Parity violation in one single trapped radium ion

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Parity violation in one single trapped radium ion

• Lotje Wansbeek
• Theory Group, KVI
• University of Groningen, The Netherlands
• ECT Workshop The lead radius experiment
• Trento, August 5, 2009

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Low-energy tests of the Standard Model
The Standard Model (SM) of particle physics is
incomplete ? searches for physics beyond the SM
at two, complementary, fronts
High energy collider experiments
Direct observation of new particles
Low energy searches
indirect, but with high precision
LHC _at_ CERN
TRI?P _at_ KVI
Requires High-energy physics
Requires Atomic and nuclear physics theory
experiment lt 1
Radium ion experiment Weak charge QW(Ra) ?
Weinberg angle Mixing angle between the photon
and the Z0-boson
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APV in one single ion

• Cs experiment
• Single valence system
• Atomic beam experiment

• Ba, Ra experiment
• Single valence system
• Single, trapped ion

• Experimental advantages of single-ion APV
• Tractable systematics
• Long coherence times
• Only trace quantities required

Single trapped Ba ion
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APV in one single ion

• The concept
• Interference between E2 and E1APV produces
  differential shift ?diff of the two ground state
  Zeeman levels
• ?diff can be measured with RF spectroscopy (about
  10 Hz)

7P3/2
7P1/2
6D5/2
e nP3/2
6D3/2
E2
E1APV
7S1/2
e nP1/2
q
q
V
Z0
A
e
e
Weak interaction (violates parity) Weak charges
of quarks in the nucleus add coherently QW
N(14 sin2?W)Z rad. corr. new
physics where ?W is the weak ? - Z0 mixing (or
Weinberg) angle.
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The scaling of the APV effect

• The Bouchiat Bouchiat (1974) faster than
  Z3-law says

where Kr is a relativistic factor, and QW N Z
Z3Kr
Z3Kr
Ra
Ra
arb. units
Z3
x DF calculation for n 2,3,4,5,6,7
Z3
Ra
Ba(Cs)
Sr
Ca
Ra
Ba
Ba
Sr
Mg
Ca
Be
Z (atomic number)
E1APV effect in Ra is 20 times larger than for
Ba, and 50 times larger than for Cs!
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Theoretical status

• Calculation of E1APV in Ra using relativistic
  coupled-cluster (CC) theory1
• E1APV 46.4(1.4) 10-11 iea0 (-Qw/N)
• Accuracy (3 ) estimated from hyperfine constants
  vs. theory
• The Delaware2 group (2009) find 45.9 10-11 iea0
  (-Qw/N)
• Dzuba et al.3 (2001) find 45.9 10-11 iea0
  (-Qw/N) with a 1 error
• Achieved in Cs 0.3
• For a SM test, we need sub-1 accuracy!

1. L.W. Wansbeek et al., Phys. Rev. A 78, 050501(R)
   (2008).
2. R. Pal et al., Phys. Rev. A 79, 062505 (2009).
3. Dzuba et al., Phys Rev. A 63, 062101 (2001).

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Improving the accuracy

• Work to be done on the theory side
• Improvement of CC theory
• Inclusion of small corrections
• Breit (magnetic) interaction
• Vacuum polarization other QED corrections
• Nuclear structure effects
• Study of different isotopes
• Experimental input is needed!
• Last and only spectroscopic data is from Ebbe
  Rasmussen (1934)
• ISOLDE _at_ CERN (1980s)
• Isotope shifts of the 7S1/2 7P1/2 line
• Hyperfine structure of this line
• Lifetimes
• Isotope shift of the of the 7P1/2 6D3/2 line
  for 212-214Ra planned _at_ KVI

With new experimental input sub-1 is a
realistic goal!
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What is the uncertainty from nuclear input?
The parity violating amplitude in the
sum-over-the-states method

• E1APV in Cs and Fr (S-S transition) is dominated
  by 3 terms
• These are of comparable size, but signs differ
• Strong cancellations, final result is half the
  size of the largest contribution
• E1APV in Ra (Ba) (S-D transition) is strongly
  dominated by 1 term
• ? Largest contribution (around 110 ) comes
  from the 7P1/2 (6P1/2) state
• ? No strong cancellations

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Factorizing the SP-matrix element

• James and Sandars (J. Phys. B 32, 1999) write
• With

Normalization constant, depends on particular
atomic states, not on isotope
Normalization constant, independent of particular
atomic states
Equivalent charge radius
Integral over the neutron density and radial
wavefunction
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Nuclear structure effects in APV

• Assume constant-density nucleus
• Solve radial Dirac equations inside nucleus
• Match solutions, near the nucleus, to atomic
  wavefunctions of the form
• Look at the effects of small variations of the
  constant-density nucleus

Higher moments of the charge distribution
Atomic wavefunctions
Measure of the neutron skin
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What data is available for radium?

• We take the radius for 214Ra R0 from the data
  table by Angeli
• R0 5.5705 (130) fm
• The difference between R0 and RN can be deduced
  from the isotope shifts measured by Ahmed et al.
• This gives RN a relative and a total error
• For the neutron skins, we use the calculation by
  Brown et al., which has a 25 error

Fractional uncertainty
Rp fm
A
A
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The total uncertainty

• To summarize the uncertainty
• Atomic structure
• The calculation of E1APV in Ra is currently
  accurate to about 3
• 1 accuracy seems feasible, provided there is
  new experimental input
• Even in Cs, the dominant theoretical (0.3 )
  error is due to atomic structure
• Nuclear structure
• Neutron skin and charge radius give additional
  0.15 0.35 uncertainty
• However
• Our aim is sub-1!
• What more can be done?

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An alternative a ratio measurement?

• The idea is (Dzuba et al.)
• Taking the ratio of two measurements of E1APV
  for two isotopes N and N will cancel the atomic
  uncertainty.
• A value for the ratio is equally informative on
  the Weinberg angle
• For radium a wide range of isotopes is available
• What about the nuclear uncertainties?
• The uncertainties in the neutron skins and charge
  radii are correlated
• ? By taking a ratio you can use this fact!

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The ratio defined
The ratio is the ratio of two parity violating
amplitudes for two different isotopes. We had

• The intermediate 7P1/2 state contributes 110
• Isotope-independent terms cancel
• To a good approximation, the ratio is given by

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The uncertainty of the ratio
With this expression for the neutron skin, the
ratio is written
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The relevant isotopes of radium
Lifetime Spin
209 4.6(2) s 5/2
211 13(2) s 1/2
212 13.0(2) s
213 2.74(6) m 1/2
214 2.46(3) s
221 28.2 s 5/2
223 11.43(5) d 3/2
224 3.6319(23) d
225 14.9(2) d 1/2
226 1600 y
227 42.2(5) m 3/2
229 4.0(2) m 5/2

Produced on-line Spectroscopy this September
Available off-line for EDM experiment
?
?
Comercially available
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Nuclear uncertainty in the ratio

• For the ratio of the isotope pair 214 and 226 we
  find
• Total fractional uncertainty 0.14
• Uncertainty due to skin 0.10 (error taken twice
  as large)
• Uncertainty due to radius 0.09
• The separate errors where 0.15 and 0.30 !
• A ratio measurement
• Cancels the atomic calculation uncertainty
• Reduces the nuclear uncertainty

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Experimental status summarized

• Ba Ra lasers set up in experimental hall
• Construction of collector and precision Paul
  traps
• Radium production with AGOR cyclotron at TRI?P
  facility
• Chain of isotopes 212Ra , 213Ra and 214Ra
  produced
• With low intensity (206Pb) beam 103
  particles/sec of each isotope
• Successful trapping of Radium isotopes
  demonstrated in January 09
• First laser spectroscopy of trapped Radium ions
  expected in September 09

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Conclusions outlook

• Ra is an excellent candidate for a competitive
  APV experiment
• The effect in Ra is very large
• Easy wavelengths
• Large range of isotopes available
• Experimentally, a fivefold improvement over Cs
  appears feasible
• The uncertainty in E1APV for Ra
• Due to atomic calculation uncertainty is about 3
  
• Due to nuclear structure uncertainties is at
  least 0.15 - 0.35
• A ratio measurement
• Is equally informative
• Cancels atomic uncertainty
• Reduces nuclear uncertainty to 0.14 for the
  214-226 pair
• Experiment is being set up

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The crew the money
www.kvi.nl/radiumion

• Experiment
• Gouri Giri (PhD)
• Oscar Versolato (PhD)
• Lorenz Willmann
• Klaus Jungmann
• Theory
• Lotje Wansbeek (PhD)
• Bijaya Sahoo (PostDoc)
• Lex Dieperink
• Rob Timmermans
• International collaborators
• B. P. Das (India)
• N. E. Fortson (USA)

• Funding
• FOM open competition
• NWO Toptalent grant
• NWO Veni fellowship

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The Boulder Cs experiment
Cs
Weak interaction causes states to acquire tiny
admixture of opposite-parity states and similar
for 7S1/2
7S1/2
No dipole transition!
E1
6S1/2
weak interaction
Cs

7S1/2
Dipole transition!
E1PNC

6S1/2
Measure
Atomic calculation
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