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I.I. Beterov1, E.A. Yakshina1, I.I. Ryabtsev1, D.B. Tretyakov1, V.M. Entin1, N.N. Bezuglov2, S. Bergamini3, E. Arimondo4
1 Institute of Semiconductor Physics, Prosp. Lavrentieva 13, Novosibirsk, 630090, RUSSIA 2 St. Petersburg State University, St. Petersburg, 198904, RUSSIA 3 The Open University, Milton Keynes, MK7 6AA, UK 4 Universita di Pisa, I-56127, ITALY Knowledge of the probabilities of spontaneous and induced transitions between low-excited, Rydberg and continuum states of alkali-metal atoms is necessary for data analysis in laser spectroscopy, plasma physics and astrophysics. Particular example is an ultracold plasma formed due to avalanche ionization in a dense gas of cold trapped Rydberg atoms. Radial matrix elements of the electric dipole transitions between arbitrary atomic states (e.g., bound-bound or bound-free transitions) should be calculated to obtain various spectroscopic properties of atoms, including oscillator strengths, lifetimes, photoionization cross-sections, and rates of collisional ionization. A universal theoretical approach can be useful in such calculations. Radial matrix elements for transitions between Rydberg states of alkali-metal atoms are usually calculated in the Coulomb approximation (CA) [1] with quantum defects taken as input parameters, or using various model potentials. In both approaches, the Schrödinger equation is integrated numerically. Applicability of these methods to highly-excited states is limited by precision of the rapidly-oscillating wave functions obtained from numerical integration. Quasiclassical method is a different approach where radial matrix elements are expressed through transcendental functions, which help to avoid inaccurateness of the direct numerical integration. This method can substantially improve both speed and precision of the calculations. However, validity of the most quasiclassical models used earlier was restricted by transitions between neighboring excited states. In this work we have shown that radial matrix elements of the dipole transitions between arbitrary low-excited, Rydberg and continuum states of alkali-metal atoms can be calculated in a universal way using a particular quasiclassical model developed by Dyachkov and Pankratov [2]. With this model we have calculated the radial matrix elements for bound-bound, bound-free and free-free transitions between various S, P, D and F states of all alkali-metal atoms. Our results on radial matrix elements are in good agreement with more complicated numerical calculations obtained by other authors. Our results are also consistent with the available experimental data on effective lifetimes of Rydberg states [4,5], oscillator strengths and photoionization cross-sections. In addition, the used quasiclassical approach allowed us to reveal several Cooper minima, both in the discrete and continuum spectra, which are interesting to confirm experimentally. We conclude that the quasiclassical model of Dyachkov and Pankratov is a universal method to calculate radial matrix elements for arbitrary transitions between quantum states of alkali-metal atoms. References: [1] D.R.Bates and A.Damgaard, Philos. Trans. R. Soc. London 242, 101 (1949). [2] L.G.Dyachkov and P.M.Pankratov, J. Phys. B 27, 461 (1994). [3] J.H.Hoogenraad and L.D.Noordam, Phys. Rev. A 57, 4533 (1998). [4] I.I.Beterov et al., Phys. Rev. A 79, 052504 (2009). [5] D.B.Branden et al., J. Phys. B 43, 015002 (2010). |
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