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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 CongressSudbury, ON

June 17, 2014

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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.

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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.

2)1)(1(

02

2

2

)1)(12(

)3(),(

Z

r a

RZ

ZRZK

[Bouchiat, 1974]

),())(1))((1(22

),(

'

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2

2/12/1

RZKNZQZG

pnVsn

rnnwF

PNC

relativistic fns correction

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State of the Art in Stable ElementsIn 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 eVE = 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 eVU 89+, (2p1/2 - 2s): 280.76 ± 0.14 eV

Conclusion: Measurements, together with known nuclear charge radii (Z < 84, Z = 92) verify QED calculations

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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).

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"Dirac" Value

]/)exp[(1)( 0

acrr

Solve Dirac equation for H-like ion including a finite nuclear charge distribution (Fermi):

(r) E= (r)(r))V + m + p̂ . ( C

http://pms.iitk.ernet.in/wiki/images/Akjain13.png

Evaluate numerically via "RADIAL" (Fortran) [4]

In Bismuth: EN (2s-2p3/2, 5.52 fm) ~ 10 eV

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One-loop QEDNumerically 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 correctionZ, , R expansions

ljnlnljnE NPVNSE ,,G,,E = ,, NSE/NPV21

N/

For G ~ 1, ENSE/NPV comes in as 1/400 the "Dirac" value.

In Bismuth: EN (2s, 5.52 fm) ~ 10 eV and GNSE, NVP ~ 10, 9

ENSE, NVP ~ 250, 225 meV want 1-2% accuracy for G

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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

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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

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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%

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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.

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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 ofManitoba Graduate Fellowship)