The FrPNC Collaboration is constructing an on-line laser cooling and trapping apparatus at TRIUMF to measure atomic parity non-conservation (PNC) and nuclear anapole moments in a series of artificially produced francium isotopes. Francium’s simple electronic structure and enhanced parity violation make it a strong candidate for precision measurements of atomic PNC: the optical PNC and anapole-induced PNC effects are expected to be an order of magnitude larger in francium than in cesium. Atomic PNC experiments provide unique high precision tests of the Standard Model’s predictions for neutral current weak interactions at very low energies. Furthermore, precision measurements of nuclear anapole moments probe inter-nucleon weak interactions within the nucleus

Aubin, S.

Behr, J. A.

Collister, R.

Flambaum, V. V.

Gomez, E.

Gwinner, G.

Melconian, D.

Orozco, L. A.

Pearson, M. R.

Sheng, D.

Sprouse, G. D.

Zhang, J.

Zhao, Y.

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2012-11264-yColloquia: PAVI11IL NUOVO CIMENTO Vol. 35 C, N. 4 Luglio-Agosto 2012Atomic parity non-conservation in francium:The FrPNC experiment at TRIUMFS. Aubin(1), E. Gomez(2), J. A. Behr(3), M. R. Pearson(3), D. Sheng(4),J. Zhang(4), R. Collister(5), D. Melconian(6), Y. Zhao(7), V. V. Flambaum(8),G. D. Sprouse(9), L. A. Orozco(4) and G. Gwinner(5)(1) Department of Physics, College of William and Mary - Williamsburg, VA 23187, USA(2) Institute of Physics, Universidad Autonoma de San Luis Potosi - San Luis Potosi, Mexico(3) TRIUMF - Vancouver, British Columbia V6T 2A3, Canada(4) Joint Quantum Institute, Department of Physics, and National Institute of Standardsand Technology - College Park, MD 20742, USA(5) Department of Physics and Astronomy, University of ManitobaWinnipeg, Manitoba R3T 2N2, Canada(6) Cyclotron Institute, Texas AM University - College Station, TX 77843, USA(7) Laser Spectroscopy Laboratory of Shanxi University, State Key Laboratory of QuantumOptics and Quantum Optics Devices, Shanxi University - Taijuan, 030006, China(8) School of Physics, University of New South Wales - Sydney 2052, Australia(9) Department of Physics and Astronomy, SUNY Stony Brook - Stony BrookNY 11794-3800, USAricevuto il 15 Ottobre 2011; approvato il 5 Maggio 2012pubblicato online il 25 Giugno 2012Summary. — The FrPNC Collaboration is constructing an on-line laser coolingand trapping apparatus at TRIUMF to measure atomic parity non-conservation(PNC) and nuclear anapole moments in a series of artificially produced franciumisotopes. Francium’s simple electronic structure and enhanced parity violation makeit a strong candidate for precision measurements of atomic PNC: the optical PNCand anapole-induced PNC effects are expected to be an order of magnitude larger infrancium than in cesium. Atomic PNC experiments provide unique high precisiontests of the Standard Model’s predictions for neutral current weak interactions atvery low energies. Furthermore, precision measurements of nuclear anapole momentsprobe inter-nucleon weak interactions within the nucleus.PACS 31.30.Gs – Hyperfine interactions and isotope effects.PACS 32.70.Cs – Oscillator strengths, lifetimes, transition moments.PACS 12.15.Ji – Applications of electroweak models to specific processes.PACS 21.10.Ky – Electromagnetic moments.c© Societa` Italiana di Fisica 8586 S. AUBIN, E. GOMEZ, J. A. BEHR, ETC.Fig. 1. – Atomic PNC processes. (a) The strongest PNC interaction in NSI optical PNC isthe exchange of a Z0 boson between an axial vector electron current and a vector nucleoncurrent. (b) The largest NSD PNC effect in heavy atoms is produced by the anapole momentof the nucleus. The remaining two diagrams provide much smaller contributions to NSD PNC:(c) NSD Z0 exchange between an axial vector nucleon current and a vector electron current,and (d) NSI Z0 exchange in combination with the hyperfine interaction.1. – IntroductionParity non-conservation (PNC) effects in atomic systems are unique low-energy probesof the electroweak sector of the Standard Model and of inter-nucleon weak interactions.While these atomic PNC effects are generally extremely small, they are enhanced suf-ficiently in heavy atoms for high precision spectroscopy to detect reliable PNC signals.The FrPNC Collaboration is constructing a dedicated laser cooling and trapping facilityat the TRIUMF nuclear physics accelerator in Vancouver, Canada, for precision atomicPNC measurements in a string of francium isotopes.The large enhancement of atomic PNC in francium makes these measurements sen-sitive to electroweak extensions of the Standard Model and can also provide strong con-straints on PNC electron-quark couplings complementary to those obtained from electronscattering. Francium anapole moment measurements in a string of isotopes will assistin separating the isovector and isoscalar parts of the weak nucleon-nucleon interaction.Nuclear anapole moment measurements in cesium and thallium and low-energy nuclearparity violation experiments do not agree on a consistent set of weak nucleon-nucleoncouplings [1, 2]. Anapole moment measurements in different francium isotopes will pro-vide strong constraints on these weak couplings and an additional nuclear system withwhich to improve the existing theoretical frameworks [3, 4].2. – Atomic PNCAtomic PNC effects can be caused by either nuclear spin-independent (NSI) or nuclearspin-dependent (NSD) interactions between orbiting electrons and the nucleus. Thelargest PNC effect in heavy atoms is the NSI exchange of a Z0 boson between an axialelectron and a vector nucleon, as shown in fig. 1(a). In this process the PNC effectadds coherently for all nucleons: In the limit of an infinitely heavy nucleus, the PNCATOMIC PARITY NON-CONSERVATION IN FRANCIUM: THE FrPNC EXPERIMENT AT TRIUMF 87Hamiltonian for a single valence electron without radiative corrections is [5]HPNC,NSI  GF√2QW2γ5ρ(r ),(1)where GF = 10−5m−2p is the Fermi constant, mp is the proton mass, γ5 refers to the Diracmatrix, ρ(r ) is the neutron distribution, and QW = 2(κ1pZ + κ1nN) ≈ −N is the weakcharge of the nucleus (Z and N are the number of protons and neutrons, respectively).The Standard Model gives the tree level values κ1p = 12 (1 − 4 sin2 θW ) and κ1n = − 12with the Weinberg angle sin2 θW ∼ 0.23. NSI parity violation increases in heavy atomsas Z3R with a relativistic enhancement factor R. The PNC effect in francium is expectedto be 18 times larger than in cesium [6,7].In heavy atoms, the dominant contribution to NSD parity violation is the electromag-netic interaction of an electron with the nuclear anapole moment of the valence nucleon(fig. 1(b)). The anapole moment is a parity violating nuclear electromagnetic momentdue to inter-nucleon weak interactions. An electron interacting with a nuclear anapolemoment has the following HamiltonianHPNC,NSD =GF√2KI · αI(I + 1)κa,iδ(r ), with κa,i=n,p =910giαμimpr˜0A2/3,(2)where K = (I + 1/2)(−1)I−l+1/2, l is the orbital angular momentum of the valence nu-cleon, I is the nuclear spin, −→α are Dirac matrices, and δ(r ) indicates that the anapolemoment produces a contact interaction for the electron dictated by the valence nucleondistribution. κa,i=n,p is the effective interaction constant for the anapole moment pro-duced by a valence neutron or proton, respectively. α is the fine-structure constant, μiis the magnetic moment of the valence nucleon in nuclear magnetons, r˜0 = 1.2 fm isthe nucleon radius, and A = Z + N is the atomic mass. While NSD Z0 exchange andNSI Z0 exchange in combination with the hyperfine interactions, shown respectively infig. 1(c) and (d), produce NSD parity violation, their contribution is calculated to bemore than an order of magnitude smaller than that due to the anapole moment. Theanapole-induced PNC effect increases in heavy atoms as Z8/3R [5, 8]. The NSD parityviolation in francium is expected to be 11 times larger than in cesium [9].3. – Experimental implementationThe FrPNC Collaboration is preparing experiments to measure both optical PNCand nuclear anapole moments in a series of francium isotopes. TRIUMF produces theisotopes by spallation of a uranium carbide target with 500MeV protons at the ISACfacility. A beamline will transport the francium to the laser laboratory, where it will belaser cooled and trapped in preparation for experiments. The proposed PNC experimentsin Fr measure the degree of PNC-induced mixing of the |s〉 and |p〉 opposite paritywavefunctions with parity-forbidden transitions. The weak mixing angle can be extractedfrom an optical PNC measurement of the parity forbidden E1 transition between the 7sand 8s levels (fig. 2(a)), originally developed by Wieman and co-workers for cesium [10].Nuclear anapole moments are measured with parity-forbidden microwave E1 transitionsbetween the hyperfine manifolds of the 7s level (fig. 2(a)) [11] or through the dependenceof optical PNC on the initial and final hyperfine states [10].88 S. AUBIN, E. GOMEZ, J. A. BEHR, ETC.Fig. 2. – Francium energy levels and coordinate-system–defining vectors. (a) The 7s, 8s, and7p energy levels of francium relevant for the PNC measurements: the optical PNC methodmeasures the parity-forbidden transition between the 7s and 8s levels, while the anapole momentexperiment measures the NSD parity forbidden transition between the hyperfine manifolds ofthe 7s level. External electromagnetic field vectors are used to define a coordinate system forthe apparatus: The handedness of the coordinate system can be changed by flipping any one ofthe defining fields in (b) the optical PNC and (c) anapole moment experiments.The PNC signal is the change in the “forbidden” transition rate upon the reversalof the handedness of the experiment, defined by three orthogonal external fields. In theoptical PNC experiment, the momentum k of the excitation photon, an external Starkshift electric field EStark, and a magnetic field BDC determine the sign of the transitionrate change, which is proportional to BDC · (k × EStark) (fig. 2(b)). Similarly, in theanapole moment measurement, the population transfer between the hyperfine levels uponapplication of an electric microwave field ERF is proportional to BDC · ( Bπ/2× ERF ). Amicrowave magnetic field Bπ/2 targeting an M1 transition is used to put the atoms inan initial equal superposition of two upper and lower hyperfine states (see fig. 2(c)).The PNC-induced E1 transitions (parity-forbidden) used to measure NSI and NSDparity violation are generally accompanied by parity-allowed M1 transitions that mimicthese E1 transitions. In the case of the optical PNC measurement on the 7s to 8stransition, the accompanying M1 transition is strongly suppressed, and is not expected tobe an important source of systematic uncertainty. In the anapole moment measurement,the accompanying microwave M1 transition is nine orders of magnitude larger than thePNC-induced E1 transition, and so must be strongly suppressed. We plan to employthree methods to sufficiently suppress this unwanted M1 transition to an acceptablelevel [11]: a) We place the atoms at an electric field anti-node of the standing wavemicrowave driving field, which is a magnetic field node (the driving magnetic field iszero); b) the orientation of the microwave field polarization is chosen so that the magneticcomponent can only drive an off-resonance ΔmF = 0 transition, whereas the PNC-induced E1 transitions require ΔmF = ±1; finally, because of the spatial extent of thecold atomic cloud placed at the microwave magnetic field node, the atoms will experiencesome unwanted M1 transitions, but the motion of the atoms will tend to average outthis effect, due to the π phase flip of M1 field at the node.ATOMIC PARITY NON-CONSERVATION IN FRANCIUM: THE FrPNC EXPERIMENT AT TRIUMF 894. – PNC measurements with multiple isotopesThe availability of a range of francium isotopes is crucial for reducing nuclear physicsuncertainties. Accurate extraction of the weak-mixing angle from an optical PNC mea-surement and of isoscalar and isovector weak nucleon-nucleon interaction parametersfrom an anapole measurement will benefit significantly from conducting a series of mea-surements in a string of isotopes in order to account for uncertainty in nuclear structureand the neutron skin thickness [12]. Existing efforts to directly measure the neutron skinthickness in 208Pb are important for reducing this source of systematic uncertainty [13,14]in the extraction of the weak mixing angle. Furthermore, the collaboration is continuinglaser spectroscopy measurements of hyperfine anomalies in a number of francium isotopesin order to constrain the change in neutron skin radius over the range of isotopes [15]:Variations in the ratio of the hyperfine A coefficients for the 7S1/2 and 7P1/2 levels fordifferent francium isotopes are primarily due to variations in the magnetization radiusof the nucleus. These hyperfine anomaly measurements provide a means of probing themagnetization distribution due to the different overlap of the S1/2 and P1/2 electronicwavefunctions with an extended nucleus. The combination of hyperfine anomaly mea-surements in francium isotopes with the accelerator-based neutron radius measurementsin lead will strongly constrain the neutron skin in francium.5. – OutlookThe FrPNC Collaboration has completed construction of a radio-frequency shieldedlaser laboratory room in the ISAC hall of TRIUMF and is installing an on-line lasercooling and trapping apparatus for francium. The ISAC facility has successfully gener-ated francium isotopes at rates in the range of 107–108 Fr/s for 206–213Fr and 220–222Fr:these rates should permit the accumulation of laser-cooled samples of more than 106 Fratoms [16], which are necessary for achieving large anapole PNC signals with projectedfundamental signal-to-noise ratios in the range of 20 for 1 s of integration [11].∗ ∗ ∗The authors thank the TRIUMF/ISAC francium production team. The collaborationgratefully acknowledges support by CONACYT, DOE, NSF, NSERC, and TRIUMF.REFERENCES[1] Haxton W. C. and Wieman C. E., Annu. Rev. Nucl. Part. Sci., 51 (2001) 261.[2] Behr J. A. and Gwinner G., J. Phys G: Nucl. Part. Phys., 36 (2009) 033101.[3] Desplanques B., Donoghue J. F. and Holstein B. R., Ann. Phys. (N.Y.), 124 (1980)449.[4] Ramsey-Musolf M. J. and Page S. A., Annu. Rev. Nucl. Par. Sci, 56 (2006) 1.[5] Khriplovich I. B., Parity Nonconservation in Atomic Phenomena (Gordon and Breach,New York) 1991.[6] Dzuba V. A., Flambaum V. V. and Sushkov O. P., Phys. Rev. A, 51 (1995) 3454.[7] Safronova M. S. and Johnson W. R., Phys. Rev. A, 62 (2000) 022112.[8] Flambaum V. V., Khriplovich I. B. and Sushkov O. P., Phys. Lett. B, 146 (1984)367.[9] Gomez E., Orozco L. A. and Sprouse G. D., Rep. Prog. Phys., 69 (2006) 79.[10] Wood C. S., Bennett S. C., Cho D., Masterson B. P., Roberts J. L., TannerC. E. and Wieman C. E., Science, 275 (1997) 1759.90 S. AUBIN, E. GOMEZ, J. A. BEHR, ETC.[11] Gomez E., Aubin S., Sprouse G. D., Orozco L. A. and DeMille D. P., Phys. Rev.A, 75 (2007) 033418.[12] Brown B. A., Derevianko A. and Flambaum V. V., Phys. Rev. C, 79 (2009) 035501.[13] PREX experiment: http://hallaweb.jlab.org/parity/prex; Michaels R., talk, PAVI2011 Conference, Rome, Italy (2011).[14] Tamii A. et al., Phys. Rev. Lett., 107 (2011) 062502.[15] Grossman J. S., Orozco L. A., Pearson M. R., Simsarian J. E., Sprouse G. D.and Zhao W. Z., Phys. Rev. Lett., 83 (1999) 935.[16] Aubin S., Gomez E., Orozco L. A. and Sprouse G. D., Rev. Sci. Instrum., 74 (2003)4342.

Atomic parity non-conservation in francium: The FrPNC experiment at TRIUMF

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Atomic parity non-conservation in francium: The FrPNC experiment at TRIUMF

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