1. 6/17/20141 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

2. 6/17/20142 Motivation currently no method to experimentally determine the absolute charge radius of nuclei for elements that have no stable or extremely long-lived isotope: The standard methods, require macroscopic amounts of the isotope for nuclei with charge Z > 83, (except uranium), no experimental data for the absolute nuclear charge radius.

3. 6/17/20143 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 For these precision measurements, nuclear charge radius information is vital. [Bouchiat, 1974] relativistic fns correction

4. 6/17/20144 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] E = 2788.139 ± 0.039 eV E = 280.645 ± 0.015 eV Bi 80+, (2p3/2 - 2s) U 89+, (2p1/2 - 2s) 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, together with known nuclear charge radii (Z < 84, Z = 92) verify QED calculations

5. 6/17/20145 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 (nuclear charge radius).

6. 6/17/20146

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

8. 6/17/20148 One-loop QED Numerically evaluate nuclear size corrections to self-energy (a) and vacuum polarization (b)Furry picture Formulas expressed as expansions in Z  and R and are a function of "Dirac" nuclear-size correction "Dirac" FNS correction Z, , R expansions For G ~ 1,  E NSE/NPV comes in as 1/400 the "Dirac" value. In Bismuth:  E N (2s, 5.52 fm) ~ 10 eV and G NSE, NVP ~ 10, 9  E NSE, NVP ~ 250, 225 meVwant 1-2% accuracy for G

9. 6/17/20149 One-photon Exchange Finite nuclear size enters through the electron wavefunction and state energies  Work in Furry picture QED [6]: 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

10. 6/17/201410 One-photon Exchange Finite nuclear size enters through the electron wavefunction and state energies  Work in Furry picture QED [6]: counter-term cancelled by corresponding term in self-energy 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

11. 6/17/201411 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 a sensitivity of ΔE/ΔR ≈ 10 eV/fm.  If the combined uncertainty of the measurement and the the QED calculation is 100 meV, the nuclear charge radius can be determined to 1/100 fm, or 0.2%

12. 6/17/201412 Future Work - Outlook Experimental Implementation:  EBIT/S devices coupled to radioactive beam facilities available (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 optical access for x-ray spectrometer.  None of the current on-line breeders achieve the 100 keV e- beams used for Bi80+ by Beiersdorfer et al.

13. 6/17/201413 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)

14. 6/17/20146/9/201514 Outline Motivation

15. 6/17/20146/9/201515 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: In heavy Li-like systems, theory including 2-loop QED is reliable at the sub-100 meV level. Finite nuclear size contributions are a correction, as the nuclear charge radii are well known for Z < 84, and Z = 92 Beiersdorfer et al. [2] U 89+, 2p1/2 - 2s 280.645 ± 0.015 eV

16. 6/17/20146/9/201516 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 (nuclear charge radius). We are currently establishing the expressions that include all Z and R dependence.

17. 6/17/20146/9/201517 We present a technique to measure the absolute charge radius of any heavy isotope of sufficient half-life (order of seconds) using precise x-ray spectroscopy of the electronic 2s-2p transition in lithium-like ions. The finite nuclear size shifts the transition energy by 20 - 30 eV in these systems, whereas experimentally, the transition energy can be measured absolutely with an accuracy below 100 meV [1,2]. In addition, recent progress in QED theory allows us to account for radiative corrections at a comparable level [3]. As a result, the contribution by the finite nuclear charge distribution can be extracted at the 100 meV level or better.