# Generalized quantum defect approximation in relativistic perturbation theory for the rydberg systems

**Authors: **A.V. Ignatenko, T.A. Florko, T.B. Tkach, T.A. Khulakhli

**Year: **2015

**Issue: **19

**Pages: **216-223

**Abstract**

The aim is to develop effective from the computational point of view of methods to describe the energy and spectral properties of Rydberg atoms in the framework of a quantum defect, the device implemented in the corresponding relativistic multiparticle perturbation theory. In the modern theory there is an urgent need to develop new, high-precision, of course, and ab initio relativistic gaugeinvariant theories of radiative transitions in the spectra of Rydberg atoms, multiply charged ions, but with mandatory use of the unique physical characteristics of these systems. In developing our version of the method of the relativistic model potential at the potential of the core is to realize the potential of the relativistic quantum defect approach Dplyus effective exchange-correlation interaction potential “foreign particle-frame.” Contained in the potential of the model parameter is defined in the framework of QED minimization procedure is gauge-violating contribution to the width of the radiation level in the generation of optimized bases relativistic wave functions (ab initio detection circuit parameter).

**Tags: **approximation of quantum defect; formalism of relativistic manybody perturbation theory; Rydberg atoms

**Bibliography**

- Grant I.P. Relativistic Quantum Theory of Atoms and Molecules. Oxford, 2008. 650 p.
- Ivanova E.P., Grant I.P. Oscillator strength anomalies in Ne isoelectronic sequence with applications to X-ray laser modeling.J.Phys.B., 1998, vol.31, pp. 2871-2883.
- Glushkov A.V. Relativistic Quantum Theory. Quantum, mechanics of Atomic Systems. Odessa: Astroprint, 2008. 700 p.
- Glushkov A.V., Ivanov L.N. Radiation Decay of Atomic States: atomic residue and gauge non-invariant contributions. Phys. Lett.A., 1992, vol.170. pp. 33-38.
- Glushkov A.V. Advanced relativistic energy approach to radiative decay processes in multielectron atoms and multicharged ions. Advances in Theory of Quantum Systems in Chem. and Phys. Ser: Frontiers in Theoretical Phys. and Chem. Berlin: Springer, 2012, vol.26, pp. 31-54.
- Seaton M.J. Quantum defect theory. Rep. Prog. Phys., 1983, vol.46, pp. 167-258.
- Martin I., Karwowski J. Quantum defect orbitals and the Dirac second-order equation. J. Phys. B: At. Mol. Opt. Phys, 1991, vol.24, pp. 1539-1544.
- Charro E., Martin I., Lavin E. Multiconfiguration Dirac-Fock and Relativistic quantum defect orbital study of triplet-triplet transitions in beryllium-like ions. J.Quant.Spectr.Rad.Transf, 1996, vol.56, no. 2, pp. 241-253.
- Kohn W., Sham S. Quantum density oscillations in an inhomogeneous electron gas. Phys. Rev.A., 1965, vol.137, pp. 1697-1710.
- Stein M. Pseudo-potential approach to the relativistic treatment of alkali atoms. J.Phys.B.: At.Mol.Opt.Phys., 1993, vol.26, pp. 2087-2097.
- Martin G., Wiese W. Atomic oscillator-strength distributions in spectral series of Li isoelectronic sequence. Phys. Rev. A., 1976, vol.13, pp. 699-714.
- Martin G., Wiese W. Tables of critically evaluated oscillator strengths for lithium isoelectronic sequence. Journ. of Phys. Chem. Ref. Data, 1976, vol.5, pp. 537-570.
- Weiss A.W. Hartree-Fock line strengths for lithium, sodium and copper isoelectronic sequences. J.Quant. Spectr. Rad. Tr., 1977, vol.18, pp. 481-491.
- Gounand F. Calculation of radial matrix elements and Radiative lifetimes for highly excites states of alkali atoms using the Coulomb approximation. Journ. de Phys., 1979, vol.40, pp. 457-460.
- Lindgard A., Nielsen S.E. Transition probabilities for the alkali isoelectronic sequences: LiI, NaI, KI, RbI, CsI, FrI. Atom. Data.Nucl.Data.Tabl., 1977, vol.19, pp. 533-633.
- Nahar S.N. Relativistic fine structure oscillator strengths for Li-like ions: C IV Si XII,SXIV,ArXVI,CaXVIII,Ti XX,Cr XXII, Ni XXVI. Astronomy and Astrophys, 2002, vol.389, pp. 716-728.
- Ivanov L.N., Ivanova E.P. Extrapolation of atomic ion energies by model potential method: Na-like spectra. Atom.Data Nucl .Data Tab., 1979, vol.24, pp. 95-121.