press, Oxford, 1980.
G. Fernandez, R. Solanilla and H. O. Di Rocco, ´ The calculation of atomic structures for non specialists, Rev. Mex. Fis. 44 (1998) 92.
H. O. Di Rocco, A simple and effective approach to calculate the energies of complex atoms, Rev. Mex. Fis. 48 (2002) 76.
H. O. Di Rocco and F. Lanzini, Breit and Quantum Electrodynamics Energy Contributions in Multielectron Atoms from the Relativistic Screened Hydrogenic Model, Braz. J. Physics 46, (2016) 175, DOI: 10.1140/epjd/e2016-70297-y.
Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2021). NIST Atomic Spectra Database (ver. 5.8), [Online]. Available: https://physics.nist.gov/asd [2021, February 3]. National Institute of Standards and Technology, Gaithersburg, MD. DOI: https://doi.org/10.18434/T4W30F.
How to Cite
Copyright (c) 2022 Julio C. Aguiar, Héctor Oscar Di Rocco
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.