Atomic Clocks and the Search for Variation of Fundamental Constants

MARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVA

University of Maryland

January 22, 2015

Outline

Blackbody radiation shifts in atomic clocks: Al+, Yb, Sr

Theoretical Method

Variation of fundamental constants: an introduction

How to search for the variation of the fine-structure constant?

Highly-charged ions for clocks and search for α-variation

Optical vs. microwave clocks

physics.aps.org

PTB Yb+

JILA Sr

Motivation:

BBR shift gave the largest uncertainty for most accurate clocks

Very difficult to measure

Theoretical calculations and atomic clocksBlackbody radiation ( BBR ) shift:

Effect due to thermal radiation

BLACKBODY RADIATION SHIFTSBLACKBODY RADIATION SHIFTSBLACKBODY RADIATION SHIFTSBLACKBODY RADIATION SHIFTS

T = 300 KT = 300 KT = 300 KT = 300 K

CLOCKCLOCKCLOCKCLOCK

TRANSITIONTRANSITIONTRANSITIONTRANSITION

LEVEL ALEVEL ALEVEL ALEVEL A

LEVEL BLEVEL BLEVEL BLEVEL B

∆BBRT = 0 KT = 0 KT = 0 KT = 0 K

Transition frequency should be corrected to account for the

effect of the black body radiation at T=300K.

BBR shift and polarizability

BBR shift of atomic level can be expressed in terms of a

scalar static polarizability to a good approximation [1]:

[1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)

4

2

BBR 0

1 ( )(0)(831.9 / ) (1+ )

2 300

T KV mν α η

∆ = −

Dynamic correction is generally small.

Multipolar corrections (M1 and E2) are suppressed by α2 [1].

Vector & tensor polarizability average out due

to the isotropic nature of field.

Dynamic correction

(0)

v vΨ = Ω Ψ

Exact wave functionMany-body operator,

describes excitations from lowest-order

Dirac-Hartree-Fock

wave function (lowest order)

Cs: 55 electrons 55-fold excitations to get exact wave function

Even for 100 function basis set 10055

Approximate methods: perturbation theory does not

converge well, need to use all-order methods (for example

coupled-cluster method)

High-precision atomic calculationsWhy is it so difficult?

Electron-electron correlation now separates into two problems

Problem 1: core-core and core-valence correlationsProblem 2: valence-valence correlations

1s2 ... 4d10 5s2 ground state

1s2...4d105s2

core

valenceelectrons

Example: Cd-like Nd12+

Two valence electrons outside of a closed core

Configuration interaction works well for systems with a few valence electrons but can not accurately account for core-valence and core-core correlations.

Coupled-cluster method accounts well for core-core and core-valence correlations (as demonstrated by work on alkali-metal atoms).

Therefore, two methods are combined to acquire benefits from both approaches.

Main idea: solve two problems by different methods

Electron-electron correlation now separates into two problems

1s2...4d105s2

core

valenceelectrons

Cd-like Nd12+

core

valence

Use configurationinteraction (CI) method to

treat valence correlations

Use all-order

(coupled-cluster)method to treat core

and core-valence

correlations

Linearized coupled-cluster method

Main idea: allow single and double excitationsof the initial wave functions to any orbital from finite basis set

1S2S

core excitation

valence

excitation

core excitations

core -

valence

excitations

Excitations are described by cluster excitation coefficients ρij, ρijkl.

valence excitation

5s 6s, 7s, ..35s, 5p, 6p, …35p, 5d, 6d, …

• Main feature: includes correlations to all orders of

perturbation theory

• Implementation has to be very efficient

• Both formula derivations and required coding are very

extensive

Coupled-cluster method

22

2

1S

2 (0)2 | | 0: :

1

2: cm n c adi j l k bv vr sa a aa a aa a a aaH aS a+ + + ++ ++ >→Ψ >

Contract operators by Wick’s theorem

800 TERMS!800 TERMS!800 TERMS!800 TERMS!

Too many terms beyond single and double excitations

• Main feature: includes correlations to all orders of

perturbation theory

• Implementation has to be very efficient

• Both formula derivations and required coding are very

extensive

Codes that write codes

Codes that write formulas

Codes that analyse results and estimate uncertainties

Coupled-cluster method

Monovalent systems: very brief summary of what we calculated with all-order method

Properties

• Energies

• Transition matrix elements (E1, E2, E3, M1)

• Static and dynamic polarizabilities & applications

Dipole (scalar and tensor)

Quadrupole, Octupole

Light shifts

Black-body radiation shifts

Magic wavelengths

• Hyperfine constants

• C3 and C6 coefficients

• Parity-nonconserving amplitudes (derived weak charge and anapole moment)

• EDM enhancement factors

• Isotope shifts (field shift and one-body part of specific mass shift)

• Atomic quadrupole moments

• Nuclear magnetic moment (Fr), from hyperfine data

Systems

Li, Na, Mg II, Al III,

Si IV, P V, S VI, K,

Ca II, In, In-like ions,

Ga, Ga-like ions, Rb,

Cs, Ba II, Tl, Fr, Th IV,

U V, other Fr-like ions,

Ra II

http://www.physics.udel.edu/~msafrono

Configuration interaction method

i i

i

cΨ = Φ∑ Single-electron valencebasis states

( ) 0H E− Ψ =

1 1 1 2 2 1 2( ) ( ) ( , )

one bodypart

two bodypart

H h r h r h r r

− −

= + +

Example: two particle system: 1 2

1

−r r

Configuration interaction +coupled-cluster method (CI+all-order)

H is modified using coupled-cluster method to calculate correction Σ

Advantages: most complete treatment of the correlations and applicable for many-valence electron systems

Note: this effectively accounts for up to dominant

quadrupole excitations

1 1 1

2 2 2

eff

eff

H H

H H

= + Σ

= + Σ

( ) 0effH E− Ψ =Run CI with effective Hamiltonian

Computational and other challenges

1. Computer calculations should finish within “reasonable time”.

2. Evaluation and reduction of numerical uncertainties

3. Estimation of “missing physics” uncertainties

Calculations should finish in “reasonable time”

Less then the lifetime of the Universe

Before your current grant proposal

runs out

Calculations should finish in “reasonable time”

Before your patience runs out

indieberries.blogspot.com

Calculations should finish in “reasonable time”

How to estimate “missing physics”uncertainties?

1. Calculate properties of similar “reference” systems where

experimental data exist.

2. Use several different methods of increasing precision and

compare results.

3. Calculate all major corrections separately, check for

possible cancelations – use to estimate uncertainty.

4. Test the methods of evaluating uncertainties on “reference”

systems.

How to estimate what we do not know?

1. Calculate properties of similar “reference” systems where

experimental data exist.

2. Use several different methods of increasing precision and

compare results.

3. Calculate all major corrections separately, check for

possible cancelations – use to estimate uncertainty.

4. Test the methods of evaluating uncertainties on “reference”

systems.

Al+ energy levels, differences with experiment

Level CI CI+MBPT CI+All

3s2 1

S0 1.2% 0.043% 0.006%

3p2 1

D2 2.3% 0.07% -0.022%

3s4s3S1 1.4% 0.07% 0.015%

3p2 3

P0 1.6% 0.04% 0.008%

3p2 3

P1 1.6% 0.03% 0.004%

3p2 3

P2 1.6% 0.02% -0.004%

3s4s1S0 1.4% 0.05% 0.003%

3s3p3P0 3.1% 0.15% 0.007%

3s3p3P1 3.1% 0.14% 0.008%

3s3p3P2 3.1% 0.12% -0.017%

3s3p1P1 0.4% -0.17% -0.14%

Precision Calculation of Blackbody Radiation Shifts for Optical Frequency Metrology , M. S. Safronova, M. G. Kozlov, and Charles W. Clark, Phys. Rev. Lett. 107, 143006 (2011) .

Al+ polarizabilities (a.u.): 3 calculations

Accuracy of ∆α ∆α ∆α ∆α (3P0 - 1S0) ?

Difference (CI+MBPT → CI + all-order) = 0.4%Difference (CI → CI + all-order) = 2.6 %Other uncertainties: 1.4% (Breit) and 2% (core)

Estimate: 10%

CI CI+MBPT CI + All-order

α α α α (3s2 1S0) 24.405 24.030 24.408

α α α α (3s3p 3P0) 24.874 24.523 24.543

∆α∆α∆α∆α(3P0 - 1S0) 0.469 0.493 0.495

Precision Calculation of Blackbody Radiation Shifts for Optical Frequency Metrology , M. S. Safronova, M. G. Kozlov, and Charles W. Clark, Phys. Rev. Lett. 107, 143006 (2011) .

Yb energy levels, differences with experiment

Level CI CI+MBPT CI+All

6s2 1S0 -7.4% 1.3% 0.7%

5d6s 3D1 4.1% 3.3% 2.5%

5d6s 1D2 -6.3% 4.2% 2.4%

6s7s 3S1 -9.4% 1.5% 1.2%

6s7s1S0 -8.7% 1.4% 1.2%

6s6p 3P0 -19% 5.6% 2.7%

6s6p 3P1 -18% 5.3% 2.5%

6s6p3P2 -18% 5.0% 2.7%

6s6p1P1 -4.7% 5.6% 3.6%

Ytterbium in quantum gases and atomic clocks: van der Waals interactions and

blackbody shifts, M. S. Safronova, S. G. Porsev, and Charles W. Clark, Phys. Rev. Lett.

109, 230802 (2012).

Yb static polarizabilities (a.u.)

Method α(1S0) α(3P0) ∆α

CI 166 258 92

CI+MBPT 138 306 168

Final CI+all-order (ab initio) 141(2) 293(10) 152

Porsev & Derevianko (2006) 111.3(5) 266(15) 155

Zhang & Dalgarno (2007) 143

Dzuba & Derevianko (2010) 141(6) 302(14) 161

Beloy (2012) from expt. data 134-142 280-290

Expt. Sherman et al. (2012) 145.726(3)

Polarizability is calculated directly by solving of the inhomogeneous

differential equation in the valence sector – we do not use sum over states.

Dynamic correction to the BBR shift in Yb

State α0 η1 η ∆νBBR(dyn)

T = 300 K

6s2 1S0 140.9 19261 0.00116 0.00116 −0.0014 Hz

6s6p 3P0 293.2 322862 0.00934 0.00963 -0.0243(8) Hz

3P0 -1S0 -0.0229(8) Hz

Expt. [1] -0.0226(6) Hz

[1] K. Beloy, J. A. Sherman, N. D. Lemke, N. Hinkley, C. W. Oates, and

A. D. Ludlow (2012).

Dynamic correction: 1.8% of the total BBRBBR uncertainty at T = 300K is reduced to 2×10-18

2

2

(0)g

gE

α∂

∂

Sr DC polarizabilities: 3 calculations

E1 matrix elements

Energies αααα(1S0) αααα(3P0) ∆α∆α∆α∆α ∆α∆α∆α∆α

#1 CI+all CI+all 197.8 458.1 260.3 [1] 261(4)

Dominant terms

[1] S. Porsev and A. Derevianko, Phys. Rev. A 74, 020502R (2006)

[2] T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, Phys. Rev. Lett. 109,

263004 (2012)

Sr DC polarizabilities: 3 calculations

E1 matrix elements

Energies αααα(1S0) αααα(3P0) ∆α∆α∆α∆α ∆α∆α∆α∆α

#1 CI+all CI+all 197.8 458.1 260.3 [1] 261(4)

#2 CI+all Expt. 198.9 453.4 254.5

Dominant terms

-2.3%

[1] S. Porsev and A. Derevianko, Phys. Rev. A 74, 020502R (2006)

[2] T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, Phys. Rev. Lett. 109,

263004 (2012)

Sr DC polarizabilities: 3 calculations

E1 matrix elements

Energies αααα(1S0) αααα(3P0) ∆α∆α∆α∆α ∆α∆α∆α∆α

#1 CI+all CI+all 197.8 458.1 260.3 [1] 261(4)

#2 CI+all Expt. 198.9 453.4 254.5

#3CI+all + 4

correctionsExpt. 194.4 441.9 247.5

247.374(7)

Expt. [2]

Dominant terms

[1] S. Porsev and A. Derevianko, Phys. Rev. A 74, 020502R (2006)

[2] T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, Phys. Rev. Lett. 109,

263004 (2012)

-2.3%

-2.8%

Dynamic correction to the BBR shift

Theory [1] PTB [2]

-0.1492(16) Hz -0.1477(23) Hz

1. 5s5p 3P0 – 5s4d 3D1 transition contributes 98.2 % to

dynamic correction in Sr

2. Dynamic correction is 7% of the BBR shift in Sr!

Differences between Sr and Yb cases:

Dynamic correction ∆νBBR (dyn)

[1] Safronova et al., Phys. Rev. A 87, 012509 (2013).

[2] Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)

Our prediction of the 5s4d 3D1 lifetime: 2171(24) ns

Measurement of the 3D1 lifetime will yield dynamiccorrection to the BBR shift with the same accuracy!

Dynamic correction to the BBR shift

Blackbody radiation shift in the Sr optical atomic clock,

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and Charles W. Clark,

Phys. Rev. A 87, 012509 (2013).

Our prediction of the 5s4d 3D1 lifetime: 2171(24) ns

Measurement of the 5s4d 3D1 lifetime: 2180(10) ns

×− total uncertainty in an atomic clock, T.L. Nicholson, S.L. Campbell, R.B. Hutson, G.E. Marti, B.J. Bloom, R.L.

McNally, W. Zhang, M.D. Barrett, M.S. Safronova, G.F. Strouse, W.L. Tew, and

J. Ye, submitted to Nature Physics, arxiv 1412.8621 (2015)

Sr JILA clock: BBR static shift uncertainty 3×10-19

BBR dynamic shift uncertainty 1.4×10-18

Atom Clock transition ∆ν∆ν∆ν∆ν/νννν0 Uncertainty Reference

Rb 5s (F=2 - F=1) -1.25 ×××× 10-14 4 ×××× 10-17 Safronova et al. 2010

Cs 6s (F=4 - F=3) -1.7 ××××10-14 3 ×××× 10-17 Simon et al. 1998

Ca+ 4s - 3d5/2 9.2 ×××× 10-16 1 ×××× 10-17 Safronova et al. 2011

Sr+ 5s - 4d5/2 5.6 ×××× 10-16 2 ×××× 10-17 Jiang et al. 2009

Yb+ 6s - 5d 2D3/2 -5.3 ×××× 10-16 1 ×××× 10-16 Tamm et al. 2007

Yb+ 6s - 4f13 6s2 2F7/2 -5.7 ×××× 10-17 1 ×××× 10-17 Hosaka et al 2009

B+ 2s2 1S0 - 2s2p 3P0 1.42 ×××× 10-17 1 ×××× 10-18 Safronova et al. 2011

Al+ 3s2 1S0 - 3s3p 3P0 -3.8 ×××× 10-18 4 ×××× 10-19 Safronova et al. 2011

In+ 5s2 1S0 - 5s5p 3P0 -1.36 ×××× 10-17 1 ×××× 10-18 Safronova et al. 2011

Tl+ 6s2 1S0 - 6s6p 3P0 -1.06 ×××× 10-17 1 ×××× 10-18 Zuhrianda et al. 2012

Sr 5s2 1S0 - 5s5p 3P0 -5.5 ×××× 10-15 1.4 ×××× 10-18 Nicholson et al. (2015)

Yb 6s2 1S0 - 6s6p 3P0 -2.6 ×××× 10-15 2 ×××× 10-18

Sherman et al. 2012Safronova et al. 2012

Hg 6s2 1S0 - 6s6p 3P0 -1.6 ×××× 10-16 Hachisu et al. 2008

Summary of the fractional uncertainties ∆ν/ν0 due to BBR shift and the fractional error in the absolute transition frequency induced by the BBR shift uncertainty at

T = 300 K in various frequency standards

ARE ARE ARE ARE

FUNDAMENTAL FUNDAMENTAL FUNDAMENTAL FUNDAMENTAL

CONSTANTS CONSTANTS CONSTANTS CONSTANTS

CONSTANT???CONSTANT???CONSTANT???CONSTANT???

Being able to compare and reproduce experiments is at the foundation of the scientific approach, which makes sense only if the laws of nature do not depend on time and space.

J.-P. Uzan, Rev. Mod. Phys. 75, 403 (2003)

The New International System of Units based on Fundamental Constants

2

0

1

4

e

cα

πε=

www.rikenresearch.riken.jp

The modern theories directed toward unifying gravitation with the

three other fundamental interactions suggest variation of the fundamental constants in an expanding universe.

www.economist.com

Life needs very specific fundamental constants!

α

ħ~1/137

If α is too big → small nuclei can not exist

Electric repulsion of the protons > strong nuclear binding force

α~1/137

α~1/10

will blow

carbon apart

www.economist.com

Life needs very specific fundamental constants!

α

ħ~1/137

Nuclear reaction in stars are particularly sensitive to α.

If α were different by 4%: no carbon produced by stars. No life.

α~/

www.economist.com

Life needs very specific fundamental constants!

α

ħ~1/137

No carbon produced by stars: No life in the Universe

α

Search for the variation of the fine-structure

constant αααα

2

0

1

4

e

cα

πε=

How to test if αααα changed with time?

Atomic transition energies depend on α2

Mg+ ion

Scientific American Time 21, 70 - 77 (2012)

Julian Berengut, UNSW, 2010

2

0

0

1ZZ

E E qα

α

= + −

Laboratory frequencyObserved from quasarabsorption spectra

Astrophysical searches for variation of fine-structure constant αααα

Conflicting results

Murphy et al., 2007

Keck telescope, 143 systems,

23 lines, 0.2<z<4.2

50.64(36) 10α α −∆ = − ×

50.06(0.06) 10α α −∆ = − ×

Srianand et al, 2004: VL

telescope, 23 systems, 12 lines,

Fe II, Mg I, Si II, Al II, 0.4<z<2.3

Molaro et al., 2007

Z=1.84

60.12(1.8) 10α α −∆ = − ×

65.7(2.7) 10α α −∆ = ×

Astrophysical searches for variation of fine-structure constant αααα

Julian Berengut, UNSW, 2010

Observed from quasarabsorption spectra

Laboratory searches for variation of fundamental constants

Ratio of two clock frequencies

N. Huntemann, B. Lipphardt, Chr. Tamm, V. Gerginov, S.

Weyers, E. Peik, Phys. Rev. Lett. 113, 210802 (2014)

Therefore, comparison of different clocks can be used to

search for α−variation.

Optical only clock test only α-variation

Example: Al+ / Hg+ atomic clocks

17 11.6(2.3) 10 yα α − −= − ×

0( )x xν ν= + q ( )2

0 1x α α= −

Different optical atomic clocks use transitions that have

different contributions of the relativistic corrections to

frequencies.

Laboratory searches for αααα−−−−variation

Rosenband et al., Science 319, 1808 (2008)

Need very precise

frequency standards

using systems with

very large q

0( )x xν ν= + q

Highly-charged ions

for Atomic Clocks(1) Metastable level(2) Near optical transition

(3) Requirement for the αααα-variation searches:two clock levels can not belong to the same fine-structure of hyperfine-structure multiplet .

0( )x xν ν= + q

HIGHLYHIGHLYHIGHLYHIGHLY----CHARGED IONS ???CHARGED IONS ???CHARGED IONS ???CHARGED IONS ???

100 200 300 400 500 600 Wavelength nm

3s2 1S0 – 3s3p 3P0 transition in Mg-like ions

Mg458 nm

Al+

267 nmSi2+

190 nm

Cl6+

102 nm

Sn-like ions(present work)

[Kr] 4d105s2 core

Sn

5p6s 3P0

5p2 1S01D2

5p2 3P0,1,2

289 nm

Sn-like Pr9+

5p4f J=3

5p2 3P0

495(13) nm

Sn –like Ba6+

163 nm

5p2 1S0

1D23P1,2

5p2 3P0

Clock proposals with highly-charged ions

1. Electron-hole transitions: Ir16+, Ir17+, W ions, …

2. Californium Cf16+, Cf17+ and similar ions

3. Nuclear-spin-zero f12 shells (clock only,

no α-variation enhancement)

4. Ag-like, Cd-like, In-like, Sn-like valence transitions

(present work)

This work:Exhaustive search of transitions in highly-charged ions that are particularly well suited for the current

experimental explorations.

Our criteria:

(1) Metastable states with transition frequencies to the ground

state ranging between 170-3000 nm.

(2) High sensitivity to α-variation.

(3) Stable isotopes.

(4) Relatively simple electronic structure:

one to four valence electrons above the closed core.

Only ions in 4 isoelectronic sequnces satisfy the criteria:

Ag-like, Cd-likeIn-like, Sn-like ions

Very difficult to accurately calculate energies!

Sn-like Pr9+

5p4f J=3

5p2 3P0

495(13) nm

- 2 497 720 cm -1

Two-electron energies

- 2 477 500 cm -1

20 220 ± 540 cm -1

Transition energy

Major corrections to the transition energy:

Higher-orders ( III+) : 2994 cm-1

Higher partial waves (l>6): -1078 cm-1

Breit interaction: -1750 cm-1

M. S. Safronova et al., Phys. Rev. Lett. 113, 030801 (2014).

Ion Level Expt. Theory Diff. Diff. (%)

Nd13+ 5s 0 0 0

4f5/2 55870 55706 164 0.29%

4f7/2 60300 60134 166 0.28%

5p1/2 185028 185028 38 0.02%

5p3/2 234864 234887 -24 -0.01%

Sm15+ 4f5/2 0 0 0

4f7/2 6555 6444 111 1.69%

5s 60384 60517 -133 -0.22%

Ce9+ 5p1/2 0 0 0

5p3/2 33427 33450 -23 -0.07%

4f5/2 54947 54683 264 0.48%

Comparison of energy levels with experiment (cm-1)

Nd13+: one valence electron (Ag-like)

5s

4f5/2

4f7/2

λ=179nm

λ=165nm

4400 cm-1

τ τ τ τ =15 days

τ =1 s

E3 q = 104 000 cm-1

0( )x xν ν= + q ( )2

0 1x α α= −

Quantity q describes sensitivity to α-variation

Pr10+: three valence electrons (In-like)

5s25p1/2

5s24f5/2

5s24f7/2

λ=2700 nm

λ=1420 nm3330 cm-1

τ τ τ τ =1 day

τ τ τ τ =2.4 s

E2 q = 74 000 cm-1

5s25p3/2

λ=256 nm

τ = 0.002 s

Pr9+: four valence electrons (Sn-like)

5s25p2 3P0

5s25p4f 3G3

λ=475 nm

λ=424 nm

τ τ τ τ = 20 000 000 years!

τ τ τ τ =58 s

M3

q = 43000 cm-1

λ=351 nm

τ = 0.003 s5s25p2 3P1

M1

5s25p4f 3F2

Selected highly-charged ions have several metastable states

representing a level structure and other properties that are

not present in any neutral and low-ionization state ions and

may be advantageous for the development of atomic clocks

as well as provide new possibilities for quantum information

storage and processing.

Estimated fractional accuracy of the transition frequency in

the clocks based on highly-charged ions can be smaller than

10-19. Estimated sensitivity to the α-variation for transitions in

highly-charged ions approaches 10-20 per year [1, 2].

[1] A. Derevianko, V. A. Dzuba, and V. V. Flambaum, PRL 109, 180801 (2012).

[2] V. A. Dzuba, A. Derevianko, and V. V. Flambaum, PRA 86, 054502 (2012).

Summary

[1] Highly Charged Ions for Atomic Clocks, Quantum

Information, and Search for α-variation, M. S. Safronova, V. A.

Dzuba, V. V. Flambaum, U. I. Safronova, S. G. Porsev, and

M. G. Kozlov, Phys. Rev. Lett. 113, 030801 (2014).

[2] Ag-like and In-like ions: M. S. Safronova et al.,

Phys. Rev. A. 90, 042513 (2014)

[3] Cd-like and Sn-like ions, M. S. Safronova et al.,

Phys. Rev. A. 90, 052509 (2014)

Recommended ions: Nd13+, Sm15+, Ce9+, Pr10+,

Nd11+, Sm13+Nd12+, Sm14+, Pr9+, Nd10+

Summary: present work

OTHER COLLABORATORSOTHER COLLABORATORSOTHER COLLABORATORSOTHER COLLABORATORS

Charles Clark, NISTAndrei Derevianko, University of Nevada-Reno Ephraim Eliav, Tel Aviv University, IsraelWalter Johnson, University of Notre Dame

Research scientist:Sergey Porsev

Graduate students:Z. Zhuriadna, D. Huang, A. Naing

HIGHLYHIGHLYHIGHLYHIGHLY----CHARGE ION COLLABORATIONCHARGE ION COLLABORATIONCHARGE ION COLLABORATIONCHARGE ION COLLABORATION

Michael Kozlov, PNPI, RussiaSergey Porsev, University of Delaware and PNPIUlyana Safronova, University of Nevada-RenoVladimir Dzuba, UNSW, AustraliaVictor Flambaum, UNSW, Australia