Neutron Radii and Atomic Parity Violation in Francium · Neutron Radii and Atomic Parity Violation in Francium • Atomic parity violation and non-Standard Model physics • Neutron

atomic PNC n hyperfine anomaly extra

Neutron Radii and Atomic Parity Violation inFrancium

• Atomic parity violation and non-Standard Modelphysics

• Neutron radii and atomic parity violation

What do we need to extract non Standard-Modelphysics?

Could we assume S.M. and measure neutron radii?

• Can other experiments help n-rich Fr info[‘Hyperfine anomaly’]?

j.a. behr, rn fr✄p


atomic parity violation experimentsBoulder Cs ✓P (Bennett PRL 82 (1999) 2484) 0.4% exp.≈ 1σ off S.M. [Dzuba Berengut Flambaum Roberts PRL109 203003 (2012) + Roberts Dzuba Flambaum 1302.0593].

Cs ��P 2%, stimulated Guena Bouchiat ModPL A20 375 2005

• current atomic ��P experiments :Ytterbium atom UC Berkeley, ✓P measured, 9% stat, 7%syst, Tsigutkin PRL 103 071601 (2009), PRA 81 032114(2010), many stable isotopes, E1 ✓P-Stark mixing, 100x Cs

Ra+ KVI, Versolato et al. Can J Phys 89 65 (2011), severalprecision hyperfine structure and charge radii papers, areproceeding to single-ion trapping. Parity-violatingfrequency shifts for an S-D E2+ ��PE1 transition.

Francium E1 ✓P-Stark, 18x Cs: Manitoba/Maryland/TRIUMF;Legnaro



atomic PNC experiments II

Xe*, Hg* optical rotation Crete (Bougas PRL 108 210801(2012))

Yb+ Los Alamos (Torgeson, Cairns ICAP2010) frequencyshift, similar also to Fortson Ba + frequency shift

H atomic spin echo Heidelberg (DeKieviet Hyp Int 200 35(2011))Deuterium atom, Dunford and Holt, Hyp Int 200:45 (2011)

molecules Yale (anapoles, C 2) D. DeMille PRL 100, 023003(2008)



FrPNC collaboration

Manitoba Maryland San Luis Potosi TRIUMFG. Gwinner L. Orozco E. Gomez Garcia M. PearsonR. Collister J. Zhang William & Mary J. BehrM. Tandecki S. Aubin A. Obertas

New South Wales Stony BrookV. Flambaum G. Sprouse

Approved TRIUMF experiments:• anapole moments (weak N-N interaction),• towards optical PNC (lepton-quark weak couplings)• ‘hyperfine anomalies’ precision spectroscopy.Supported by NSF and DOE USA, NSERC and NRC Canada,CONACYT Mexico.



✓✓P Francium: atome e

N N

γ

e e

Z 0

NN

8p

7p

7s

8s

Z0 mixesstates ofoppositeparity, allowing✓P E1 amplitude∼ 10−9

Cs ✓P accuracy 0.5%. Effect 18x bigger in Fr.

• In some ’little Higgs’ models (Diener Godfrey Turan1111.4566) larger Z’ 1st-generation couplings: 0.1%measurement of ✓P E1 in Fr sensitive to m Z ′∼3.3 TeV

• Constraints on processes to generate observed Fermilabt t asymmetry: Gresham 1203.1320, Grinstein 1203.2183

• Weakly coupled bosons 1 - 500 MeV(astrophysics, µ g-2)tightly constrained by Cs ✓P.



µ g-2 3.6σ and Atomic PNCDavoudiasi, Lee,and Marciano PRL,1205.2709

10-500 MeV Zd

Lint = −eǫZµd Jem

µ

Z → Z − mZdmZ

δZd

Atomic and e −

scattering ��Pconstrain differentmZd



Stark - Weak interference: flip E field

Emulating Boulder Cs scheme in Fr:|A7s→8s|

2 = |E1Stark + E1PNC + M1|28p

7p

7s

8s

• Minimize the M1 by light polarization, standing wave|A7s→8s|

2 ≈ |E1stark|2 + 2E1StarkE1PNC

The interference term is ∼ 10−9 of an allowed E1 transitionamplitude (rather than 10 −18).

• Then calculate (or, preferably, measure) E1Stark to extractE1PNC



foibles of the trap I

Photoionization of atoms withthe 507 nm lightBoulder lost several % from hisatomic beam from Cs excited 7sto continuum 7p3/2

7p1/2

8s

nm507

7sWe will lose more:• trap• Fr will ionize P3/2 state, and cross-section is 100x biggerfor P states (measured at TRIUMF 2012)The good news: it’s OK to turn down the 507nm power toavoid this. You still have good E1PNC/E1Stark



S/N

• Time to obtain certain S/N:

t = (S/N)2/(Asym 2 R N)

Asym = 2 × 10−4

R = 30 Hz 7S → 8s excitation rate (need to avoidphotoionization)

N = 106 trapped atoms

• Requires 2.5 hours to get to 1% statistics

• Boulder’s main systematic was the residualM1-E1stark interference; smaller in Fr by about 2 ×



ISAC TRIUMF Fr Yields

207−213Fr and220−223Fr haveoptical PNCexperimentspossible



Atomic ✓✓P calculations and n radii, incompletehistory

Fortson Yang Wilets PRL 1990 ‘identified problem’atomic ��P ∝ (1 − 3

70(Zα)2[1 + 5R2n

R2p]) →

δQwn.s.Qw ∼ −3

7(Zα)2 δRn.s.R

Pollock Wilets Fortson PRC 1992 explored many models

Chen Vogel PRC 1993 Dedicated calculation to Cs isotopes‘under control’

Derevianko Porsev PRA 65 052115 2002 reevaluated usingTrzcinska PRL 87 082501 2001 antiprotonic atom work : ‘okin Cs but problems at higher Z’

Sil Centelles Vi nas Piekarewicz PRC 71 045502 2005 QHDwith IS-IV ΛV Rn.s.[ 208Pb]=0.28-0.21

Brown Derevianko Flambaum PRC 79 035501 2009spherical Skyrme HF, parameters tuned from p dataRn.s.[ 208Pb]=0.20±0.05



Atomic PNC calculations and n radiiBrown et al. PRC 2009,spherical Skyrme H-F,tuningRns[208Pb]=0.20±0.05,Sil PRC 2005QHD Rns[208Pb]=0.28-0.21213Fr 0.0013 atomic PNCdetermination → 0.05 fmaccuracy for ∆Rnp (needsbetter atomic theory)207Fr, 225Fr 0.0013experiment →∆Rns to 0.05?similar for Yb, Ra +



Chain of isotopes and n radii: Sil

PRC 71 045502(2005) global QHDmodel results forFr

observablesinsensitive to ΛV



Charge Radii very regular N <126

N>126 not as regular;deformationKilgallon PLB 405 31 →

We gain a lot of new physics leverage from N>126; can we getdirect info for these extra n’s?j.a. behr, rn fr✄p


Hyperfine anomaly

Measure µ=gI, compare toatomic hyperfine As

H = A~I · ~J =∫ ~µ(r) · ~B(r)d3r

Atomic s wavefunction varies overnucleus, so As/g can change ifnuclear radius changesBohr and Weisskopf interpreted thisas 〈r2

magnetism〉Reviews: Buttgenbach, Persson

from S1010 proposal

• Stony Brook version: ratio As/Ap, as the latter changes lessover the nucleus. (Could combine with point µ)Similar integral of nucleus over s1/2, p1/2 wavefunctionsneeded by atomic ��P, but for valence nucleon only



Hyperfine anomaly in FranciumAssuming we are given R n for N=126

7P1/2 hyperfine structure

6 GHz

PM

T F

luor

esce

nce

8 MHz

209Fr

For N>126, experimental µ, Q modelled in EkstromRobertsson Rosen Phys Scripta 1984223−225Fr by simple Nilsson orbital configurations220−222Fr situation is more complex.Would HFA provide more direct info on 〈r2

n〉 that we need?



Neutron Radii and Atomic Parity Violation inFrancium

What do we need to extract non Standard-Modelphysics?Rns[208Pb] to 0.05 fm and some other observable forN6=126

Could we assume S.M. and measure neutron radii?σ=0.001 Fr ��P ∼ 0.05 fm Rnsbut that needs theory to 0.001σ=0.0013 ∆ Fr ��P ∼ 0.05 fm ∆ RnsFr,Ra+ would be similar; Yb also likely to be sensitive

• Other experiments like hyperfine anomally shouldeventually be needed to help with deformed n-rich FrWe are curious about Fr inverse kinematics reactions



Stark - Weak interference: flip E fieldEmulating Boulder Cs scheme:|A7s→8s|

2 = |E1Stark + E1PNC + M1|28p

7p

7s

8s

• Minimize the M1 by light polarization, standing wave(note M1 ≈ 10+4E1PNC ) →|A7s→8s|

2 ≈ |E1stark|2 + 2E1StarkE1PNC

The interference term is ∼ 10−9 of an allowed E1 transitionamplitude (rather than 10 −18).• E1stark(F ,m → F ′,m′) =

α~E · ~ǫ δF ,F ′δm,m′ + iβ(~E × ~ǫ) · 〈F ′m′|~σ|Fm〉

flipping ~E changes the rate, with an asymmetry linear inE1PNC. You are free to choose |~E|.• Then calculate (or, preferably, measure) E1Stark to extractE1PNC



scheme for Aweak in Fr

507

7s

8s

7p1/2

817nm 7s

8s

7p1/2

817nm7s

8s

nm

• depopulate one hyperfine ground state by opticalhyperfine pumping• Drive 7S to 8S transition, with ~E=250 V/cm• Measure remaining population by resonantfluorescence– so you get good statistics on each atom

Boulder did this in an atomic beam, with spatiallyseparated regions

Using laser-cooled atoms in a MOT, we will separate thesesteps in time



foibles of trap II

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The 507 nm light power buildup cavity makes an ‘opticallattice’: cold atoms will try to go to minimum ofblue-detuned standing wave. Possible solutions:• add sideband to light 1 FSR away• use a travelling wave on-resonance standing wave isneeded to kill M1• the lower power to avoid photoionization will help withthis as well.

(Wieman and Vieira pointed out this feature in a Los Alamos1992 proposal. Their suggested solution was to heat theatoms.)



First measure the M1 strength|A7s→8s|

2 = |E1Stark + M1|2 ≈|E1Stark|

2 + 2E1StarkM1~E≈ 20 V/cm makes E1Stark > M1B∼10 G to split m levelsη = 2 |E1+M1|2−|E1−M1|2

|E1+M1|2+|E1−M1|2 = 0.21ns → (n+1)s is forbidden non-relativistically.

8p

7p

7s

8s

Some relativistic corrections are more interesting than others.Can separate M1hyperfine from M1relativistic by dependence onhyperfine levels

Savukov et al. PRL 83 2914 (1999) Rb has highest% contributionof ‘negativeenergy states’;pursued at U.Manitoba (andUSAFA)



Heavy-ion reactions

Fr reactions are possible in inverse kinematics(RexISOLDE, TRIUMF?, ...)see this workshopthe example I was considering doesn’t workOur favorite was to plan 221Fr(d,p) isobaric analogresonance (Nolen Schiffer Williams PL 27B 1 1968) notnoticing that the answer comes in low for 208PbAnti-analog GDR Krasznahorkay Paar Vretenar HarakehPLB 720 428 (2013)Pygmy giant resonance: this workshop



Chain of isotopes and n radii

From a theory error on global parameter on p onlyCan local info help?

Brown DereviankoFlambaum PRC 79035501 (2009)UsingRn[208Pb]=0.20±0.05from p atomsErrors from a chain,removing correlations

Spherical Skyrme H-F calculation: N>126 needs deformationYb has wide range of stable isotopes



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Radiative correctionsSince Cs ✓P is still moving from higher-order corrections,there is value in a result in a higher-Z system to test these

Milstein SushkovTerekhov PRL 89283003 2002Radiativecorrections as afunction of Z


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Neutron Radii and Atomic Parity Violation in Francium · Neutron Radii and Atomic Parity Violation in Francium • Atomic parity violation and non-Standard Model physics • Neutron