Calculation of radiative parameters for alkali-dimer cations of lithium, sodium and potassium

The author calculates radiative parameters (Einstein coefficients of spontaneous radiation, oscillator strengths for absorption, Frank-Condon factors, wave numbers of electronic-vibrational bandwidths in electronic transition (1)²П_u - X²Σ⁺_g) of molecular ions Li⁺₂ (0 ≤ v’ ≤ 25, 0 ≤ v’’ ≤ 64), Na⁺₂ (0 ≤ v’ ≤ 25, 0 ≤ v’’ ≤ 74), K⁺₂ (0 ≤ v’ ≤ 25, 0 ≤ v’’ ≤ 88) and radiative lifetimes of the excited electronic states. The calculaitons are performed on the basis of the potential energy curves presented in this paper. Necessary vibrational energies and respective wave functions were obtained in order to calculate the radiative parameters. It became possible due to finding a numerical solution of the radial wave equation. The radiative parameters and lifetimes are calculated for the first time ever.

References

[1] Lang F., Winkler K., Strauss C., Grimm R., Densсhlag J.K. Ultracold triplet molecules in the rovibrational ground state. Phys. Rev. Lett., 2008, vol. 101, pp. 133005-133009.

[2] Mark M.J., Danzl J.G., Haller E., Gustavsson M., Bouloufa N., Dulieu O., Salami H., Bergeman T., Ritsch H., Hart R., Nagerl H.C. Dark resonances for ground state transfer of molecular quantum gases. Appl. Phys. B, 2009, vol. 95, pp. 219-225.

[3] Aikawa K., Akamatsu D., Hayashi M., Oasa K., Kobayashi J., Naidon P., Kishimoto T., Ueda M., Inouye S. Coherent transfer of photoassociated molecules into the rovibrational ground state. Phys. Rev. Lett., 2010, vol. 105, pp. 203001-203005.

[4] Smirnov A.D. Calculation of Radiative Parameters of the A1Σ+u–X1Σ+g Transition of Cesium Dimer. Zhurn. prikl. Spektroskopii [J. Applied Spectroscopy], 2010, vol. 77, no. 5, pp. 661-667 (in Russ.).

[5] Smirnov A.D. Calculation of Spectroscopic Constants and Radiative Parameters for A1Σ+u –X1Σ+g and B1Πu–X1Σ+g Electronic Transitions of Sodium Dimer. Opt. Spektrosk. [Opt. Spectrosc.], 2010, vol. 109, no. 5, pp. 739-745 (in Russ.).

[6] Smirnov A.D. Calculation of Spectroscopic Constants and Radiative Parameters for A1Σ+u –X1Σ+g and B1Πu–X1Σ+g Electronic Transitions of Lithium Dimer. Opt. Spektrosk. [Opt. Spectrosc.], 2012, vol. 113, no. 4, pp. 387-394 (in Russ.).

[7] Smirnov A.D. Calculation of Radiative Parameters for A1Σ+u –X1Σ+g and B1Πu–X1Σ+g Electronic Transitions of Potassium Dimer. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2013, no. 2 (49), pp. 67-85 (in Russ.).

[8] Smirnov A.D. Energy and Radiative Properties of the B1Πu–X1Σ+g Electronic Transition of the Cesium and Rubidium dimers. Jelektr. nauchno-tehn. Izd. "Inzhenernyy zhurnal: nauka i innovacii" [El. Sc.- Techn. Publ. "Eng. J.: Science and Innovation", 2013, iss. 6. URL: http://engjournal.ru/catalog/fundamentals/physics/790.html (accessed 10.11.2014).

[9] Smirnov A.D. Calculation of Spectroscopic Constants and Radiative Parameters for B1Π–X1Σ+ Electronic Transition of the Molecules NaK, NaRb, NaCs. Opt. Spektrosk. [Opt. Spectrosc.], 2014, vol. 117, no. 3, pp. 373-380 (in Russ.).

[10] Bernheim R.A., Gold L.P., Tipton T. Rydberg states of 7Li2 by pulsed optical-optical double resonance spectroscopy. J. Chem. Phys., 1983, vol. 78, pp. 3635-3647.

[11] Martin S., Chevaliere J., Valignat S., Perrot J.P., Broyer M. Autoionizing rydberg states of the Na2 molecule. Chem. Phys. Lett., 1982, vol. 87, pp. 235-239.

[12] Leutwyler S., Herrmann A., Woste L., Schumacher E. Isotope selective two-step photoionization study of K2 in a supersonic molecular beam. Chem. Phys., 1983, vol. 48, pp. 253-267.

[13] Bouzouita H., Ghanmi C., Berriche H. Ab initio study of the alkali-dimer cation Li+2. J. Molecul. Structure, 2006, vol. 777, pp. 75-80.

[14] Kirby-Docken K., Cerjan C.J., Dalgarno A. Oscillator strengths and photodissociation cross sections for Li+2 and Na+2. Chem. Phys. Lett., 1976, vol. 40, pp. 205-209.

[15] Llyabaev E., Kaldor U. Ground and excited states of K2 and K+2 by the open-shell coupled cluster method. J. Chem. Phys., 1993, vol. 98, pp. 7126-7131.

[16] Jasik P., Wilczynski J., Sienkiewicz J.E. Calculatoin of adiabatic potentials of Li+2. Eur. Phys J. Special Topics, 2007, vol. 144, pp. 85-91.

[17] Berriche H. Potential energy and dipole moment of the Na+2 ionic molecule. Int. J. Quant. Chemistry, 2013, vol. 113, pp. 2405-2412.

[18] Magnier S., Aubert-Frecon M. Theoretical determination of the K+2 electronic structure. J. Quant. Spectr. Radiat. Transfer, 2003, vol. 78, pp. 217-225.

[19] Jraij A., Alouche A. R., Magnier S., Aubert-Frecon M. Theoretical spin-orbit structure on the alkali dimer cation K+2. Can. J. Phys., 2008, vol. 86, pp. 1409-1415.

[20] Herzberg G. Molecular Spectra and Molecular Structure: Spectra of Diatomic Molecules. Princeton; D. Van Nostrand Co., 1950.

[21] Zulicke L. Quantenchemie. Ein Lehrgang. Band 1. Grundlagen und allgemeine Methoden. Berlin, VEB Deutscher Verlag der Wissenschaften, 1973.

[22] Kratzer A. Die ultraroten rotationsspektren der halogenwasserstoffe. Z. Phys. 1920, vol. 3, pp. 289-296.

[23] Kemble E.C., Birge R.T., Colby W.F. et al. Molecular Spectra in Gases. National Research Council, Washington, D.C., 1930, p. 57.

[24] Laher R.R., Khakoo M.A., Antic-Jovanovic A. Radiative transition parameters for the A1Σ+u –X1Σ+g band system of 107,109Ag2. J. Mol. Spectr., 2008, vol. 248, pp. 111-121.