On the interpretation of the energy levels of ground configurations of free ions Mo$^{3+}$ and Pd$^{3+}$

A. M. Leushin   ; E. N. Irinyakov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 1, pp. 12-21

Résumé

The positions of the energy levels of free ions of the palladium group Mo$^{3+}$, whose ground configuration is 4d$^3$ and Pd$^{3+}$, whose configuration is 4d$^7$, are interpreted theoretically within the framework of the single-configuration approximation with a Hamiltonian that takes into account real electrostatic, spin-orbit, and spin-spin interactions, as well as electrostatic and spin-orbit interactions correlated by configuration mixing. It is shown that the correct positions of all the energy levels are determined when the Hamiltonian includes the operators of the theory of the nonlinear configuration interaction. The most correct theoretical description of the experimental spectra is obtained by taking into account relativistic interactions and correlation effects of spin-orbit interactions. Semiempirical parameters of the interactions included into the Hamiltonian are found for both the ions.

Bibliographie

[1] Pasternak A., Goldshmidt Z. B., “Spin-dependent interactions in the 3d$^N$ configurations of the third spectra of the iron group”, Phys. Rev. A, 6:1 (1972), 55–68 | DOI

[2] Pasternak A., Goldshmidt Z. B., “Spin-dependent interactions in Mn III 3d$^5$”, Phys. Rev. A, 9:2 (1974), 1022–1025 | DOI

[3] Judd B. R., Hansen J. E., Raassen A. J. J., “Parametric fits in atomic d shell”, J. Phys. B, 15:10 (1982), 1457–1472 | DOI | MR

[4] Uylings P. H. M., “Energies of $N$ equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. I: Theory”, J. Phys. B, 17:12 (1984), 2375–2392 | DOI

[5] Uylings P. H. M., Raassen A. J. J., Wyart J. F., “Energies of $N$ equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. II: Application to 3d$^N$ configurations”, J. Phys. B, 17:20 (1984), 4103–4126 | DOI

[6] Leushin A. M., Irinyakov E. N., “K interpretatsii opticheskikh spektrov ionov elementov gruppy zheleza”, Opt. i spektr., 100:3 (2006), 368–373

[7] Carnall W. T., Goodman G. L., Rajnak K., Rana R. S., “A systematic analysis of the spectra of the lanthanides doped into single crystal LaF$_3$”, J. Chem. Phys., 90:7 (1989), 3443–3457 | DOI

[8] Tanner P. A., Kumar V. V. R. K., Jayasakar C. K., Reid M. F., “Analysis of spectral data and comparative energy level parametrizations for Ln$^{3+}$ in cubic elpasolite crystals”, J. Alloys and Comp., 215:1–2 (1994), 349–370 | DOI

[9] Wells J. P. R., Dean T., Reeves R. J., “Site selective spectroscopy of the C$_{3v}$ symmetry centre in Er$^{3+}$ doped BaF$_2$”, J. Lumin., 96:2–4 (2002), 239–248 | DOI

[10] Fernandez M. T., Cabeza I., Iglesias L., Garcia-Riquelme O., Rico F. R., “Fundamental configurations in Mo IV spectrum”, Phys. Scr., 35 (1987), 819–826 | DOI

[11] Barakat M. M., Van Kleef Th. A. M., Raassen A. J. J., “Analysis of the fourth spectrum of palladium: Pd IV 1. 4d$^7$-4d$^6$5p transitions”, Physica C, 132 (1985), 240–250 | DOI

[12] Barakat M. M., Van Kleef Th. A. M., Joshi Y. N., “The Analysis of the fourth spectrum of palladium: Pd IV 2. 4d$^6$5s-4d$^6$5p transitions”, Physica C, 132 (1985), 251–259 | DOI

[13] Rajnak K., Wybourne B. G., “Configuration interaction effects in l$^N$ configurations”, Phys. Rev., 132:1 (1963), 280–290 | DOI

[14] Wybourne B. G., “Orbit-orbit interactions and the “linear” theory of configuration interaction”, J. Chem. Phys., 40:5 (1964), 1457–1458 | DOI

[15] Feneuille S., “Operateurs a trois particules pour des electrons d equivalents”, C. R. Acad. Sci. Paris, 262 (1966), 23–26

[16] Marvin H. H., “Mutual magnetic interactions of electrons”, Phys. Rev., 71:2 (1947), 102–110 | DOI | Zbl

[17] Judd B. R., Crosswhite H. M., Crosswhite H., “Intra-atomic magnetic interactions for f electrons”, Phys. Rev., 169:1 (1968), 130–138 | DOI | MR

[18] Hansen J. E., Judd B. R., “Fine structure analyses with orthogonal operators”, J. Phys. B, 18:12 (1985), 2327–2338 | DOI

[19] Judd B. R., Operator techniques in atomic spectroscopy, McGraw-Hill, N. Y., 1963, 242 pp.

[20] Wybourne B. G., Spectroscopic properties of rare earths, John Wiley and Sons, Inc., N. Y.–London–Sydney, 1965, 236 pp.

[21] Yutsis A. P., Savukinas A. Yu., Matematicheskie osnovy teorii atoma, Mintis, Vilnyus, 1973, 480 pp. | MR

[22] Sobelman I. I., Vvedenie v teoriyu atomnykh spektrov, Nauka, M., 1977, 640 pp.

[23] Nikitin A. A., Rudzikas Z. B., Osnovy teorii spektrov atomov i ionov, Nauka GRFML, M., 1983, 320 pp.

[24] Nielsen C. W., Koster G. F., Spectroscopic coefficients for the p$^n$, d$^n$, and f$^n$ configurations, The M.I.T. Press, Cambridge, Massachusetts, 1963, 294 pp. | MR | Zbl

[25] Irinyakov E. N., Kogerentnaya optika i opticheskaya spektroskopiya. Sb. statei, Vyp. IX, Kazan. gos. un-t, Kazan, 2005, 174–178

[26] Hansen J. E., Judd B. R., Raassen A. J. J., Uylings P. H. M., “Interpretation of higher order magnetic effects in the spectra of transition metal ions in terms of SO(5) and Sp(10)”, Phys. Rev. Lett., 78:16 (1997), 3078–3081 | DOI

[27] Blume M., Freeman A. J., Watson R. E., “Theory of spin-orbit coupling in atoms, III”, Phys. Rev., 134:2A (1964), A320–A327 | DOI