ATOMIC CALCULATIONS FOR TESTS OF FUNDAMENTAL PHYSICSmsafrono/Talks/ASOS-2010.pdf · ATOMIC CALCULATIONS FOR TESTS OF FUNDAMENTAL PHYSICS ATOMIC CALCULATIONS FOR TESTS OF FUNDAMENTAL

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



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


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



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).



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





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

All-orderCorrelation potential

CI+MBPT

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


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.


METHOD + ALLMETHOD + ALLMETHOD + ALLMETHOD + ALL----ORDERORDERORDERORDER


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

ATOMIC CALCULATIONS FOR TESTS OF FUNDAMENTAL PHYSICSmsafrono/Talks/ASOS-2010.pdf · ATOMIC CALCULATIONS FOR TESTS OF FUNDAMENTAL PHYSICS ATOMIC CALCULATIONS FOR TESTS OF FUNDAMENTAL

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