1. Outline
“Search for octupole-deformed nuclei for enhancement of atomic EDM”
1Umesh Silwal,
2Prajwal Mohanmurthy, 1Durga P. Siwakoti, 1Jeff A. Winger
1Mississippi State University
2LNS, Massachusetts Institute of Technology
June 06, 2019
MENU-2019
Cohen University Center, CMU
June Pittsburgh, PA

2. Outline MENU-2019 Introduction: why is EDM important?
Attempts to measure the EDM
General technique of measuring EDM
Need of Octupole deformed nuclei
EDM enhancement
Survey results, and
Future Research
MENU-2019
October 25-28, 2017
Pittsburgh, PA
Cohen University Center, CMU
June Pittsburgh, PA

3. - + Introduction 𝑑 =𝑞 𝑙 l What is EDM?
Any two point charges with equal magnitude but opposite signs separated by small distance is called electric dipole.
Source of EDM is mainly,  in CKM matrix, and QCD-θs . But CPT-Violation, SUSY all can cause and may also enhance the SM-EDM. 
Source of EDM?
225Ra
Fig: source google

4. Introduction Why EDM is Interesting? P-violation: τ-θ puzzle
Parity is conserved in electro-magnetic and strong interactions but must not conserved in weak interaction.
𝑃 𝐿𝐻𝑆 =−1) 𝜅 + ( 𝜏 + )= 𝜋 + + 𝜋 + + 𝜋 − ( 𝑃 𝑅𝐻𝑆 =−1 𝑃 𝐿𝐻𝑆 =−1) 𝜅 + ( 𝜃 + )= 𝜋 + + 𝜋 ( 𝑃 𝑅𝐻𝑆 =+1
Wu et al., in 1957 observed that β-decay of 60Co preferentially emitted against the direction of the spin of it which tells that weak interactions violates parity maximally.
CP-violation: Natural kaon decay
CP is marginally violated as neutral kaons oscillated to their anti-particles.
𝐶 𝑃 𝐿𝐻𝑆 =1) 𝜅 1 → 𝜋 + + 𝜋 − (𝐶 𝑃 𝑅𝐻𝑆 =1) ( 𝜏 1 =8.95× 10 −11 𝑠 𝐶 𝑃 𝐿𝐻𝑆 =−1) 𝜅 2 → 𝜋 + + 𝜋 − + 𝜋 0 (𝐶 𝑃 𝑅𝐻𝑆 =−1) ( 𝜏 2 =5.11× 10 −8 𝑠

5. Introduction dn ~ θs .(6×10-17) e.cm dn < 3 × 10-26 e.cm
Why EDM is Interesting?
CP-violation: Natural kaon decay cont..
CP violation shows that weak interactions don’t treat the matter the same as anti-matter and this would leave the abundance of matter over anti-matter. Source of CP violation comes from the SM-CKM matrix in the form of δCP .
Strong CP problem
Ref.
J M Pendlebury et al. Phys. Rev. D 92.9 (Nov. 2015)
Maxim Pospelov and Adam Ritz. Ann. Phys (July 2005),
dn ~ θs .(6×10-17) e.cm
dn < 3 × 10-26 e.cm
θs  < 5 × 10-10
The Smallness of the value of θs is unknown, also known as CP problem.
CPT (and Lorentz) Symmetry
Quantum field theory is invariant under CPT transformation –recover the original vector after successive C, P, T transforms. Any deviation from CPT invariance is beyond the SM and will involve new physics. Hence precision test of CPT invariance is a powerful way to gain insights into aspects of possible new physics.

6. Introduction Why EDM is Interesting?
Baryon Asymmetry of the Universe (BAU)
BAU is quantified as the a ratio between the density of surviving matter (nB) to photons (nγ).
Precisely measured value of  ηB in cosmic microwave background observation reported by planks telescope is [Ref. Canetti et al.]
BAU computed using the known source of CP violation in CKM-matrix [Ref. Riotto et al.]:
BAU calculated using known source of CP violation is too small and there should be additional new source of CP-violations and corresponding new physics Beyond the Standard Model (BSM).
Laurent Canetti, Marco Drewes, and Mikhail Shaposhnikov. “Matter and antimatter in the universe”. en. In: New J. Phys.14.9 (Sept. 2012
Antonio Riotto and Mark Trodden. “Recent progress in Baryogenesis”. In: Annu. Rev. Nucl. Part. Sci (Dec. 1999)

7. Introduction 𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏 Why EDM is Interesting?
EDM and CP-Violation
A. Yoshimi RIEKN (
𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏 T
EDM
Spin _ + P
Zheng-Tian Lu et al.

8. Attempts to Measure the EDM
EDM may generate from one or many CP violating mechanism.
Non-zero EDM is elementary particles, subatomic composite particles , nuclei and atoms in their ground state indicates CPV.
Only non-degenerate states possessing non-zero EDM violates CP
Non-zero EDM of molecule does not necessarily indicate the CPV.
Attempts over the last five decades at measuring a CPV EDM in many systems have resulted in stringent upper limit. Ref. Jungmann et. al., 2017 (

9. Attempts to Measure the EDM
Attempts over the last five decades at measuring a CPV EDM in many systems have resulted in stringent upper limit. Ref. Jungmann et. al., 2017.

10. General Technique
Ramsey Method:

11. General Technique Ramsey Method:
Begins with polarized ensemble, magnetization is aligned in z axis same as magnetic field
RF-oscillating field is applied in xy direction
Figure illustrating the steps involved in the Ramsey method. An initial state with magnetization: Courtesy: P. Schmidt-Wellenburg (2016).

12. Measured and Theoretical EDM Value
10-23
10-26
10-29
10-32
10-32
10-38
10-44
Fig: panel showing the measured and theoretical value of EDM for leptons and baryons.
The measured upper limit of EDM at 90% C.L. has been shown in red. The gray portion represents the contributions of QCD-θs, where as the purple color shows the contribution from SM-CKM matrix. [Ref. P. Mohanmurthy]

13. Measured and Theoretical EDM Value
10-22
10-26
10-32
The measured upper limit of atomic EDM at 90% C.L. has been shown in red. The gray portion represents the contributions of QCD-θs, where as the purple color shows the contribution from SM-CKM matrix. [Ref. P. Mohanmurthy]

14. Need of Octupole-Deformed Nuclei
Octupole deformed nuclei and EDM
EDM searches in different systems are complementary since they are sensitive to different linear combination of CP-violation sources.
Paramagnetic molecules and atoms: Tl, YbF, ThO, HfF+ have single unpaired electrons and are sensitive to an intrinsic electron EDM.
The contribution of electron EDM in paramagnetic system is amplified by the relativistic atomic structure of the heavy alkali-like atoms and are sensitive to nuclear spin independent CP-violating electron-nucleon interactions.
The diamagnetic atoms and molecules:   199Hg, 129Xe, 225Ra, TIF have a appearance of partially screened nucleus and are sensitive to isoscalar and isovector CP-violating interaction inside the nucleus. Diamagnetic atoms have relatively very small contributions from individual electron, proton or neutron EDM, compared to contributions from nuclear Schiff moment.
According to Schiff theorem, nuclear EDM in diamagnetic systems is almost completely screened by the surrounding electron cloud. This screening is not perfect for the heavy nuclei due to relativistic atomic structure, and contribute residual effect to the atomic EDM also called Schiff moment. [Ref. Jaideep Singh 2019,

15. Need of Octupole-Deformed Nuclei
Octupole deformed nuclei and EDM
Nuclei
EDM enhancement w.r.t 99Hg
221,223Rn
102
225Ra
103
229Pa
105
Ref. Jaideep Singh 2019
199Hg currently sets the most stringent limits on CP-violating interactions originating from nuclear medium.
Diamagnetic atoms such as 225Ra, 221,223Rn, 229Pa have a pear-shaped (octupole-deformed) nuclei.
Octupole deformed characterized by β3 has nearly degenerate parity doublets. Due to the parity-violating nucleon-nucleon interaction, the two states that make up the parity doublet mix and result in an enhanced Schiff moment.

16. Need of Octupole-Deformed Nuclei
Octupole deformation zone in Z, N isotope plot
A = 270
N =
Z =
N =
Z =
Octupole deformation in the nuclear chart based on the 3D Skyrme Hartree-Fock plus BCS Ebata et al. (

17. Need of Octupole-Deformed Nuclei
Octupole deformed nuclei and EDM
Contribution of atomic EDM due to Schiff moment:
β2 - quadrupole deformation parameter
β3 - octupole deformation parameter
∆E - energy different between the parity doublets
Larmor frequency of spin-1/2 particles:
For the uniform magnetic field, ∆B =0, and frequency difference is directly proportional to EDM. Hence, the uncertainty in EDM is solely given by the uncertainty in frequency measurement.
The difference in two frequency is:
Ref.
Jaidep Singh et al.,
Spevak et. Al., Phys. Rev. C 56, 1357
Auerbach et. Al., Phys. Rev. Lett. 76, 4316 

18. Need of Octupole-Deformed Nuclei
Octupole deformed nuclei and EDM
Contribution of atomic EDM due to Schiff moment:
β2 - quadrupole deformation parameter
β3 - quadrupole deformation parameter
∆E - energy different between the parity doublets
Which is ideally the inverse of spin precession time (τ):
Nm = number of frequency different measurements
Na  = total number of particles probed
T = total integration time
ε = experimental efficiency
[Ref. Jaideep Singh 2019,

19. Need of Octupole-Deformed Nuclei
Statistical Sensitivity to EDM measurement
Sector
Exp. Limit
(e-cm)
Method
Standard
Model
Electron
1.1 x 10-29
ThO in a beam
10-44
Neutron
3 x 10-26
UCN in a bottle
10-32
199Hg
6.2 x 10-30
Hg atoms in a cell
10-35
Ref. M. Ramsey-Musolf (2009)
No experimental evidence for a permanent EDM in any System

20. Need of Octupole-Deformed Nuclei
Statistical Sensitivity to EDM measurement
Nuclei shorting were based on:
Nuclei with better octupole deformation than 225Ra.
Nuclei with relative quiet branches of decay (not too noisy): i.e., long halftimes.
Relatively well known magnetometry and atomic spectroscopy like Fr, Ra, Hg, Cs, TI, Y and so on.
EDM enhance were calculated based on:
a Theoretical Enhancement→(β2 β32 Z3 A2∕3)/ΔE
bStatistical Sensitivity→ √(Beam rates × T1∕2)
cBeam Sensitivity→ √(T1∕2)
dComparison of Theoritical Sensitivity w.r.t Statistical Sensitivity →Theoretical Enhancement × Statistical Sensitivity

21. Survey Results

22. Results and Conclusions…
Table-I: Potential Octupole Deformed Nuclei for EDM Measurement
Results and Conclusions…
S.N.
Nuclei
T1/2 β3 β2
𝑱 𝝅 𝜟E
Th. enh.
FRIB Yield (×106)
Stat. Sens.
Beam Sens.
EDM enh. 1
221Rn86
25(2)min [Jain2007]
0.142 [ATNDT]
0.119 [ATNDT]
7/2+ [Jain2007]
NoState - 
2.29
0.02
0.60 - 2
223Rn86
24.3(4) min [Browne2001]
0.117 [ATNDT]
0.155 [ATNDT]
7/2 [Brwone2001]  -
0.9
0.01
0.37 3
225Rn86
4.66(4) min [Jain2008]
0.077 [ATNDT]
0.163 [ATNDT]
7/2- [Jain2008]
0.27
0.00
0.21 4
223Ra88
11.43(5)days [Browne2001]
0.156 [ATNDT]
3/2+ [Browne2001]
50.13(1) [Brwone2001]
1.36
6.08
0.85
0.97
1.33 5
225Ra88
14.9(2) days [Jain2009]
0.124 [ATNDT]
0.164 [ATNDT]
1/2+ [Jain2009]
55.16(6) [Jain2009]
1.00
6.41 6
225Ac89
9.9203(3) days [Jain2009]
0.127 [ATNDT]
3/2- [Jain2009]
40.1 [Spevak1996]
1.49
5.1
0.73
0.89 7
226Ac89
29.37(12) hours [Akovali1996]
0.12 [ATNDT]
1 [Akovali1996]
5.78
0.95 8
221Fr87
4.9(2) min [Jain2007]
0.1 [Apevak1996]
0.106 [Spevak1996]
5/2- [Jain2007]
234.51(5) [Jain2007]
0.09
6.13
0.98 9
223Fr87
22.00(7) min [Browne2001]
0.135 [ATNDT]
0.146 [ATNDT]
3/2- [Browne2001]
160.51(5) [Spevak1996]
0.35
4.26
0.03
0.82
0.28 10
225Fr87
3.95 (14)min [Jain2008]
0.108 [ATNDT]
2.08
0.57 11
227Fr87
2.47(3) min [ICTP2016]
0.07 [ATNDT]
0.181 [ATNDT]
1/2+ [ICTP2016]
62.97(7) [ICTP2016]
0.30
7.02
1.05
0.31 12
229Th90
7880(120) yr [Brwone2008]
0.24 [Minkov2017]
0.115 [Minkov2017]
5/2+ [Browne2008]
133.3 [Flambaum2019]
1.07
6.19
431.75 13
229Pa91
1.50(5) days [Browne2008]
0.082 [Spevak1996]
0.19 [ATNDT]
5/2+ [Brwone2008]
0.06(5) [Ahmad2015]
521.13
20.7
1.80
936.49

23. Results and Conclusions…
Table-I: Potential Deformed Nuclei for EDM Measurement (cont..)
Results and Conclusions…
S.N.
Nuclei
T1/2 β3 β2
𝑱 𝝅 𝜟E
Th. enh.
FRIB Yield (×106)
Stat. Sens.
Beam Sens.
EDM enh. 14
223Ac89
2.10(5)min [Jain2007]
[ATNDT]
0.147 [ATNDT]
5/2- [Browne2001]
50.7(1) [Browne2001]
1.49
8.18
0.01
0.9 15
227Ac89
21.772(3) year [ICTP2014]]
0.105 [ATNDT]
0.172 [ATNDT]
3/2- [Brwone2001]
27.369(11) [ICPT2014]
 1.56
6.4
23.08
1.0
1.56 16
221Ra88
104(1) s [Jain2008]
Not measured
0.207 [ATNDT]
5/2+ [Brwone2013]
95.50(9) [Browne2013] -
6.34
0.91
Numbers are normalized to 225Ra at FRIB

24. Results and Conclusions…
Table-I: Octupole Deformed Nuclei for EDM Measurement
S.N.
Nuclei
T1/2 β3 β2
𝑱 𝝅 𝜟E
Th. enh.
FRIB Yield (×106)
Stat. Sens.
Beam Sens.
EDM enh. 1
221Rn86
25(2)min [Jain2007]
0.142 [ATNDT]
0.119 [ATNDT]
7/2+ [Jain2007]
NoState - 
2.29
0.02
0.60 - 2
223Rn86
24.3(4) min [Browne2001]
0.117 [ATNDT]
0.155 [ATNDT]
7/2 [Brwone2001]  -
0.9
0.01
0.37 3
225Rn86
4.66(4) min [Jain2008]
0.077 [ATNDT]
0.163 [ATNDT]
7/2- [Jain2008]
0.27
0.00
0.21 4
223Ra88
11.43(5)days [Browne2001]
0.156 [ATNDT]
3/2+ [Browne2001]
50.13(1) [Brwone2001]
1.36
6.08
0.85
0.97
1.33 5
225Ra88
14.9(2) days [Jain2009]
0.124 [ATNDT]
0.164 [ATNDT]
1/2+ [Jain2009]
55.16(6) [Jain2009]
1.00
6.41 6
225Ac89
9.9203(3) days [Jain2009]
0.127 [ATNDT]
3/2- [Jain2009]
40.1 [Spevak1996]
1.49
5.1
0.73
0.89 7
226Ac89
29.37(12) hours [Akovali1996]
0.12 [ATNDT]
1 [Akovali1996]
5.78
0.95 8
221Fr87
4.9(2) min [Jain2007]
0.1 [Apevak1996]
0.106 [Spevak1996]
5/2- [Jain2007]
234.51(5) [Jain2007]
0.09
6.13
0.98 9
223Fr87
22.00(7) min [Browne2001]
0.135 [ATNDT]
0.146 [ATNDT]
3/2- [Browne2001]
160.51(5) [Spevak1996]
0.35
4.26
0.03
0.82
0.28 10
225Fr87
3.95 (14)min [Jain2008]
0.108 [ATNDT]
2.08
0.57 11
227Fr87
2.47(3) min [ICTP2016]
0.07 [ATNDT]
0.181 [ATNDT]
1/2+ [ICTP2016]
62.97(7) [ICTP2016]
0.30
7.02
1.05
0.31 12
229Th90
7880(120) yr [Brwone2008]
0.24 [Minkov2017]
0.115 [Minkov2017]
5/2+ [Browne2008]
133.3 [Flambaum2019]
1.07
6.19
431.75 13
229Pa91
1.50(5) days [Browne2008]
0.082 [Spevak1996]
0.19 [ATNDT]
5/2+ [Brwone2008]
0.06(5) [Ahmad2015]
521.13
20.7
1.80
936.49
Results and Conclusions…

25. Results and Conclusions…
Table-I: Octupole Deformed Nuclei for EDM Measurement (cont..)
Results and Conclusions…
S.N.
Nuclei
T1/2 β3 β2
𝑱 𝝅 𝜟E
Th. enh
FRIB Yield (×106)
Stat. Sens.
Beam Sens.
DM enh. 14
223Ac89
2.10(5)min [Jain2007]
[ATNDT]
0.147 [ATNDT]
5/2- [Browne2001]
50.7(1) [Browne2001]
1.49
8.18
0.01
0.9 15
227Ac89
21.772(3) year [ICTP2014]]
0.105 [ATNDT]
0.172 [ATNDT]
3/2- [Brwone2001]
27.369(11) [ICPT2014]
 1.56
6.4
23.08
1.0
1.56 16
221Ra88
104(1) s [Jain2008]
Not measured
0.207 [ATNDT]
5/2+ [Brwone2013]
95.50(9) [Browne2013] -
6.34
0.91
Numbers are normalized to 225Ra at FRIB

26. Table-II: Additional Nuclei with Suspected Octupole Deformation
(No calculation performed yet)
S.N
Nuclei
T1/2
β3 pred.
β2 pred.
𝑱 𝝅 𝜟E
Th. Sens
FRIB Yield (×106)
Stat. Sens.
Beam Sens.
EDM enhancement 1
187Au79
8.3(2) min [Basunia2009] ?
0.156 [ATNDT]
1/2+ [Basunia2009]
274.91(16) [Basaunia2009] - 
33.8
0.05
2.30 - 2
189Au79
28.7(4) min [Johnson2017]
0.148 [ATNDT]
1/2+ [Johnson2017]
814.30(25) [Johnson2017]  -
58.6
0.11
3.02 3
231Ac89
7.5(7) min [Brwone2013]
0.207 [ATNDT]
1/2+ [Browne2013]
372.28(8) [Browne2013]
52.7
2.87 4
233Ac89
2.4(2) min [Singh2005]
0.215 [ATNDT]
1/2+ [Singh2005]
1/2- state not measured
26.7
0.02
2.04 5
235Th90
7.2(7) min [Browne2014]
0.215 [ATNDT]]
1/2+ [Brwone2014]
6.72
1.02 6
233Th90
21.83(4) min [Singh2005]
539.61(2) [Singh2005]
6.43
0.03
1.00 7
237Pa91
8.7(2) min [Basunia2006]
1/2+ [Basunia2006]
6.91
1.04 8
239Pu94
24110(30) year [Brwone20014]
0.223 [ATNDT]
Not measured
Data Not available 9
241Cm96
32.8(2) days [Nesaraja2005]
1/2+ [Nesaraja2005]
Octupole deformations come in clusters. These species here are inside the region, but haven't been calculated as most previous calculations used some simplified system like even-even systems (Ref. Sylvester et. al.,)

27. Table-III: Additional Octupole Deformed Nuclei
(might be useful for different EDM measurement techniques)
S.N
Nuclei
T1/2
β3 pred.
β2 pred.
𝑱 𝝅 𝜟E
Th. Sens
FRIB Yield (×106)
Stat. Sens.
Beam Sens.
EDM enhancement 1
220Ra88
18(2)ms
0.144 [ATNDT]
0.103 [ATNDT]
 0+ -
0.8 2
224Ra88
3.6319(23)days [Singh2015]
0.131 [ATNDT]
0.164 [ATNDT]
0+ [Singh2015]
6.8 3
226Ra88
1600(7) Year [Akovali1996]
0.108 [ATNDT]
0.172 [ATNDT]
0+ [Akovali1996]
5.61 4
224Ac89
2.78(16) hour
0.165 [ATNDT] 0-
4.45

28. Results and Conclusions…

29. Results and Conclusion
We have performed the global survey of potential octupole deformed candidate atomic nuclei for the EDM enhancement
Figure out 7 viable nuclei for the future measurement at FRIB facility which are equally or more sensitive than 225Ra.
Nuclei
EDM Sensitivity compared to 225Ra
223Ra88
1.33
225Ra88
1.00
223Ac89
1.34
225Ac89
227Ac89
1.56
229Th90
1.05
229Pa91
936.49
Numbers are normalized to 225Ra at FRIB

30. Future Research
We have requested the Dr. Anatoli’s for the theoretical calculation of β3 value of some of our suspected octupole-deformed nuclei.
Will be writing the proposal at FRIB for measuring the EDM value of some of the most EDM sensitive nuclei.

31. List of selected references1
[Singh2011]
S. Singh et al. Nucl Data Sheet 111, 2851 (2011) 3
[ATNDT]
P. Moller et al., Atomic Data & Nuclear Data Table, 59, (1995) 2
[FRIB] 4
[Browne2001]
E. Browne, Nucl Data Sheet 93, 843 (2001) 5
[Jain2009]
A. K. Jain et al. Nucl Data Sheet 110, 1409 (2009) 6
[Akovali1996]
Y. A. Akovali Nucl Data Sheet 77, 443 (1996) 7
[ICTP2016]
Ictp-2014 Worskhoop Group, Nucl Data Sheet 132, 257 (2016) 8
[Brwone2008]
E. Brwone et al., Nucl Data Sheet 109, 2657 (2008) 9
[Basunia2009]
M. S. Basunia Nucl Data Sheet 110, 999 (2009) 10
[Johnson2017]
T. D. Johnson et al., Nucl Dtat Sheet 142, 1(2017) 11
[Browne2013]
E. Browne et al., Nucl Data Sheet 114, 751, 2013 12
[Singh2005]
B. Singh et al., Nucl Data Sheet105, 109 (2005) 13
[Brwone2014]
E. Brwone et al., Nucl Data Sheet 122, 205 (2014) 14
[Basunia2006]
M. S. Basunia Nucl Data Sheet 107, 2323 (2006) 15
[Nesaraja2005]
C. D. Nesaraja , Nucl Data Sheet 130, 183(2005) 16
[Singh2015]
S. Singh et al. Nucl Data Sheet 130, 127 (2015) 17
E. Browne et al., NDS 109, 2657 (2008) 18
[Minkov2017]
N. Minkov et al., Phys. Rev. Lett (2017) 19
Y. A. Akovali NDS 77, 433 (1996) 20
E. Browne et al., NDS 93, 846 (2001) 21
[Jain2008]
A. K. Jain et al., NDS 110, 1409 (2009) 22
[Jain2007]
A. K. Jain et al., NDS 108, 883 (2007) 23
[SIngh2006]
B. Singh, NDS 108, 79 (2007) 24
[Timar2014]
J. Timar et al., NDS 121, 143, (2014) 25
[Ahmad2015]
I Ahmad et al., Phys. Rev. C 92, (2015) 26
[Spevak1996]
V. Spevak et al., Phys. Rev. C 56,3 (1997) 27
[Lender1988]
G. A. Lender et al., Phys. Rev. C 37 (1988) 28
[Flambaum2019]
V. V. Flambaum, Phys. Rev. C 99, (2019)

32. MENU-2019 Thank You! My major advisor Dr. Jeff A. Winger.
Acknowledgement
My major advisor Dr. Jeff A. Winger.
Co-authors of this work: Mr. P. Mohanmurthy and Mr. D. P. Siwakoti
Office of Science, Department of Energy for supporting through travel fund.
Thank You!
MENU-2019
October 25-28, 2017
Pittsburgh, PA
Cohen University Center, CMU
June Pittsburgh, PA

34. General Technique Ramsey Method:
Fig. comparison between Rabi and Ramsey method. Ramsey oscillation is much narrow
Statistical Sensitivity in Ramsey method is:

35. Measured and Theoretical EDM Value
The measured upper limit of molecular EDM at 90% C.L. has been shown in red. The gray portion represents the contributions of QCD-θs, where as the purple color shows the contribution from SM-CKM matrix. Ref. P. Mohanmurthy.

36. 𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏
Ongoing Effort for EDM Measurement
𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏

37. Results and Conclusions…
EDM of 225Ra enhanced and more reliably calculated
Results and Conclusions…
Closely spaced parity doublet – Haxton & Henley, PRL (1983)
Large Schiff moment due to octupole deformation – Auerbach, Flambaum & Spevak, PRL (1996)
Relativistic atomic structure (225Ra / 199Hg ~ 3) – Dzuba, Flambaum, Ginges, Kozlov, PRA (2002)
- = (|a - |b)/2
+ = (|a + |b)/2
55 keV
|a
|b
Parity doublet
Enhancement Factor: EDM (225Ra) / EDM (199Hg)
Isoscalar
Isovector
Skyrme SIII
300
4000
Skyrme SkM*
2000
Skyrme SLy4
700
8000
Schiff moment of 225Ra, Dobaczewski, Engel, PRL (2005)
Schiff moment of 199Hg, Dobaczewski, Engel et al., PRC (2010)
“[Nuclear structure] calculations in Ra are almost certainly more reliable than those in Hg.”
– Engel, Ramsey-Musolf, van Kolck, Prog. Part. Nucl. Phys. (2013)
Constraining parameters in a global EDM analysis.
– Chupp, Ramsey-Musolf, arXiv (2014)

38. Results and Conclusions…
Nuclei shorting based on:
Find nuclei with better octupole deformation than 225Ra
Species is at least long lived as 225Ra
With relative quiet branches of decay (not too noisy)
Relatively well known magnetometry and atomic spectroscopy like Fr, Ra, HG, Cs, TI, Y and so on.
No experimental evidence for a permanent EDM in any System
𝑑 𝑒 <1.6× 10 −27 𝑒.𝑐𝑚 𝑑 𝐻𝑔 <2.1× 10 −28 𝑒.𝑐𝑚 𝑑 𝑛 <6.3× 10 −20 𝑒.𝑐𝑚
B.C. Regan et al., Phys. Rev. Lett. 88, (2002) (90% C.L.)
M.V Romalis et al., Phys. Rev. Lett. 86, 2505 (2001) (90% C.L.)
P.G. Harris et al., Phys. Rev. Lett. 82, 904 (1999) (90% C.L.)

39. Results and Conclusions…J.