1. NEW DIRECTIONS IN ATOMIC PARITY VIOLATION
PANIC 2008
EILAT, ISRAEL
NEW DIRECTIONS IN ATOMIC PARITY VIOLATION
Marianna Safronova
November 11, 2008

2. PNC studies in atoms: Atomic physics tests of the standard model
Goal: Study (very precisely!) quantities which Standard Model predicts and compare the result with its prediction.
The results lead to restrictions of possible extensions of the Standard Model.
Quantity of interest:
Weak charge QW
Low energies
Cs experiment, University of Colorado

3. Parity selection rule: “Radiative (E1) transitions take place only
PNC studies in atoms Cs 6s 7s E1
Electric –dipole transition is
forbidden by parity selection rules
Parity selection rule:
“Radiative (E1) transitions take place only
between states of opposite parity.”

4. PNC studies in atoms Cs Electric –dipole transition is
forbidden by parity selection rules e q Z0
Z0 exchange: parity selection rule
is violated!

5. Non-zero transition amplitude
PNC studies in atoms 6s 7s Cs
Non-zero transition amplitude
PNC amplitude EPNC E1
Both 6s and 7s states acquire an
opposite-parity (np1/2 ) admixture e q Z0
Z0 exchange: parity selection rule
is violated!

6. Nuclear density function
PNC studies in atoms
Nuclear density function
GF -Universal Fermi coupling constant
g5 - Dirac matrix
Option 1: PNC experiment with a single isotope:
need both theory and experiment.
Option 2: PNC experiments with isotope chains:
use ratios of PNC amplitudes for different isotopes
to mostly remove dependence on the theory
Neuron skin problem: new results
B. A. Brown, A. Derevianko, and V. V. Flambaum, arXiv: (2008)

7. experimental
PNC
Studies

8. Experimental
PNC
Studies
1.2%
0.35%
1.4% 2%

9. theory
PNC
Studies

10. New developments in thEory ( University of Delaware )
New calculation of PNC amplitude in Ra+
as well as calculations of energy levels, lifetimes,
hyperfine constants, quadrupole moments,
dipole and quadrupole polarizabilities.
2. Development of new high-precision method
for PNC calculations in atoms with few valence
electrons (Tl, Bi, Pb, Yb, etc.)

11. Preliminary results for Ra+

12. Ra+ level scheme E1 E1 E2 7p3/2 7p1/2 6d5/2 6d3/2 7s1/2 802 nm 1080 nm
Photoionisation can produced these low abundant isotopes. zeeman shift can be made equal to zero by making total projection of the total moment on the B field equal to zero. Transition frequency is: 4*10^14 Hz E2
828 nm
728 nm
7s1/2

13. Ra+ lifetimes Present Ref. [1] Ref. [2] 8.72 4.73 0.638 0.627(4) 0.641
0.303
0.297
0.302
(ns)
(ns)
(s)
(s)
B.K. Sahoo, B.P. Das, R.K. Chaudhuri, D. Mukherjee, R.G.E. Timmermans,
and K. Jungmann, Phys. Rev. A 76, (2007)
2. V.A. Dzuba, V.V.Flambaum, and J.S.M. Ginges, Phys. Rev. A 63, (2001)

14. Further calculations including uncertainties are in progress.
PNC amplitude
Main term of the E1PNC amplitude (n=7-10), prelim. results,
Units: HF SD
SDpT
Ref. [2]
39.0
39.6
38.1
38.4
Further calculations including uncertainties are in progress.
Ref.[2] V.A. Dzuba, V.V.Flambaum, and J.S.M. Ginges, Phys. Rev. A 63, (2001)

15. Development of new methods: MORe COMPLICATED SYSTEMS

16. theory
PNC
Studies

17. Summary of theory methods for PNC studies
Configuration interaction (CI)
Many-body perturbation theory
Relativistic all-order method (coupled-cluster)
Perturbation theory in the screened Coulomb
interaction (PTSCI), all-order approach
Configuration interaction + second-order MBPT
(Tl PNC: 3%accuracy)
Configuration interaction + all-order method*
*under development

18. Configuration interaction + all-order method
CI works for systems with many valence electrons but can not accurately account for core-valence and core-core correlations.
All-order method ( linearized coupled-cluster method ) can not accurately describe valence-valence correlation for large systems but accounts well for core-core and core-valence correlations.
Therefore, two methods are combined to
acquire benefits from both approaches.

19. CI + ALL-ORDER: PRELIMINARY RESULTS
Ionization potentials, differences with experiment
CI CI + MBPT CI + All-order
Mg % % 0.03%
Ca 4.1% % 0.3%
Zn 8.0% % %
Sr 5.2% % 0.3%
Cd 9.6% % %
Ba 6.4% % 0.5%

20. Cd energies, differences with experiment
Expt.
DIF(%)
State J CI
CI+MBPT
CI+All-order
5s2 1S
208915 10
-1.0
0.02
5s5p
3P°
30114 19
-3.2
-0.53 1
30656
-3.1
-0.40 2
31827
-0.46
1P°
43692 11
-0.09
5s6s 3S
51484 14
-1.6
-0.49
53310 13
-1.4
-0.35
5s5d 1D
59220
-1.5
-0.24 3D
59486
-0.22
59498 3
59516

21. Cd, Zn, and Sr Polarizabilities, preliminary results (a.u.)CI
CI+MBPT
CI+All-order
4s2 1S0
44.13
37.22
37.02
4s4p 3P0
75.94
66.20
64.97 Cd
5s2 1S0
52.66
41.50
42.11
5s5p 3P0
86.94
70.72 Sr
CI+ All-order
Recomm.*
197.4
197.2
*From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, R (2006).

22. Cs spin-dependent PNC: ANApole moment

23. Spin-dependent parity violation: Nuclear anapole moment
Valence
nucleon
density
Parity-violating nuclear moment 6s 7s
F=4
F=3 1 2
Anapole moment
Nuclear anapole moment is parity-odd, time-reversal-even
E1 moment of the electromagnetic current operator.

24. Constraints on nuclear weak coupling contants
W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl. Part. Sci. 51, 261 (2001)

25. Nuclear anapole moment
The constraints obtained from the Cs experiment
were found to be inconsistent with constraints
from other nuclear PNC measurements, which
favor a smaller value of the133Cs anapole moment.
The analysis of the Cs PNC experiment includes
atomic theory calculation of spin-dependent PNC amplitude.
No high-precision calculation has been done at that time.
Can atomic theory explain the difference?

26. Nuclear anapole moment
The constraints obtained from the Cs experiment
were found to be inconsistent with constraints
from other nuclear PNC measurements, which
favor a smaller value of the133Cs anapole moment.
All-order calculation of spin-dependent PNC amplitude:
k = 0.110(16)* [ 1% theory accuracy ]
No significant difference with previous value k = 0.112(16) is found.
NEED NEW EXPERIMENTS!!!
*M.S. Safronova, E. Iskrenova-Tchoukova, and W.R. Johnson,
to be submitted to Phys. Rev. Lett.

27. Need new experiments! Conclusion
Atomic physics tests of the Standard Model
Preliminary results for Ra+
Transition E1, E2, and M1 matrix elements
Lifetimes, Quadrupole moments
Dipole and quadrupole polarizabilities
PNC amplitude
Development of new CI + all-order method for more complicated systems: promising preliminary results!
Spin dependent PNC: new analysis of Cs experiment:
Atomic theory can not explain the discrepancy with nuclear physics
Need new experiments!

28. Bindiya Arora (graduated August 2008) Rupsi Pal (graduating Fall 2008)
Graduate students:
Bindiya Arora (graduated August 2008)
Rupsi Pal (graduating Fall 2008)
Jenny Tchoukova (graduated August 2008)
Dansha Jiang
Other collaborations:
Michael Kozlov (Petersburg Nuclear Physics Institute)
(Visiting research scholar at University of Delaware)
Walter Johnson (University of Notre Dame)
Ulyana Safronova (University of Nevada-Reno)