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E. P. Gurnitskaya

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1. /Gurnitsk.docE. P. Gurnitskaya
УДК 539.184, 539.186



Odessa National Polytechnical University, P.O.Box 108, Odessa-9, 65009, Ukraine

E-mail: glushkov@paco.net

A brief analysis of the heavy ion storage ring experiment on determination of the lifetimes for levels of the iron ion and corresponding results are given. New theoretical data, obtained within new quantum calculation scheme, are presented.

Key words: heavy ion storage ring experiment, ion levels lifetime theory

In last years it is of a great interest the experimental and theoretical studying the ion levels lifetimes and developing the new methods of their determination (c.f. [1-4]). Similar interest is also stimulated by importance of this information for correct determination of the characteristics for plasma in thermonuclear (tokamak) reactors, searching new mediums for X-ray range lasers. The X-ray laser problem has stimulated a great number of papers devoting to development of theoretical methods for the modelling the elementary processes in a collisionally pumped plasma. There is a hope to find lasing effects on the transitions in the Ne-, Cl- Ni-like plasma. Very shocking example is a scheme for accomplishing tabletop x-ray lasing in Li-like ion of Ne at 98 Å in an optically ionized plasma during recombination in the transient regime which was carried out in the Lawrence Livermore National Laboratory (University of California) [4]. Saturation effects and parametric heating processes by stimulated Raman scattering are analyzed and found to allow energy efficiencies in excess of 10-5 for a 100-fsec duration, 0.25-µm laser driver of intensity 1017 W/cm.

A great progress in development of laser technique, tokamaks and accelerators experiments resulted to a new class of problems. Recently an excellent experiment employed a heavy ion storage ring (TSR at Heildelberg) [1]. There are measured and theoretically calculated the lifetimes for some levels in the ions of Fe, Co, Ni,Cu. Here we give a brief analysis of the heavy ion storage ring determination of the lifetimes in the iron ions FeX and present the results of our theoretical calculation within new scheme [8,9].

I ref.[1] it is given description of the heavy ion storage ring experiment. All ion beams were produced as negative ions from a sputter-type ion source. These ions were then accelerated in the first half of a tandem accelerator, stripped to the desired charge state in a foil stripper and accelerated further to final energies of about 83.5 MeV for Fe 9+ ,98MeVforCo 10+ , 120 MeV for Ni 11+ and 143 MeV for Cu 12+ , respectively. In all cases, only a selected-charge state ion beam was transported to and injected into the storage ring. Multiturn injection and stacking of the ions over about 30 turns increased the number of stored ions, so that ion currents in the ring reached up to about 15 µA for Fe 9+ , and 80 to 120 µA for the other ion species. The ions were left coasting for 200 ms. Then the stored ion beam was dumped and the procedure repeated. A few-per cent fraction of the ion beam was expected to be in excited levels from the stripping and excitation processes that take place inside the injector. The ion beam travels about 100 m from the injector to the ion storage ring, which at these ion energies takes about 6 µs, that is, about twice the revolution time of the ions in the storage ring (circumference 55 m). Injection extended over .0.3 ms; the pulsed magnetic field used to inflect the ions settles down at .0.8 ms after the start of the injection. After the end of the settling time the ions are stored in stable orbits. The storage time constants (limited by collisional losses) depend on the background gas pressure (here a few times 10... 11 mbar); they ranged from about 20 to 29 s for the presently studied ions. The actual ion beam current was monitored on-line by a beam profile monitor which detects rest gas ions that are collisionally produced by the circulating ion beam. In principle, the ion beam lifetime is important as a systematic correction of the apparent optical decay data, but in the present case this is mostly a 10... 3 effect and thus almost negligible. Moreover, relativistic time dilation (with a ã factor near 1.002 for all our ions) is of the same magnitude, but of opposite sign. The full injection and settling time is faster than the shortest of the expected radiative lifetimes of present interest, but very long compared to all cascade transitions from higher lying levels except for those that involve some high-J 3d levels that dominantly decay via M1 E2 M2 transitions. The other details can be found in the original ref.[1].

One of the key theoretical problems is a highly accurate definition of the ion lifetimes, transition probabilities, rate coefficients. This is regarding necessity of development new adequate calculation schemes for defining the wavelengths, level populations. Despite of great number papers, devoting to solving cited problems (c.f. [1-12] and references in them), they are at present time quite far from final adequate solution. The most consistent approach to considered problems solving must base on the consistent quantum approach. In ref. [8,9] we develop a consistent quantum approach for calculation of the spectroscopic characteristics of the ions. Let us now describe the key moments of the method [8,9], which is based on the gauge invariant energy approach [10-12]. The wave functions zeroth basis is found from the Dirac equation solution with potential, which includes the core ab initio potential, electric, polarization potentials of nucleus (the gaussian form for charge distribution in the nucleus is used). All correlation corrections of the PT second and high orders (electrons screening, particle-hole interaction etc.) are accounted for. Formally one can solve the one-electron Dirac equations with potential:

V(r)=2V(r|core)+V(r|nlj)+Vex+V(r|R). (1)

This potential includes the electrical and polarization potentials of the nucleus. The core potential V(r|core) has been chosen in the form of the Ivanov-Ivanova potential with one parameter, which is defined according to the procedure [10]. The part accounts for exchange inter-electron interaction. The main exchange effect will be taken into account in the one–electron approximation. The rest of the exchange-correlation effects are accounted for in the first two PT orders by the total inter-electron interaction [9]. The core electron density is defined by iteration algorithm within gauge invariant QED procedure [10].

, (2)

where is for electron and for vacancy in the electron core of the ion (our case). The potential in (2) is as follows:

. (3)

Separated members of sum in (2.1) are contributions of different radiative channels and a probability of the dipole transition is as follows:


The oscillator strength of the corresponding transition is:


where g is the degeneracy degree, is the wavelength of transition (in Ǻ). The lifetime for the concrete level is directly connected with values of (4). Other details of the calculation procedure, including definition of the matrix elements (3) with effective account of the exchange-correlation effects can be found in ref. [8,9].

In table 1 we present the predicted and measured lifetimes  for the 3s23p5 2P1/2 level in Fe X iron ion. Of the available calculations only those which explicitly give transition rates have been cited. The measurement of the lifetimes has been performed in the above described heavy ion storage ring experiment (experiment of Trabert-Saathoff-Wolf; 2004) and experiment of Moehs et al (2000, 2001). Details are given in ref.[1]. Analyses of presented data and carried out experiments show that the most reliable data are obtained by Mason and Nussbaumer (1977), Eidelsberg et al (1981) and in the present paper.

Table 1. Predicted and measured lifetimes ô for the 3s23p5 2P1/2 level in Fe X iron ion. Of the available calculations only those which explicitly give transition rates have been cited.


Wavelength (nm)

Lifetime (ms)


Lifetime (ms)


Fe 9+













13.64 ±0.25l

14.41 ±0.14no

Note to table (see details in ref.[1]): a Krueger and Czyzak (1966); b Warner (1968); c Smith and Wiese (1973); d Kastner (1976); e Mason and Nussbaumer (1977); f Kafatos and Lynch (1980); g Eidelsberg et al (1981); h Huang et al (1983); i Kaufman and Sugar (1986); j Bhatia and Doschek (1995); k Kohstall et al (1999), Dong (1999); l Moehs et al (2000, 2001); m Martin et al (2003); n Trabert-Saathoff-Wolf (2004); derived by isoelectronic extrapolation; o- Trabert-Saathoff-Wolf (2004); p – present paper


  1. Trabert E., Saathoff G., Wolf A., M1/E2 decay rates in CoXI, NiXII, Cu XIII measured at a heavy-ion storage ring// J.Phys.B.At.Mol.Opt.Phys. 37(4),pp.945-952 (2004).

  2. Rosmej F.B., Hoffman D.H., Geissel M. et al, Advanced X-ray diagnostics based on an observation of high-energy Rydberg transitions from autoionizing levels in dense laser-produced plasmas// Phys. Rev.A. 63,pp. 063409-063418 (2001).

  3. Aglitsky E.V., Safronova U.I. Spectroscopy of autoionization states of atomic systems.-Moscow: Nauka, 2001.

  4. Letokhov V.S, Laser Spectroscopy, Acad.Press, N.-Y. (2001).

  5. Seely J.F., Ekberg J.O. Brown C.M. et al, Laser –Produced Spectra and QED Effects for Fe-, Co-, Cu-, Zn-like ions of Au, Pb, Bi, Th, and U// Phys.Rev.Lett. 230,pp.2924-2926 (1996).

  6. Glushkov A.V., Ambrosov S.V., Svinarenko A.A. etal, QED calculation of the super heavy elements ions: energy levels and hyperfine structure for different nuclear models// Nucl. Phys.A.-734, pe.21-24 (2004).

  7. Glushkov A.V.,Malinovskaya S.V., Svinarenko A.A., Chernyakova Yu.G., QED Calculation of Electron Satellites Spectra in Intense Laser Field in Multicharged Ion//Int.J.Quant.Chem. 99(5), pp.673-678 (2004).

  8. Glushkov A.V., Gurnitskaya E.P., New QED approach to calculation of the superheavy ions // Proc. of the International conference on Quantum Systems.-Spetses, Greece (2004).

  9. Gurnitskaya E.P., New QED approach to calculation of the superheavy ions// {Preprint of NIIF, I.I.Mechnikov National University, Odessa. №A-3 (2004).

  10. Glushkov A.V., Ivanov L.N. Radiation Decay of Atomic States: atomic residue and gauge non-invariant contributions // Phys. Lett.A. 170 (1),pp.33-37 (1992).

  11. Glushkov A.V.,Malinovskaya S.V., Svinarenko A.A., Chernyakova Yu.G., QED Calculation of Electron Satellites Spectra in Intense Laser Field in Multicharged Ion//Int.J.Quant.Chem. 99(5),pp. 673-678 (2004).

  12. Glushkov A.V., Malinovskaya S.V., Co-operative laser nuclear processes: border lines effects// In: New projects and new lines of research in nuclear physics. Eds. G.Fazio and F.Hanappe, Singapore : World Scientific,pp. 242-250 (2003).

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