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Relativistic Calculations for Trapped Ions

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Abstract

We present recent results in the field of total binding energy calculations, Landщ factors, quantum electrodynamics corrections and lifetime that are of interest for ion traps and ion sources. We describe in detail MCDF and RMBPT calculation of ionic binding energies, which are needed for the determination of atomic masses from highly charged ion measurements. We also show new results concerning Landщ factor in 3-electron ions. Finally we describe how relativistic calculations can help understand the physics of heavy ion production ion sources.

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References

  1. DiFilippo, F., Natarajan, V., Boyce, K. R. and Pritchard, D. E.,Accurate atomic masses for fundamental metrology,Phys. Rev. Lett. 73 (1994),1481–1484.

    Article  ADS  Google Scholar 

  2. Carlberg, C., Fritioff, T. and Bergström, I., Determination of the 133Cs and proton mass ratio using highly charged ions,Phys. Rev. Lett. 83 (1999),4506–4509.

    Article  ADS  Google Scholar 

  3. Bradley, M. P., Porto, J. V., Rainville, S., Thompson, J. K. and Pritchard, D. E., Penning trap measurements of the masses of 133Cs, 87,85Rb, and 23Na with uncertainties 0.2 ppb,Phys. Rev. Lett. 83 (1999),4510–4513.

    Article  ADS  Google Scholar 

  4. Hermanspahn, N., Häffner, H., Kluge, H.-J., Quint, W., Stahl, S., VerdÚ, J. and Werth, G., Observation of the continuous Stern-Gerlach effect on an electron bound in an atomic ion, Phys. Rev. Lett. 84 (2000),427–430.

    Article  ADS  Google Scholar 

  5. Weiss, D. S., Young, B. C. and Chu, S., Precision measurement of the photon recoil of an atom using atomic interferometry, Phys. Rev. Lett. 70 (1993),2706–2709.

    Article  ADS  Google Scholar 

  6. Mohr, P. J. and Taylor, B. N., CODATA recommended values of the fundamental physical constants: 1998, Rev. Modern Phys. 72 (2000),351–495.

    Article  ADS  Google Scholar 

  7. Van Dyck, R. S., Jr., Schwinberg, P. B. and Dehmelt, H. G., New high-precision comparison of electron and positron g factors, Phys. Rev. Lett. 59 (1987),26–29.

    Article  ADS  Google Scholar 

  8. Douysset, G., Khodja, H., Girard, A. and Briand, J. P.,Highly charged ion densities and ion confinement properties in an electron-cyclotron-resonance ion source,Phys. Rev. E 61 (2000), 3015–3022.

    Article  ADS  Google Scholar 

  9. Beiersdorfer, P., Knapp, D., Marrs, R. E., Elliot, S. R. and Chen, M. H., Structure and Lambshift of 2 s1/2-2 p3/2 levels in lithiumlike U89+ through neonlike U82+,Phys. Rev. Lett. 71 (1993),3939–3942.

    Article  ADS  Google Scholar 

  10. Beiersdorfer, P., Osterheld, A., Elliott, S. R., Chen, M. H., Knapp, D. and Reed, K., Structure and Lamb shift of 2 s1/2-2 p3/2 levels in lithiumlike Th87+ through neonlike Th80+,Phys. Rev. A 52 (1995),2693–2706.

    Article  ADS  Google Scholar 

  11. Beiersdorfer, P., Osterheld, A. L., Scofield, J. H., Crespo López-Urrutia, J. R. and Widmann, K., Measurement of QED and hyperfine splitting in the 2 s1/2-2 p3/2 X-ray transition in Li-like 209Bi80+, Phys. Rev. Lett. 80 (1998),3022–3025.

    Article  ADS  Google Scholar 

  12. Santos, J. P., Marques, J. P., Parente, F., Lindroth, E., Boucard, S. and Indelicato, P., Multicon-figuration Dirac-Fock calculation of 2 s1/2-2 p3/2 transition energies in highly ionized bismuth, thorium, and uranium,European Phys. J. D 1 (1998),149–163.

    Article  ADS  Google Scholar 

  13. Martins, M. C., Costa, A. M., Santos, J. P., Indelicato, P. and Parente, F., Interpretation of X-ray spectra emitted by Ar ions in an electron cyclotron resonance ion source,J. Phys. B 34 (2001),533–543.

    Article  ADS  Google Scholar 

  14. Mohr, P. J., Plunien, G. and Soff, G., QED corrections in heavy atoms,Phys. Rep. 293 (1998), 227–372.

    Article  Google Scholar 

  15. Indelicato, P., Projection operators in multiconfiguration Dirac-Fock calculations, application to the ground state of heliumlike ions,Phys. Rev. A 51 (1995),1132–1145.

    Article  ADS  Google Scholar 

  16. Brown, G. E. and Ravenhall, D. E., On the interaction of two electrons,Proc. Roy. Soc. London Ser. A 208 (1951),552–559.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. Sucher, J., Foundation of the relativistic theory of many-electron atoms,Phys. Rev. A 22 (1980),348–362.

    Article  MathSciNet  ADS  Google Scholar 

  18. Mittleman, M. H., Theory of relativistic effects on atoms: Configuration-space Hamiltonian, Phys. Rev. A 24 (1981),1167–1175.

    Article  ADS  Google Scholar 

  19. Blundell, S. A., Mohr, P. J., Johnson, W. R. and Sapirstein, J.,Evaluation of two-photon exchange graphs for highly charged heliumlike ions,Phys. Rev. A 48 (1993),2615–2626.

    Article  ADS  Google Scholar 

  20. Lindgren, I., Persson, H., Salomonson, S. and Labzowsky, L., Two-photon exchange for helium-like systems,Phys. Rev. A 51 (1995),1167–1195.

    Article  ADS  Google Scholar 

  21. Lindgren, I. and Morrison, J., Atomic Many-Body Theory, Springer, Berlin, 1982.

    Google Scholar 

  22. Huang, K. N., Kim, Y.-K., Cheng, K. T. and Desclaux, J. P., Correlation and relativistic effects in spin-orbit splitting,Phys. Rev. Lett. 48 (1982),1245–1248.

    Article  ADS  Google Scholar 

  23. Kim, Y. K., Parente, F., Marques, J., Indelicato, P. and Desclaux, J. P., Failure of multiconfiguration Dirac-Fock wave function in the nonrelativistic limit,Phys. Rev. A 58 (1998), R1885–R1888.

    Article  ADS  Google Scholar 

  24. Mohr, P. J., Self-energy of the n = 2 states in a strong Coulomb field,Phys. Rev. A 26 (1982), 2338–2354.

    Article  ADS  Google Scholar 

  25. Mohr, P. J. and Kim, Y.-K., Self-energy of excited states in a strong Coulomb field,Phys. Rev. A 45 (1992),2727–2735.

    Article  ADS  Google Scholar 

  26. Mohr, P. J., Self-energy correction to one-electron energy levels in a strong Coulomb field, Phys. Rev. A 46 (1992),4421–4424.

    Article  ADS  Google Scholar 

  27. Mohr, P. J. and Soff, G., Nuclear size correction to the electron self-energy,Phys. Rev. Lett. 70 (1993),158–161.

    Article  ADS  Google Scholar 

  28. Indelicato, P. and Mohr, P. J.,6s and 8d states self-energy for hydrogenlike ions and new results on the self-energy screening,Hyp. Interact. 114 (1998),147–153.

    Article  ADS  Google Scholar 

  29. Indelicato, P., Gorceix, O. and Desclaux, J. P., MCDF studies of two electron ions II: Radiative corrections and comparison with experiment,J. Phys. B 20 (1987),651.

    Article  ADS  Google Scholar 

  30. Indelicato, P. and Desclaux, J. P., Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions,Phys. Rev. A 42 (1990), 5139.

    Article  ADS  Google Scholar 

  31. Indelicato, P. and Lindroth, E., Relativistic effects, correlation, and QED corrections on Ka transitions in medium to very heavy atoms, Phys. Rev. A 46 (1992),2426–2436.

    Article  ADS  Google Scholar 

  32. Indelicato, P., Boucard, S. and Lindroth, E.,Relativistic and many-body effects in K, L, and M shell ionization energy for elements with 10⩽Z⩽100 and the determination of the 1s Lamb shift for heavy elements,European Phys. J. D 3 (1998),29–41.

    Article  ADS  Google Scholar 

  33. Indelicato, P. and Mohr, P. J., Quantum electrodynamic effects in atomic structure,Theoret. Chem. Acta 80 (1991),207–214.

    Article  Google Scholar 

  34. Blundell, S. A., Accurate screened QED calculations in high-Z many electron ions,Phys. Rev. A 46 (1992),3762.

    Article  ADS  Google Scholar 

  35. Blundell, S. A., Ab initio calculations of QED effects of Li-like, Na-like and Cu-like ions,Phys. Scripta T46 (1993),144–149.

    ADS  Google Scholar 

  36. Ynnerman, A., James, J., Lindgren, I., Persson, H. and Salomonson, S.,Many-body calculation of the 2 p1/2 , 3/2-2s1/2 transition energies in Li-like 238U,Phys. Rev. A 50 (1994),4671–4677.

    Article  ADS  Google Scholar 

  37. Persson, H., Salomonson, S., Sunnergren, P. and Lindgren, I., Two-electron Lamb-shift calculations on heliumlike ions,Phys. Rev. Lett. 76 (1996),204–207.

    Article  ADS  Google Scholar 

  38. Persson, H., Lindgren, I., Labzowsky, L. N., Plunien, G., Beier, T. and Soff, G., Second-order self-energy-vacuum-polarization contributions to the Lamb shift in highly charged few-electron ions,Phys. Rev. A 54 (1996),2805–2813.

    Article  ADS  Google Scholar 

  39. Indelicato, P.,Correlation and negative continuum effects for the relativistic M1 transition in two-electron ions using the multiconfiguration Dirac-Fock method,Phys. Rev. Lett. 77 (1996), 3323–3326.

    Google Scholar 

  40. Derevianko, A., Savukov, I.M. and Johnson, W. R., Negative-energy contributions to transition amplitudes in heliumlike ions,Phys. Rev. A 58 (1998),4453–4461.

    Article  ADS  Google Scholar 

  41. Savukov, I. M., Derevianko, A., Berry, H. G. and Johnson, W. R., Large contributions of negative-energy states to forbidden magnetic-dipole transition amplitudes in alkali-metal atoms, Phys. Rev. Lett. 83 (1999),2914–2917.

    Article  ADS  Google Scholar 

  42. Desclaux, J. P.,A multiconfiguration relativistic Dirac-Fock program,Comput. Phys. Commun. 9 (1975),31–45.

    Google Scholar 

  43. Desclaux, J. P., A relativistic multiconfiguration Dirac-Fock package, In: E. Clementi (ed.), Methods and Techniques in Computational Chemistry, Vol. A, STEF, Cagliary, 1993.

    Google Scholar 

  44. Indelicato, P., Parente, F. and Marrus, R., Effect of the hyperfine structure on the 2 3 P 1 and the 2 3 P 1 lifetime in heliumlike ions,Phys. Rev. A 40 (1989), 3505–3514.

    Article  ADS  Google Scholar 

  45. Boucard, S. and Indelicato, P.,Relativistic many-body and QED effects on the hyperfine structure of lithium-like ions,European Phys. J. D 8(2000),59–73.

    Article  ADS  Google Scholar 

  46. Schäfer, A., Soff, G., Indelicato, P., Müller, B. and Greiner, W.,Prospects for an atomic parityviolation experiment in U90+, Phys. Rev. A 40 (1989),7362–7365.

    Article  ADS  Google Scholar 

  47. Marques, J. P., Parente, F., Indelicato, P. and Desclaux, J. P., Estimation of the ratio of double and single Auger transition rates for the L shell of Kr, Nb and Gd,J. Phys. B. 31 (1998), 2897–2901.

    Article  ADS  Google Scholar 

  48. Santos, J. P., Marques, J. P., Parente, F., Lindroth, E., Indelicato, P. and Desclaux, J. P., Relativistic 2 s1/2 (L1) atomic subshell decay rates and fluorescence yields for Yb and Hg,J. Phys. B. 32 (1999),2089–2097.

    Article  ADS  Google Scholar 

  49. Santos, J. P., Parente, F. and Indelicato, P., Application of B-splines finite basis sets to relativistic two-photon decay rates of 2s level in hydrogenic ions,Europeran Phys. J. D 3 (1998), 43–52.

    Article  ADS  Google Scholar 

  50. Cheng, K. T. and Childs, W. J., Ab initio calculation of 4f n6s 2 hyperfine structure in neutral rare-earth atoms,Phys. Rev. A 31 (1985),2775–2784.

    Article  ADS  Google Scholar 

  51. Parpia, F. A., Froese Fischer, C. and Grant, I. P., 1996.

  52. Persson, H., Salomonson, S., Sunnergren, P. and Lindgren, I., Radiative corrections to the electron g-factor in H-like ions, Phys. Rev. A 56 (1997),R2499–R2502.

    Article  ADS  Google Scholar 

  53. Beier, T., Lindgren, I., Persson, H., Salomonson, S., Sunnergren, P., H. Häffner and N. Hermanspahn, gj factor of an electron bound in a hydrogenlike ion,Phys. Rev. A 62 (2000), 032510.

    Article  ADS  Google Scholar 

  54. Blundell, S. A., Cheng, K. T. and Sapirstein, J., Radiative corrections in atomic physics in the presence of perturbing potentials,Phys. Rev. A 55 (1997),1857–1865.

    Article  ADS  Google Scholar 

  55. Persson, H., Schneider, S. M., Greiner, W., Soff, G. and Lindgren, I., Self-energy correction to the hyperfine structure splitting of hydrogenlike atoms,Phys. Rev. Lett. 76 (1996),1433–1436.

    Article  ADS  Google Scholar 

  56. Shabaev, V. M., Shabaeva, M. B., Tupitsyn, I. I., Yerokhin, V. A., Artemyev, A. N., Kühl, T. and Tomaselli, M., Transition energy and lifetime for the ground-state hyperfine splitting of high-Z lithiumlike ions,Phys. Rev. A 57 (1998),149–156.

    Article  ADS  Google Scholar 

  57. Indelicato, P. and Mohr, P. J., Quantum electrodynamic effects in atomic structure,Theoret. Chem. Acta. 80 (1991),207–214.

    Article  Google Scholar 

  58. Rodrigues, G. C., Ourdane, M. A., Bieron, J., Indelicato, P. and Lindroth, E., Relativistic and many-body effects on total binding energies of cesium ions,Phys. Rev. A 63 (2001),012510.

    Article  ADS  Google Scholar 

  59. Lindroth, E. and Ynnerman, A., Ab initio calculations of gj factors for Li, Be+ and Ba+,Phys. Rev. A 47 (1993),961–970.

    Article  ADS  Google Scholar 

  60. Kim, Y.-K. and Rudd, M. E., Binary-encounter-dipole model for electron-impact ionization, Phys. Rev. A 50 (1994),3954–3967.

    Article  ADS  Google Scholar 

  61. Shevelko, V. P. and Tawara, H., J. Phys. B. 28 (1995),L589.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire Kastler-Brossel, Unité Mixte de Recherche du CNRS n○8552, École Normale Supérieure et Université Pierre et Marie Curie, Case 74, 4 place Jussieu, F-75252, Paris Cedex 05, France

    P. Indelicato

  2. Department of Atomic Physics, Stockholm University, Frescativ. 24, S-104 05, Stockholm, Sweden

    E. Lindroth & M.A. Ourdane

  3. Department of Physics, Chalmers University of Technology and Gö teborg University, S-412 96, Göteborg, Sweden

    T. Beier, I. Lindgren, A.-M. MÅrtenson-Pendrill & S. Salomonson

  4. Instytut Fizyki imienia Mariana Smoluchowskiego, Universytet Jagielloński, Reymonta 4, 30-059, Kraków, Poland

    J. Bieroń

  5. Centro de Física Atómica da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    A.M. Costa, J.P. Marques, M.C. Martins, F. Parente, P. Patté & J.P. Santos

  6. Laboratoire Kastler-Brossel, Unité Mixte de Recherche du CNRS n○ C8552, École Normale Supérieure et Université Pierre et Marie Curie, Case 74, 4 place Jussieu, F-75252, Paris Cedex 05, France

    G.C. Rodrigues

  7. Universidade Nova de Lisboa, Monte de Caparica, 2825-114, Caparica, Portugal

    J.P. Santos

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  1. P. Indelicato
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  2. E. Lindroth
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  3. T. Beier
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  14. S. Salomonson
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  15. J.P. Santos
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Indelicato, P., Lindroth, E., Beier, T. et al. Relativistic Calculations for Trapped Ions. Hyperfine Interactions 132, 347–361 (2001). https://doi.org/10.1023/A:1011917316335

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