atomic calculations for tests of fundamental physicsmsafrono/talks/asos-2010.pdf · atomic...
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ATOMIC CALCULATIONS FOR ATOMIC CALCULATIONS FOR ATOMIC CALCULATIONS FOR ATOMIC CALCULATIONS FOR
TESTS OF FUNDAMENTAL PHYSICSTESTS OF FUNDAMENTAL PHYSICSTESTS OF FUNDAMENTAL PHYSICSTESTS OF FUNDAMENTAL PHYSICS
ATOMIC CALCULATIONS FOR ATOMIC CALCULATIONS FOR ATOMIC CALCULATIONS FOR ATOMIC CALCULATIONS FOR
TESTS OF FUNDAMENTAL PHYSICSTESTS OF FUNDAMENTAL PHYSICSTESTS OF FUNDAMENTAL PHYSICSTESTS OF FUNDAMENTAL PHYSICS
10th International Colloquium on10th International Colloquium on
Atomic Spectra and Oscillator StrengthsAtomic Spectra and Oscillator Strengths
for Astrophysical and Laboratory Plasmasfor Astrophysical and Laboratory Plasmas
August 5, 2010
MARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVAMARIANNA SAFRONOVA
• Atomic physics tests of fundamental physics
• Parity violation
• Search for permanent electric-dipole moment (EDM)
• Variation of fundamental constants and atomic clocks
• Methods for high-precision atomic calculations
• Overview & examples of results
• Present challenges
• Development of the CI + all-order method
• How accurate are theory values?
OUTLINEOUTLINEOUTLINEOUTLINEOUTLINEOUTLINEOUTLINEOUTLINE
TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND
SYMMETRIESSYMMETRIESSYMMETRIESSYMMETRIES
TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND
SYMMETRIESSYMMETRIESSYMMETRIESSYMMETRIES
Translation Momentum conservation
Translation in time Energy conservation
Rotation Conservation of angular
momentum
[C] Charge conjugation C-invariance
[P] Spatial inversion Parity conservation (P-invariance)
[T] Time reversal T-invariance
[CP]
[CPT]
Parity-transformed world:
Turn the mirror image upside down.
The parity-transformed world is not identical
with the real world.
Parity is not
conserved.
Parity ViolationParity Violationr → ─ r
PARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMS
NUCLEAR NUCLEAR NUCLEAR NUCLEAR
SPINSPINSPINSPIN----INDEPENDENTINDEPENDENTINDEPENDENTINDEPENDENT
PNC: PNC: PNC: PNC:
SEARCHES FOR NEW SEARCHES FOR NEW SEARCHES FOR NEW SEARCHES FOR NEW
PHYSICSPHYSICSPHYSICSPHYSICS
BEYOND THE BEYOND THE BEYOND THE BEYOND THE
STANDARD MODEL STANDARD MODEL STANDARD MODEL STANDARD MODEL
Weak Charge QWWeak Charge QW
NUCLEAR NUCLEAR NUCLEAR NUCLEAR
SPINSPINSPINSPIN----DEPENDENTDEPENDENTDEPENDENTDEPENDENT
PNC:PNC:PNC:PNC:
STUDY OF PNCSTUDY OF PNCSTUDY OF PNCSTUDY OF PNC
IN THE NUCLEUS IN THE NUCLEUS IN THE NUCLEUS IN THE NUCLEUS
e
e
q
qZ0
a
Nuclear anapole
moment
Nuclear anapole
moment
PARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMS
NUCLEAR NUCLEAR NUCLEAR NUCLEAR
SPINSPINSPINSPIN----INDEPENDENTINDEPENDENTINDEPENDENTINDEPENDENT
PNC: PNC: PNC: PNC:
SEARCHES FOR NEW SEARCHES FOR NEW SEARCHES FOR NEW SEARCHES FOR NEW
PHYSICSPHYSICSPHYSICSPHYSICS
BEYOND THE BEYOND THE BEYOND THE BEYOND THE
STANDARD MODEL STANDARD MODEL STANDARD MODEL STANDARD MODEL
Weak Charge QWWeak Charge QW
e
e
q
qZ0
Quantifying the strength
of the electroweak
coupling between
atomic electrons and
quarks of the nucleus.
STANDARD MODELSTANDARD MODELSTANDARD MODELSTANDARD MODELSTANDARD MODELSTANDARD MODELSTANDARD MODELSTANDARD MODEL
(1) Search for new processes or particles directly
(2) Study (very precisely!)quantities which Standard Model predicts and compare the result with its prediction
High energies
http://public.web.cern.ch/, Cs experiment, University of Colorado
Searches for New Physics Beyond the Standard Model
Searches for New Physics Beyond the Standard Model
Weak charge QWLow energies
6s
7s
E1 Forbidden by parity selection rules
Cs
e
e
q
qZ0
Z0 exchange: Laporte’s rule is violated!
Atomic Parity violationAtomic Parity violation
E1 NonNon--zero transition amplitudezero transition amplitude
PNC amplitude EPNC amplitude EPNCPNC6s
7s
Cs
e
e
q
qZ0
Z0 exchange: Laporte’s rule is violated!
Both 6s and 7s states acquire an opposite-parity (np1/2 ) admixture
Atomic Parity violationAtomic Parity violation
C.S. Wood et al. Science 275, 1759 (1997)
0.3% accuracy0.3% accuracy
THE MOST PRECISE MEASUREMENT THE MOST PRECISE MEASUREMENT THE MOST PRECISE MEASUREMENT THE MOST PRECISE MEASUREMENT
OF PNC AMPLITUDE (IN CESIUM)OF PNC AMPLITUDE (IN CESIUM)OF PNC AMPLITUDE (IN CESIUM)OF PNC AMPLITUDE (IN CESIUM)
THE MOST PRECISE MEASUREMENT THE MOST PRECISE MEASUREMENT THE MOST PRECISE MEASUREMENT THE MOST PRECISE MEASUREMENT
OF PNC AMPLITUDE (IN CESIUM)OF PNC AMPLITUDE (IN CESIUM)OF PNC AMPLITUDE (IN CESIUM)OF PNC AMPLITUDE (IN CESIUM)
6s
7sF=4
F=3
F=4
F=3
12
Stark interference scheme to measure ratio of the
PNC amplitude and the Stark-induced amplitude β
( ) mVcmPNC
mVcm
1.6349(80)Im
1.5576(77)
E
β
−=
−
1
2
ATOMIC PHYSICS TESTS OF THE ATOMIC PHYSICS TESTS OF THE ATOMIC PHYSICS TESTS OF THE ATOMIC PHYSICS TESTS OF THE
STANDARD MODEL, CSTANDARD MODEL, CSTANDARD MODEL, CSTANDARD MODEL, Cs NUCLEUSNUCLEUSNUCLEUSNUCLEUS
ATOMIC PHYSICS TESTS OF THE ATOMIC PHYSICS TESTS OF THE ATOMIC PHYSICS TESTS OF THE ATOMIC PHYSICS TESTS OF THE
STANDARD MODEL, CSTANDARD MODEL, CSTANDARD MODEL, CSTANDARD MODEL, Cs NUCLEUSNUCLEUSNUCLEUSNUCLEUS
Standard Model QW = −73.16(3)
1999 analysis of Cs experiment showed 2.5σ deviation from the Standard Model
Most current result:
Atomic physics [1] QW = −73.16(29)exp(20)th
[1] S. G. Porsev, K. Beloy and A. Derevianko, PRL 102, 181601 (2009)
WHAT DID WE LEARN FROM WHAT DID WE LEARN FROM WHAT DID WE LEARN FROM WHAT DID WE LEARN FROM
CS PARITY VIOLATION STUDY?CS PARITY VIOLATION STUDY?CS PARITY VIOLATION STUDY?CS PARITY VIOLATION STUDY?
WHAT DID WE LEARN FROM WHAT DID WE LEARN FROM WHAT DID WE LEARN FROM WHAT DID WE LEARN FROM
CS PARITY VIOLATION STUDY?CS PARITY VIOLATION STUDY?CS PARITY VIOLATION STUDY?CS PARITY VIOLATION STUDY?
(1) This is the most accurate to-date test of the low-energy electroweak sector of the SM.
(2) Confirms fundamental “running” (energy dependence) of the electroweak force: the interaction strength of particles depends on their relative collision energy E.
(3) Constraints are placed on a variety of new physicsscenarios beyond the SM (for example, limits the masses of extra Z-bosons predicted by models of grand unification and string theories).
PARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMSPARITY VIOLATION IN ATOMS
NUCLEAR NUCLEAR NUCLEAR NUCLEAR
SPINSPINSPINSPIN----DEPENDENTDEPENDENTDEPENDENTDEPENDENT
PNC:PNC:PNC:PNC:
STUDY OF PNCSTUDY OF PNCSTUDY OF PNCSTUDY OF PNC
IN THE NUCLEUS IN THE NUCLEUS IN THE NUCLEUS IN THE NUCLEUS
a
Nuclear anapole
moment
Nuclear anapole
moment
(a)
PNC 2( )
vaFG
rH ρκ= ⋅α I
Valence nucleon density
Parity-violating nuclear moment
Anapole moment
SPINSPINSPINSPIN----DEPENDENT PARITY VIOLATION: DEPENDENT PARITY VIOLATION: DEPENDENT PARITY VIOLATION: DEPENDENT PARITY VIOLATION:
NUCLEAR ANAPOLE MOMENTNUCLEAR ANAPOLE MOMENTNUCLEAR ANAPOLE MOMENTNUCLEAR ANAPOLE MOMENT
SPINSPINSPINSPIN----DEPENDENT PARITY VIOLATION: DEPENDENT PARITY VIOLATION: DEPENDENT PARITY VIOLATION: DEPENDENT PARITY VIOLATION:
NUCLEAR ANAPOLE MOMENTNUCLEAR ANAPOLE MOMENTNUCLEAR ANAPOLE MOMENTNUCLEAR ANAPOLE MOMENT
Nuclear anapole moment is parity-odd, time-reversal-even
E1 moment of the electromagnetic current operator.
6s
7sF=4
F=3
F=4
F=3
12
a
CONSTRAINTS ON NUCLEAR WEAK CONSTRAINTS ON NUCLEAR WEAK CONSTRAINTS ON NUCLEAR WEAK CONSTRAINTS ON NUCLEAR WEAK
COUPLING CONTANTSCOUPLING CONTANTSCOUPLING CONTANTSCOUPLING CONTANTS
CONSTRAINTS ON NUCLEAR WEAK CONSTRAINTS ON NUCLEAR WEAK CONSTRAINTS ON NUCLEAR WEAK CONSTRAINTS ON NUCLEAR WEAK
COUPLING CONTANTSCOUPLING CONTANTSCOUPLING CONTANTSCOUPLING CONTANTS
W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl. Part. Sci. 51, 261 (2001)
NUCLEAR ANAPOLE MOMENT:NUCLEAR ANAPOLE MOMENT:NUCLEAR ANAPOLE MOMENT:NUCLEAR ANAPOLE MOMENT:
TEST OF HADRONIC WEAK INTERATIONSTEST OF HADRONIC WEAK INTERATIONSTEST OF HADRONIC WEAK INTERATIONSTEST OF HADRONIC WEAK INTERATIONS
NUCLEAR ANAPOLE MOMENT:NUCLEAR ANAPOLE MOMENT:NUCLEAR ANAPOLE MOMENT:NUCLEAR ANAPOLE MOMENT:
TEST OF HADRONIC WEAK INTERATIONSTEST OF HADRONIC WEAK INTERATIONSTEST OF HADRONIC WEAK INTERATIONSTEST OF HADRONIC WEAK INTERATIONS
*M.S. Safronova, Rupsi Pal, Dansha Jiang, M.G. Kozlov,W.R. Johnson, and U.I. Safronova, Nuclear Physics A 827 (2009) 411c
NEED NEW EXPERIMENTS!!!
The constraints obtained from the Cs experimentwere found to be inconsistentinconsistent with constraintsfrom other nuclear PNC measurements, which
favor a smaller value of the133Cs anapole moment.
All-order (LCCSD) calculation of spin-dependent PNC amplitude:
k = 0.107(16)* [ 1% theory accuracy ]
No significant difference with previous value k = 0.112(16) is found.
Fr, Yb, Ra+
WHY DO WE NEED ATOMIC CALCULATIONS WHY DO WE NEED ATOMIC CALCULATIONS WHY DO WE NEED ATOMIC CALCULATIONS WHY DO WE NEED ATOMIC CALCULATIONS
TO STUDY PARITY VIOLATION? TO STUDY PARITY VIOLATION? TO STUDY PARITY VIOLATION? TO STUDY PARITY VIOLATION?
WHY DO WE NEED ATOMIC CALCULATIONS WHY DO WE NEED ATOMIC CALCULATIONS WHY DO WE NEED ATOMIC CALCULATIONS WHY DO WE NEED ATOMIC CALCULATIONS
TO STUDY PARITY VIOLATION? TO STUDY PARITY VIOLATION? TO STUDY PARITY VIOLATION? TO STUDY PARITY VIOLATION?
(1)Present experiments can not be analyzed without
theoretical value of PNC amplitude in terms of Qw.
(2)Theoretical calculation of spin-dependent PNC
amplitude is needed to determine anapole moment
from experiment.
(3) Other parity conserving quantities are needed.
Note: need to know theoretical uncertainties!
QW = −73.16(29)exp(20)th
TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND
SYMMETRIESSYMMETRIESSYMMETRIESSYMMETRIES
TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND TRANSFORMATIONS AND
SYMMETRIESSYMMETRIESSYMMETRIESSYMMETRIES
Translation Momentum conservation
Translation in time Energy conservation
Rotation Conservation of angular
momentum
[C] Charge conjugation C-invariance
[P] Spatial inversion Parity conservation (P-invariance)
[T] Time reversal T-invariance
[CP]
[CPT]
PERMANENT ELECTRICPERMANENT ELECTRICPERMANENT ELECTRICPERMANENT ELECTRIC----DIPOLE DIPOLE DIPOLE DIPOLE
MOMENT ( EDM )MOMENT ( EDM )MOMENT ( EDM )MOMENT ( EDM )
PERMANENT ELECTRICPERMANENT ELECTRICPERMANENT ELECTRICPERMANENT ELECTRIC----DIPOLE DIPOLE DIPOLE DIPOLE
MOMENT ( EDM )MOMENT ( EDM )MOMENT ( EDM )MOMENT ( EDM )
Time-reversal invariance must be violated for an
elementary particle or atom to possess a permanent
EDM.
S
d
S
dt t→ −
→ −
→
S S
d d
� �
� �
0
dS
d
=
=
Sd
�
�
EDM AND NEW PHYSICSEDM AND NEW PHYSICSEDM AND NEW PHYSICSEDM AND NEW PHYSICSEDM AND NEW PHYSICSEDM AND NEW PHYSICSEDM AND NEW PHYSICSEDM AND NEW PHYSICS
Many theories beyond the Standard Model predict EDM within or just beyond the present experimental capabilities.
10-40
10-39
10-34
10-33
10-32
10-31
10-30
10-29
10-28
10-27
10-26
10-25
de (e⋅cm)
Naïve SUSY
Multi-Higgs
Heavy sFermions
Standard Model
Left-Right Symmetric
Accidental Cancellations
ExtendedTechnicolor
Yale I(projected)
Yale II(projected)
~
Berkeley(2002)
ExactUniversality
Split SUSY
Seesaw Neutrino Yukawa Couplings
Lepton Flavor-Changing
Approx. Universality
Approx. CP
SO(10) GUT
Alignment
10-40
10-39
10-34
10-33
10-32
10-31
10-30
10-29
10-28
10-27
10-26
10-25
de (e⋅cm)
Naïve SUSY
Multi-Higgs
Heavy sFermions
Standard Model
Left-Right Symmetric
Accidental Cancellations
ExtendedTechnicolor
Yale I(projected)
Yale II(projected)
~
Berkeley(2002)
ExactUniversality
Split SUSY
Seesaw Neutrino Yukawa Couplings
Lepton Flavor-Changing
Approx. Universality
Approx. CP
SO(10) GUT
Alignment
David DeMille, Yale
PANIC 2005
ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM ATOMIC CALCULATIONS AND SEARCH FOR EDM
EDM effects are enhanced in some heavy atoms
and molecules.
Theory is needed to calculate enhancement factors
and search for new systems for EDM detection.
Recent new limit on the EDM of 199Hg
Phys. Rev. Lett. 102, 101601 (2009)
| d(199Hg) | < 3.1 x 10-29 e cm
ATOMIC CALCULATIONS AND VARIATION OF ATOMIC CALCULATIONS AND VARIATION OF ATOMIC CALCULATIONS AND VARIATION OF ATOMIC CALCULATIONS AND VARIATION OF
FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS
ATOMIC CALCULATIONS AND VARIATION OF ATOMIC CALCULATIONS AND VARIATION OF ATOMIC CALCULATIONS AND VARIATION OF ATOMIC CALCULATIONS AND VARIATION OF
FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS
(1) Astrophysical constraints on variation of α:Study of quasar absorption spectra
Atomic calculations: need to know isotope shifts
Changes in isotopic abundances mimic shift of α
(2) Laboratory atomic clock experiments:
compare rates of different clocks over long
period of time to study time variation of
fundamental constants
Need: ultra precise clocks!
ATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKS
Microwave
Transitions
Optical
Transitions
Blackbody Radiation Shifts and Theoretical Contributions to Atomic Clock Research, M. S. Safronova, Dansha Jiang, Bindiya Arora, Charles W. Clark, M. G. Kozlov, U. I. Safronova, and W. R. Johnson, in press, Special Issue of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control (2010).
MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT
GENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKS
MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT
GENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKS
Next - generation ultra precise atomic clock
Atoms trapped by laser light
http://CPEPweb.org
The ability to develop more precise optical frequency
standards will open ways to improve global positioningsystem (GPS) measurements and tracking of deep-space
probes, perform more accurate measurements of the physical constants and tests of fundamental physics such as
searches for gravitational waves, etc.
(1)Prediction of atomic properties required for new clock proposals
New clock proposals require both estimation of the atomic
properties for details of the proposals (transition rates, lifetimes, branching rations, magic wavelength, scattering
rates, etc.) and evaluation of the systematic shifts (Zeeman
shift, electric quadruple shift, blackbody radiation shift, ac Stark shifts due to various lasers fields, etc.).
(2)Determination of the quantities contributing to the uncertainty budget of the existing schemes.
In the case of the well-developed proposals, one of the main
current uncertainty issues is the blackbody radiation shift.
ATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKSATOMIC CALCULATIONS & MORE PRECISE CLOCKS
THEORY METHODS FOR THEORY METHODS FOR THEORY METHODS FOR THEORY METHODS FOR
FUNDAMENTAL FUNDAMENTAL FUNDAMENTAL FUNDAMENTAL
SYMMETRY STUDIESSYMMETRY STUDIESSYMMETRY STUDIESSYMMETRY STUDIES
THEORY METHODS FOR THEORY METHODS FOR THEORY METHODS FOR THEORY METHODS FOR
FUNDAMENTAL FUNDAMENTAL FUNDAMENTAL FUNDAMENTAL
SYMMETRY STUDIESSYMMETRY STUDIESSYMMETRY STUDIESSYMMETRY STUDIES
SUMMARY OF THEORY METHODS USED FOR SUMMARY OF THEORY METHODS USED FOR SUMMARY OF THEORY METHODS USED FOR SUMMARY OF THEORY METHODS USED FOR
FUNDAMENTAL SYMMETRY STUDIESFUNDAMENTAL SYMMETRY STUDIESFUNDAMENTAL SYMMETRY STUDIESFUNDAMENTAL SYMMETRY STUDIES
SUMMARY OF THEORY METHODS USED FOR SUMMARY OF THEORY METHODS USED FOR SUMMARY OF THEORY METHODS USED FOR SUMMARY OF THEORY METHODS USED FOR
FUNDAMENTAL SYMMETRY STUDIESFUNDAMENTAL SYMMETRY STUDIESFUNDAMENTAL SYMMETRY STUDIESFUNDAMENTAL SYMMETRY STUDIES
• Configuration interaction (CI)
• Many-body perturbation theory
• Relativistic all-order method (coupled-cluster)
• Correlation - potential method
• Configuration interaction + second-order MBPT
• Configuration interaction + all-order method*
*under development
Sum over infinite sets of manymany--body perturbation theorybody perturbation theory(MBPT) terms.
Calculate the atomic wave functions and energies
Calculate various matrix elements
Calculate “derived” properties
useful for particular problems
Scheme:
RELATIVISTIC ALLRELATIVISTIC ALLRELATIVISTIC ALLRELATIVISTIC ALL----ORDER METHODORDER METHODORDER METHODORDER METHODRELATIVISTIC ALLRELATIVISTIC ALLRELATIVISTIC ALLRELATIVISTIC ALL----ORDER METHODORDER METHODORDER METHODORDER METHOD
Ψ Ψv v
H = E
Na3p1/2-3s
K4p1/2-4s
Rb5p1/2-5s
Cs6p1/2-6s
Fr7p1/2-7s
All-order 3.531 4.098 4.221 4.478 4.256
Experiment 3.5246(23) 4.102(5) 4.231(3) 4.489(6) 4.277(8)
Difference 0.18% 0.1% 0.24% 0.24% 0.5%
Experiment Na,K,Rb: U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996),
Cs: R.J. Rafac et al., Phys. Rev. A 60, 3648 (1999),
Fr: J.E. Simsarian et al., Phys. Rev. A 57, 2448 (1998)
Theory M.S. Safronova, W.R. Johnson, and A. Derevianko,
Phys. Rev. A 60, 4476 (1999)
RESULTS FOR ALKALIRESULTS FOR ALKALIRESULTS FOR ALKALIRESULTS FOR ALKALI----METAL ATOMS:METAL ATOMS:METAL ATOMS:METAL ATOMS:
E1 TRANSITION MATRIX ELEMENTS E1 TRANSITION MATRIX ELEMENTS E1 TRANSITION MATRIX ELEMENTS E1 TRANSITION MATRIX ELEMENTS
RESULTS FOR ALKALIRESULTS FOR ALKALIRESULTS FOR ALKALIRESULTS FOR ALKALI----METAL ATOMS:METAL ATOMS:METAL ATOMS:METAL ATOMS:
E1 TRANSITION MATRIX ELEMENTS E1 TRANSITION MATRIX ELEMENTS E1 TRANSITION MATRIX ELEMENTS E1 TRANSITION MATRIX ELEMENTS
Example: “Best set” Rb E1 matrix elements
Blackbody radiation shift in 87Rb frequency standard, M.S. Safronova, Dansha Jiang, and U.I. Safronova, in press, Phys. Rev. A (2010)
MONOVALENTMONOVALENTMONOVALENTMONOVALENT SYSTEMS: SYSTEMS: SYSTEMS: SYSTEMS:
VERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WE
CALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALL----ORDER METHODORDER METHODORDER METHODORDER METHOD
MONOVALENTMONOVALENTMONOVALENTMONOVALENT SYSTEMS: SYSTEMS: SYSTEMS: SYSTEMS:
VERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WE
CALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALL----ORDER METHODORDER METHODORDER METHODORDER METHOD
Properties
• Energies• Transition matrix elements (E1, E2, E3, M1) • Static and dynamic polarizabilities & applications
Dipole (scalar and tensor) Quadrupole, OctupoleLight shiftsBlack-body radiation shiftsMagic wavelengths
• Hyperfine constants• C3 and C6 coefficients• Parity-nonconserving amplitudes (derived weak charge and anapole moment)
• 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
GOALS OF THE OUR PRESENT GOALS OF THE OUR PRESENT GOALS OF THE OUR PRESENT GOALS OF THE OUR PRESENT
PROJECT:PROJECT:PROJECT:PROJECT:
1.1.1.1. CALCULATE PROPERTIES OF GROUP II CALCULATE PROPERTIES OF GROUP II CALCULATE PROPERTIES OF GROUP II CALCULATE PROPERTIES OF GROUP II
ATOMS WITH PRECISION COMPARABLE ATOMS WITH PRECISION COMPARABLE ATOMS WITH PRECISION COMPARABLE ATOMS WITH PRECISION COMPARABLE
TO ALKALITO ALKALITO ALKALITO ALKALI----METAL ATOMSMETAL ATOMSMETAL ATOMSMETAL ATOMS
2. 2. 2. 2. EXTEND THIS APPROACH TO MOREEXTEND THIS APPROACH TO MOREEXTEND THIS APPROACH TO MOREEXTEND THIS APPROACH TO MORE
COMPLICATED SYSTEMSCOMPLICATED SYSTEMSCOMPLICATED SYSTEMSCOMPLICATED SYSTEMS
GOALS OF THE OUR PRESENT GOALS OF THE OUR PRESENT GOALS OF THE OUR PRESENT GOALS OF THE OUR PRESENT
PROJECT:PROJECT:PROJECT:PROJECT:
1.1.1.1. CALCULATE PROPERTIES OF GROUP II CALCULATE PROPERTIES OF GROUP II CALCULATE PROPERTIES OF GROUP II CALCULATE PROPERTIES OF GROUP II
ATOMS WITH PRECISION COMPARABLE ATOMS WITH PRECISION COMPARABLE ATOMS WITH PRECISION COMPARABLE ATOMS WITH PRECISION COMPARABLE
TO ALKALITO ALKALITO ALKALITO ALKALI----METAL ATOMSMETAL ATOMSMETAL ATOMSMETAL ATOMS
2. 2. 2. 2. EXTEND THIS APPROACH TO MOREEXTEND THIS APPROACH TO MOREEXTEND THIS APPROACH TO MOREEXTEND THIS APPROACH TO MORE
COMPLICATED SYSTEMSCOMPLICATED SYSTEMSCOMPLICATED SYSTEMSCOMPLICATED SYSTEMS
• Study of parity violation
• Search for EDM
• Atomic clocks
• Degenerate quantum gases,
alkali-group II mixtures
• Quantum information
• Variation of fundamental constants
MOTIVATION: MOTIVATION: MOTIVATION: MOTIVATION:
STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II –––– TYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMS
MOTIVATION: MOTIVATION: MOTIVATION: MOTIVATION:
STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II –––– TYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMS
Divalent ions:Al+, In+, etc.Divalent ions:Al+, In+, etc.
Mg
Ca
Sr
Ba
Ra
Zn
Cd
Hg
Yb
Mg
Ca
Sr
Ba
Ra
Zn
Cd
Hg
Yb
CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION
METHODMETHODMETHODMETHOD
CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION
METHODMETHODMETHODMETHOD
i i
i
cΨ = Φ∑ Single-electron valence
basis states
( ) 0effH E− Ψ =
1 1 1 2 2 1 2( ) ( ) ( , )eff
one bodypart
two bodypart
H h r h r h r r
− −
= + +������� �����
Example: two particle system: 1 2
1
−r r
CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +
ALLALLALLALL----ORDER METHOD ORDER METHOD ORDER METHOD ORDER METHOD
CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +
ALLALLALLALL----ORDER METHOD ORDER METHOD ORDER METHOD ORDER METHOD
CI works for systems with many valence electrons
but can not accurately account for core-valence
and core-core correlations.
All-order (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 Therefore, two methods are combined to
acquire benefits from both approaches. acquire benefits from both approaches.
CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION
METHOD + ALLMETHOD + ALLMETHOD + ALLMETHOD + ALL----ORDERORDERORDERORDER
CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION
METHOD + ALLMETHOD + ALLMETHOD + ALLMETHOD + ALL----ORDERORDERORDERORDER
1 1 1
2 2 2
1 2,
h h
h h
→ + Σ
→ + Σ
Σ Σ
Heff is modified using all-order calculation
are obtained using all-order method
used for alkali-metal atoms with appropriate
modification
( ) 0effH E− Ψ =
In the all-order method, dominant correlation corrections are summed to all orders of perturbation theory.
CI + ALLCI + ALLCI + ALLCI + ALL----ORDER RESULTSORDER RESULTSORDER RESULTSORDER RESULTSCI + ALLCI + ALLCI + ALLCI + ALL----ORDER RESULTSORDER RESULTSORDER RESULTSORDER RESULTS
Atom CI CI + MBPT CI + All-order
Mg 1.9% 0.11% 0.03%
Ca 4.1% 0.7% 0.3%
Zn 8.0% 0.7% 0.4 %
Sr 5.2% 1.0% 0.4%
Cd 9.6% 1.4% 0.2%
Ba 6.4% 1.9% 0.6%
Hg 11.8% 2.5% 0.5%
Ra 7.3% 2.3% 0.67%
Two-electron binding energies, differences with experiment
Development of a configuration-interaction plus all-order method for
atomic calculations, M.S. Safronova, M. G. Kozlov, W.R. Johnson, Dansha Jiang, Phys. Rev. A 80, 012516 (2009).
CCCCd, Z, Z, Z, Zn, AND , AND , AND , AND SSSSr POLARIZABILITIES, POLARIZABILITIES, POLARIZABILITIES, POLARIZABILITIES,
PRELIMINARY RESULTS PRELIMINARY RESULTS PRELIMINARY RESULTS PRELIMINARY RESULTS (a.u.)
76.5476.7591.25s5p 3P0
46.5545.8259.25s2 1S0
CI+All-orderCI+MBPTCICd
67.9769.1877.94s4p 3P0
39.2839.4546.24s2 1S0
CI + All-orderCI+MBPTCIZn
*From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, 020502R (2006).
458.3(3.6)459.4483.65s5p 3P0
197.2(2)198.0195.65s2 1S0
Recomm.*CI+all-orderCI +MBPTSr
HOW TO EVALUATEHOW TO EVALUATEHOW TO EVALUATEHOW TO EVALUATE
UNCERTAINTY OF UNCERTAINTY OF UNCERTAINTY OF UNCERTAINTY OF
THEORETICAL THEORETICAL THEORETICAL THEORETICAL
CALCULATIONS? CALCULATIONS? CALCULATIONS? CALCULATIONS?
HOW TO EVALUATEHOW TO EVALUATEHOW TO EVALUATEHOW TO EVALUATE
UNCERTAINTY OF UNCERTAINTY OF UNCERTAINTY OF UNCERTAINTY OF
THEORETICAL THEORETICAL THEORETICAL THEORETICAL
CALCULATIONS? CALCULATIONS? CALCULATIONS? CALCULATIONS?
THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE
UNCERTAINTYUNCERTAINTYUNCERTAINTYUNCERTAINTY
THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE
UNCERTAINTYUNCERTAINTYUNCERTAINTYUNCERTAINTY
HOW TO ESTIMATE WHAT YOU DO NOT KNOW?HOW TO ESTIMATE WHAT YOU DO NOT KNOW?
I. Ab initio calculations in different approximations:
(a) Evaluation of the size of the correlation corrections
(b) Importance of the high-order contributions(c) Distribution of the correlation correction
II. Semi-empirical scaling: estimate missing terms
EXAMPLE:EXAMPLE:EXAMPLE:EXAMPLE:
QUADRUPOLEQUADRUPOLEQUADRUPOLEQUADRUPOLE MOMENT OF MOMENT OF MOMENT OF MOMENT OF
3D3D3D3D5/25/25/25/2 STATE IN CSTATE IN CSTATE IN CSTATE IN Ca++++
EXAMPLE:EXAMPLE:EXAMPLE:EXAMPLE:
QUADRUPOLEQUADRUPOLEQUADRUPOLEQUADRUPOLE MOMENT OF MOMENT OF MOMENT OF MOMENT OF
3D3D3D3D5/25/25/25/2 STATE IN CSTATE IN CSTATE IN CSTATE IN Ca++++
Electric quadrupole moments of metastable states of Ca+, Sr+, and Ba+, Dansha Jiang and Bindiya Arora and
M. S. Safronova, Phys. Rev. A 78, 022514 (2008)
Coupled-cluster SD (CCSD)
1.822
All order (SDpT)
1.837
All order (SD)
1.785
Third order
1.610
Lowest order
2.451
3D3D3D3D5/25/25/25/2 QUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CA++++3D3D3D3D5/25/25/25/2 QUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CA++++
Estimateomittedcorrections
All order (SD), scaled 1.849All-order (CCSD), scaled 1.851All order (SDpT) 1.837All order (SDpT), scaled 1.836
Third order
1.610
Final results: 3d5/2 quadrupole momentFinal results: 3d5/2 quadrupole moment
Lowest order
2.454
1.849 (13)1.849 (13)
Experiment1.83(1)
Experiment1.83(1)
Experiment: C. F. Roos, M. Chwalla, K. Kim, M. Riebe, and R. Blatt, Nature 443, 316 (2006).
CONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSION
Development of new method for calculating atomic properties of divalent systems is reported.
• Improvement over best present approaches is demonstrated.
• Results for group II atoms from Mg to Ra are presented.
Future plans:
• Addition of other all-order contributions
• Precision calculation of group II atom properties for study of fundamental symmetries and development of optical frequency standards
• New calculations of parity violation in Yb
• More complicated systems
NEED EXPERIMENTAL BENCHMARKS!
OTHER COLLABORATIONS:OTHER COLLABORATIONS:OTHER COLLABORATIONS:OTHER COLLABORATIONS:
Michael Kozlov (PNPI, Russia)(Visiting research scholar at the University of Delaware)
Walter Johnson (University of Notre Dame), Charles Clark (NIST)Ulyana Safronova (University of Nevada-Reno)
GRADUATEGRADUATEGRADUATEGRADUATE
STUDENTS: STUDENTS: STUDENTS: STUDENTS:
Rupsi PalDansha JiangBindiya AroraJenny TchoukovaCesar Caro