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Andrew Senchuk, Gerald Gwinner, Khodr Shamseddine 2014 CAP Congress Sudbury, ON June 17, 2014

Absolute nuclear charge radii for elements without stable isotopes via precision x-ray spectroscopy of lithium-like ions. Andrew Senchuk, Gerald Gwinner, Khodr Shamseddine 2014 CAP Congress Sudbury, ON June 17, 2014. 1. Motivation.

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Andrew Senchuk, Gerald Gwinner, Khodr Shamseddine 2014 CAP Congress Sudbury, ON June 17, 2014

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  1. Absolute nuclear charge radii for elements without stable isotopes via precision x-ray spectroscopy of lithium-like ions Andrew Senchuk, Gerald Gwinner, Khodr Shamseddine 2014 CAP Congress Sudbury, ON June 17, 2014 1

  2. Motivation currently no method to experimentally determine the absolutechargeradius of nuclei for elements that have no stable or extremely long-lived isotope: The standard methods, require macroscopic amounts of the isotope fornuclei with charge Z > 83, (except uranium), no experimentaldata for the absolute nuclear charge radius. 2

  3. Importance of Experimentally Determined Nuclear Charge Radii • Fr, Rd, Ra (without stable isotopes): candidates for fundamental symmetry tests • searches for physics beyond the Standard Model: permanent electric dipole moments and atomic parity non-conservation relativistic fns correction [Bouchiat, 1974] For these precision measurements, nuclear charge radius informationis vital. 3

  4. State of the Art in Stable Elements • In heavy, Li-like ions, the 2s-2p transitions can now be measured and calculated to better than 100 meV. Experiments:Beiersdorfer et al. [1,2] U 89+, (2p1/2 - 2s) Bi 80+, (2p3/2 - 2s) E = 280.645 ± 0.015 eV E = 2788.139 ± 0.039 eV Theory:Yerohkin et al. [3] Bi 80+, (2p3/2 - 2s): 2788.12 ± 0.07 eV U 89+, (2p1/2 - 2s): 280.76 ± 0.14 eV Conclusion:Measurements, togetherwith known nuclear charge radii (Z < 84, Z = 92) verify QED calculations 4

  5. Experiments on Elements without Stable Isotopes Proposal: Turn this scheme around, now that QED is verified: Challenge: All contributions (Dirac value, photon exchange, QED) are nuclear-size sensitive and must all be evaluated as a function of Z and R (nuclearcharge radius). 5

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  7. "Dirac" Value • Solve Dirac equation for H-like ion including a finite nuclear charge distribution (Fermi): • Evaluate numerically via "RADIAL" (Fortran) [4] http://pms.iitk.ernet.in/wiki/images/Akjain13.png In Bismuth: DEN (2s-2p3/2, 5.52 fm) ~ 10 eV 7

  8. One-loop QED Numerically evaluate nuclear size corrections to self-energy (a) and vacuum polarization (b) Furry picture Formulas expressed as expansions in Za and R and are a function of "Dirac" nuclear-size correction "Dirac" FNS correction Z, a, R expansions For G ~ 1, DENSE/NPV comes in as 1/400 the "Dirac" value. In Bismuth:DEN (2s, 5.52 fm) ~ 10 eV and GNSE, NVP ~ 10, 9 DENSE, NVP ~ 250, 225 meV want 1-2% accuracy for G 8

  9. One-photon Exchange • Work in Furry picture QED [6]: Finite nuclear size enters through the electron wavefunction and state energies photon-exchange integral (a), separates into a Coulomb photon term (c), and a transverse photon part (d) [6] In Bismuth (R = 5.52 fm), finite nuclear size contributes a ~ 9 eV difference wrt a point nucleus in 2s-2p transition 9

  10. One-photon Exchange • Work in Furry picture QED [6]: counter-term cancelled by corresponding term in self-energy Finite nuclear size enters through the electron wavefunction and state energies photon-exchange integral (a), separates into a Coulomb photon term (c), and a transverse photon part (d) [6] In Bismuth (R = 5.52 fm), finite nuclear size contributes a ~ 9 eV difference wrt a point nucleus 10

  11. Estimates for Francium (Z=87) • For francium (Z=87), the finite nuclear size (R ≈ 5fm) shifts the transition by around ΔE ≈ 25 eV,and the shift is quadratic in R. From this we get asensitivity of • ΔE/ΔR ≈ 10 eV/fm. • If the combined uncertainty of the measurementand the the QED calculation is 100 meV, the nuclearcharge radius can be determined to 1/100fm, or 0.2% 11

  12. Future Work - Outlook Experimental Implementation: • EBIT/S devices coupled to radioactive beam facilitiesavailable(TITAN-EBIT at ISAC, REXEBIS at ISOLDE, ReA EBIT, • NSCL) and more are coming online (e.g. CANREB/TRIUMF). • Challenges: • Li-like breeding at Z > 83, good opticalaccess for x-ray spectrometer. • None of the current on-line breeders achieve the 100 keV e-beamsused for Bi80+ by Beiersdorfer et al. 12

  13. References: [1] Beiersdorfer et al., Phys. Rev. Lett. 80, 3022 (1998) [2] Beiersdorfer et al., Phys. Rev. Lett. 95, 233003 (2005) [3] Yerokhin et al., Phys. Rev. Lett. 97, 253004 (2006) [4] Salvat et al., Comp. Phys. Commun. 90, 151 (1995) [5] Yerokhin, Phys. Rev. A 83, 012507 (2011) [6] Sapirstein et al., Phys. Rev. A 64, 022502 (2001) Financial support by NSERC (Canada) and the University of Manitoba (A.S. acknowledges support by the Faculty of Science and a University of Manitoba Graduate Fellowship) 13

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