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The Table of Nuclear Magnetic Dipole and Spectroscopic Electric Quadrupole Moments. Status of Table/Compilation Brief summary of active methods and recent results Next step: standards and recommended values Nick Stone IAEA Nuclear Data Meeting, Vienna, March 2011

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Nuclear magnetic dipole moment. Nuclear magnetism has contributions from all angular motion with unit the nuclear magneton (n.m.) Orbital angular momentum: Single particle - proton charge 1 neutron charge 0 Collective -whole nucleus charge Z/A valence nucleons - variable Spin angular momentum Single particle - proton s 1/2 moment n.m. neutron s 1/2 moment n.m. A sensitive, non-quantised, measure of state wavefunctions

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Nuclear electric quadrupole moment. Measures the departure from sphericity of the nuclear charge distribution. Ellipsoidal shape with major axis a and minor axis b and uniform charge density The Intrinsic quadrupole moment [for small eccentricity = (1 - b 2 /a 2 ))] is given by Q 0 = 2/5 ZR m 2 (1 + 2 /3) where the mean radius is R m 3 = ab 2 And the largest measurable value of this is the Spectroscopic quadrupole moment. Qs = Q 0 [2I + 1)/(2I + 2)] For a PROLATE ellipsoid (a > b, football shape) Q 0 is positive For an OBLATE ellipsoid (a < b, cushion shape) Q 0 is negative A sensitive, non-quantised, measure of nuclear shape

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Reported compilation status 2009 Moment measurements continue to be a vigorous area of nuclear research, providing detailed data for nuclear model development and testing Printed Table appeared in ADNDT in Succeeded Raghavan Table is out-of-date. Needs some months of work to cover last 4 years. Longer to set up 'recommended values'. Done! Thanks to NDS, IAEA support. Table current to end 2010 now accessible through IAEA Nuclear Data website Livechart. Contact with ADNDT editor David Schultz established that update would be accepted by the journal. Supplement Table in preparation. IAEA Report – NSR Recommended Value Table is straightforward for many entries. Some policy questions. Approved for action starting 2011 Consultation available in all cases from NJS. Still true

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Updated Table Summary of additions and regions of recent activity Excel spreadsheet for late lines [ 6 months after published version] Update to end lines Entrieslast isotope in 2010line entry of same new entries in this rangeisotope in 2005 total this region Ar Zn Rb Ru Sn Xe Pm Dy Hf Pt Pb Es

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Hf K-isomers by On-Line Nuclear Orientation [OLNO] Cu ground states towards N = 78 by Laser, LTNO and Beta-NMR methods RIB Te ps excited states by Recoil into Vacuum [IPAC] ns excited states in fission fragments by recoil substitution into iron [IPAC] Wide ranges of nuclei, lifetime and method Beta-NMR

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At least 80% of new results are for ground states: Techniques beta – NMRoriginally only below about A ~ 20, now up to A ~ 70 with fragmentation accelerators [e.g MSU] Laser spectroscopyever more efficient for weaker beams, new ion sources allow extension to more refractory elements On-Line nuclear orientation few new results Far fewer new results for excited states Techniques longer lifetime [ms, s, ns] PAC, TDPAD, etc shorter lifetime [ps]Transient Field, RIV Why?Loss of accelerators for stable beams Limited applicability of old methods half-life, count rate, angular distribution needed.

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Future experimental prospects Long-lived Laser and beta-NMR methods dominate ground state moment studies however these are finite in number lack of activity in lanthanide region – large ranges measured Shorter lived Numbers of known ms, s, ns isomers grows slowly For ps states no really general method: limited accuracy TF needs large count rates and strong anisotropies – stable beams calibration is a problem applicable to states of lower spin [2, max ~ 4?] RIVonly gives magnitude – where known can it be calibrated without previous examples? Tough Innovation required!!

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To revert to nuclear data and the Tabulation Main interest is a need to offer ‘Recommended Values’ in addition to a listing of all published results.

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Magnetic Dipole Moments: The Standards The basic standards of nuclear magnetism are: The proton and the deuteron [values from Fundamental Physical Constants see e.g. PR D (02)] Principle secondary standards are: 23 Na, 203,205 TlFrom these other standards are derived 165 Ho, 207 Pbby ratio to give a complete reference structure 185,187 Re, 209 Bithroughout the periodic table. 199 Hg, Gustavsson and Martensson-Pendrill reviewed the status of knowledge of these secondary standards [PR A (1998)] - little change since but the more precise older moments based on earlier values will require adjustment.

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Nuclear magnetic moment measurements can be divided into two categories: 1. Measurements involving an external applied magnetic field [uniform]. NMR in liquids, gases. Atomic beam experiments [includes lasers] Optical pumping in atoms. In these methods, to extract the true nuclear dipole moment the measured energy splitting has to be corrected for: a) the diamagnetic correction caused by the action of the applied field on the electrons. Calculated for neutral atoms in various approximations. Increases with Z reaching ~ 2% for Bi [Johnson et al ADNDT (83)] b) any chemical shift caused by action of the applied field on the surrounding molecules. Hard to calculate, estimated uncertainty 1 in [Gustavsson and Martensson-Pendrill PRA (98)] [Recent work of Jaszunski et al. to be published] These provide the basic standards for nuclear magnetic moments

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Only for the most precise measurements is there a real problem in setting 'recommended values' for magnetic moments. For most the experimental error is larger than diamagnetic corrections and hyperfine anomalies. When are these small corrections important? 1.For some light nuclei theory can make accurate prediction - but this is rare! 2. Increased precision gives access to more sensitive phenomena e.g. for hydrogen like systems hyperfine interactions can probe QED effects which reach 0.5% for heavier elements. To provide a critical test of QED requires the moment to be known to higher precision than this.

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2. Measurements involving internal fields [Hyperfine interactions in atoms and ions, hyperfine fields e.g in ferromagnetic metals.] NMR in magnetic materials, including ferromagnetic metals, where field at nucleus is dominated by local electrons. These are liable to corrections for: Variation in local field over the nuclear volume [Bohr-Weisskopf Effect or Hyperfine Anomaly]. This involves the distribution of nuclear magnetism within the nucleus and variation of the field over the nuclear volume. The correction can be as large as 10% but is more usually 0.l - 1%. In metals, the Knight shift which describes polarisation of the conduction electrons and the field they produce at the nucleus. Such measurements are NOT the basic standards of nuclear moment determination but require correction for the latest field value.

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Electric Quadrupole Moments: The Standards The basic standards have long been accepted as those from muonic atoms. Reason:Measure product Q s x electric field gradient (efg) at nucleus THE EFG IS NEVER DIRECTLY MEASURED Muon wavefunction clean calculation of efg few light elementsNa, Mg, Al,Cu, As, Nb, Pd almost all above ~ Sm Since ~ late 90’s challenged and supplemented by atomic hfs theorists [Bieron, Pyykko, Sundholm, Kello, Sadlej ……] Agreement between muonic and atomic results good only to a few %. New atomic results also lead to revised Q’s with serious differences from previous ‘best values’ in elements where there were no muonic data.

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Examples related to recent (since ~ 2000) atomic efg calculations Table entriesAtomic efg results 14 N (10) (3) +2%, error down 19 F (197 keV) (5) [also (4) (9) -21 or +31% 27 Al Mu-X+0.150(6) (10)error down 49 Ti +0.24(1) and (3)+0.247(11) -31% 63 Cu Mu-X (15)-0.211(4) -4% error down 69 Ga (8) and (11)+173(3) +1 or 5%, error down 73 Ge -0.17(3)-0.196(6) +15% 81 Br (6) and (4) (2.5) +3% or -5.5% 91 Zr (10) and (13)-0.176(3) -15% or -32% 121 Sb (40)-0.556(24) +54% N.B.also ‘solid state’ calc (15)even larger 131 Xe (12) and better-0.117(6)good Pb No muonic data: Q’s related to B(E2) in 4027 keV trans in 206Pb.[ ]

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Situation:calculated efgs atomic and molecular wavefunctions (light and medium nuclei) and mesonic atom (heavier nuclei) now provide a systematic consistent basis for electric quadrupole moment measurements for many elements to precision of a few %. Many present Table entries still rely on older efg estimates, and/or old B[E2] values The time is clearly ripe for a review of all quadrupole moments!

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Conclusions Plan of action: 1. Continue to update new entries at 12 month intervals. Publish update frequency to 5 years? 2.Attack need for recommended values by a)review of standards, followed by b) appropriate reanalysis in the light of revised standards – including Fuller listings c) averaging of results to obtain ‘best values’.

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Thank you

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Only for the most precise measurements is there a real problem in setting 'recommended values' for magnetic moments. For many the experimental error is larger than such considerations as diamagnetic corrections and hyperfine anomalies. Why are these small corrections important? 1. For some light nuclei theory can make accurate prediction - but this is rare! 2. Increased precision gives access to more sensitive phenomena e.g. for hydrogen like systems hyperfine interactions can probe QED effects which reach 0.5% for heavier elements. To provide a critical test of QED requires the moment to be known to higher precision.

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Current activity: recommended values What's involved ? Magnetic dipole moments: –Basic NMR ratios –The diamagnetic correction –Hyperfine anomalies –The Knight shift Electric quadrupole moments: –Basic NMR ratios –The Sternheimer correction

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Only for the most precise measurements is there a real problem in setting 'recommended values' for magnetic moments. For many the experimental error is larger than such considerations as diamagnetic corrections and hyperfine anomalies. Why are these small corrections important? 1. For some light nuclei theory can make accurate prediction - but this is rare! 2. Increased precision gives access to more sensitive phenomena e.g. for hydrogen like systems hyperfine interactions can probe QED effects which reach 0.5% for heavier elements. To provide a critical test of QED requires the moment to be known to higher precision.

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Recoil in Vacuum In the late 1960's it was found that when ions emerge from a target after excitation by Coulomb excitation and enter vacuum, the angular properties of their decay gamma radiations are perturbed. The anisotropy of the angular distribution is attenuated. The attenuations are determined by the precession of the excited state nuclear spin in the hyperfine interaction of the ion It is established that magnetic effects are dominant, thus the attenuation was a measure of the g-factor [g = magnetic moment / spin I ] of the decaying nuclear state. This is the basis of the Recoil In Vacuum [RIV] method of g- factor determination [ see e.g. Broude, Goldring et. al. NPA (1973)]. 7 g-factor [g = magnetic moment / spin I ]

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Recoil in Vacuum Beam Target Foil Total angular momentum F Nuclear spin Coulex Recoil Target recoil In vacuum, recoiling ion electron angular momentum J has random direction. Recoiling Coulex nuclear spin I, initially aligned in plane of target, precesses about resultant F=I+J. Anisotropy of angular distribution of decay gamma emission becomes attenuated

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UNATTENUATED Distribution for 126 Te stopped in Cu. Brief description of the recent RIB 132 Te RIV measurement at HRIBF [N.J.Stone et al PRL (2005)] RIV ATTENUATED distributions from states in 122,126,130 Te [known g-factors and lifetimes]. G k are the g-factor dependent attenuation coefficients. For the RIV method we need to extract g from the G k.

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Compared unattenuated with attenuated to obtain G 2, G 4 from isotopes with known g-factors and lifetimes to form calibration for their g dependence. Result: |g-factor| Te = 0.35(5). N.B. ps lifetime Plotted curves are result of empirical 'theory' with fitting parameter to stable isotope results - not an a priori theory.

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New Opportunities and challenges for the study of ps state g-factors: RIB's having beam intensity < 10 8 ions/s - orders of magnitude weaker than conventional beams. With the advent of RIB's and inevitable poorer statistics the RIV method offers prospects of useful g-factor study for ps lifetimes Calibration as for the Te 2+ states not possible for other spins and odd-A isotopes - too few measured g-factors exist. An a priori approach is required. The problem In principle the recoiling ion is an attractive system for theoretical approach. The number of electrons is fixed [neglecting Auger effects] and the physics is fully understood [Coulomb] although complex. Can we hope to provide a sound theoretical grounding for the CALIBRATION OF RIV ATTENUATIONS?

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Ground State Magnetic Moments of Cu isotopes [Lifetime range: stable - ms] Methods On-Line Nuclear Orientation with NMR/ON Fragment polarisation allied to beta-NMR In-source Laser spectroscopy High resolution collinear laser spectroscopy Objectives Full study of moments between major shell closures N = 28 - N = 40 for single proton beyond Z = 28 Towards establishing reliable nuclear models for the region of N = 50 [A = 78] - R process importance

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Only three, mid-shell, values known: isotopes 63,65 Cu are stable Pre 1998

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J. Rikovska-Stone et al. PRL (2000) Magnetic moment 69 Cu(3/2 - ) = 2.84(1) n.m. Starting from extreme single particle (Schmidt limit) and based on full treatment of moment operator, including meson exchange, gave value 2.85 n.m Cu Laser ion source at ISOLDE : 67,69 Cu moments measured by NMR/ON at NICOLE on-line nuclear orientation facility, ISOLDE, CERN using the new laser Cu ion source. At 28,40 double shell closure: Full agreement with best shell model theory [calculations by Ian Towner] [J.Rikovska et al. PRL (2000)]

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Down to shell closure at N = Cu measured by Leuven group at NICOLE by On-Line NMR/ON ( 59 Cu, 3/2 - ) = 1.891(9) n.m. [V.V.Golovko et al. PR C (2004)] 57 Cu measured by NMR at MSU fragment separator ( 57 Cu, 3/2 - ) = 2.00(5) n.m [K.Minamisono et al. PRL (2006)] N.B. Narrow resonance

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p 3/2 proton moments across full sub-shell N = First complete shell - shell sequence BUT 57 Cu result shows little sign of predicted return to close to the value found for 69 Cu Major discrepancy with shell model theory. Is 56 Ni truly double magic?

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68 Cu ΔE=const=δ( 1 / 2 mv 2 )≈mvδv Resolution ~ MHz, resulting from the velocity compression of the line shape through energy increase. In Source, Doppler width resolution ~ 250 MHz Collinear Concept - add constant energy to ions On-Line Laser spectroscopy Collinear and In-Source Methods With nuclear spin I these each form a doublet with F (= I + J) = I +1/2 and I - 1/2. Transitions between these doublets give four lines in two pairs with related splittings. - can be fitted with poor resolution only for the A (magnetic dipole) splitting and in good resolution, for both A and B (electric quadrupole splitting) In Cu+ ion, electron states involved are s 1/2 and p 1/2.

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63 Cu 59 Cu 58 Cu = 2.22(9) n.m. [Ref 2.23] = 1.84(3) n.m. [Ref. 1.89] = 0.52(8) n.m. Measurement of moment of 58 Cu (I = 1) at ISOLDE: Established fitting parameters using data on 63 Cu, confirmed by 59 Cu fit agreement with previous NMR/ON result. 58 Cu [odd-odd] predictions - based on shell model 57 Cu 0.68(1) n.m. - based on MSU 57 Cu result 0.40(2) n.m. Nature not kind: experimental result 0.52(8) n.m. no decisive answer. PR C (2008)

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E(keV) Mass number 1/2 - 5/2 - I=5/2 - level: Remains static between Cu at ~1MeV Systematically drops in energy as the ν(g9/2) shell begins to fill Predictions on the inversion of the ground state lie between 73 Cu and 79 Cu. Experimental evidence for the inversion to occur at 75 Cu. A.F. Lisetskiy et al. Eur. Phys. J. A, 25:95, 2005 N.A. Smirnova et al. Phys. Rev. C, 69:044306, 2004 S. Franchoo et al. Phys. Rev. C /2- level associated with the π(f5/2) orbital I. Stefanescu Phys. Rev. Lett 100 (2008) 75 ? From Kieren Flanagan

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The relative intensity of the two (unresolved doublet) peaks in the In-Source method is related to the nuclear spin through the statistical weight (2F + 1) Fitted data for 77Cu for I = 3/2 and I = 5/'2 - clearly favours 5/2 assignment. N.B. peaks well resolved

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Magnetic moments A > 70 Cu NMR/ON I = 3/2 = 2.28(1) n.m. 73 Cu collinear laser I = 3/2 = 1.748(1) n.m. [Isolde laser group, unpublished] 77 Cu in-source laser I = 5/2 = 1.75(5) n.m. [in-source laser group, unpublished]

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In source laser data, 75 Cu, fits for I = 3/2,5/2 Peaks barely resolved, but clear preference for spin 5/2 Moment of 75 Cu(I = 5/2) = 0.99(4) n.m. [Aug 2008] Confirmed during collinear run, later Aug 08, which used the in-source moment to set line search frequencies.

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A > 71 Cu NMR/ON I = 3/2 = 2.28(1) n.m. 73 Cu collinear laser I = 3/2 = 1.748(1)* n.m. [Isolde laser group, to be published] 75 Cuin-source laser I = 5/2 = 1.005(1)* n.m. and collinear laser [combined group, to be published] 77 Cu in-source laser I = 5/2 = 1.75(5)* n.m. [in-source laser group, to be published] * preliminary values

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Overall situation: ground state spin change positively identified at A = 75 Schmidt limit for f 5/2 is at +0.8 n.m.

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STOP PRESS UPDATE!!! Isolde Feb 16th MSU result for 57 Cu is WRONG. New data from Leuven show resonance at higher frequency. New [est N.J.S.] value 57 Cu = 2.6(1) n.m. [Cocolios, Van Duppen et al. to be published]

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The Final Picture

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Conclusions 1. Shell model has managed to calculate odd-A magnetic moments at N = 28, 40 very well and between them adequately. 2. Now that shift of the f 5/2 state has been identified, magnetic moments of 75,77 Cu should be calculated reasonably well. This residual interaction effect is established. 3. Models which give these results successfully may be expected to give useful predictions concerning the A = 78 shell closure. Others which fail to reproduce these may not be trusted in other predictions. The magnetic moments are a valuable constraint.

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Moment measurements in Fission Fragments - towards the neutron drip-line Methods involving rotation of angular correlation of gamma transitions in a polarised iron foil [Manchester group - Gavin Smith et al.] and attenuation of angular correlation of gamma transitions in an unpolarised iron foil [Vanderbilt group - Goodin et al.] Both these give measurable effects for ns states Applied to recoiling fragments from 252 Cf sample Huge data sets > multifold coincidences

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Table of Magnetic Dipole and Electric Quadrupole Static Nuclear Moments History: Gladys Fuller ~ very comprehensive Pramila Ragahavan 1989 ADNDS - older averaged NJS - Raghavan + listing of all published since »Started ~ 1998 setting up first spreadsheet electronic version »To publish - required retype as word document Table published [after extended discussions Dunford/Raman]: –Atomic Data and Nuclear Data Tables N. J. Stone ADNDT [2005]. Contains all reported nuclear magnetic dipole moments and electric quadrupole moments of ground and excited states total ~ 4000 entries available from to late 2005.

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Further possible action: recommended values What's involved ? Magnetic dipole moments: –Basic NMR ratios –The diamagnetic correction –Hyperfine anomalies –The Knight shift Electric quadrupole moments: –Basic NMR ratios –The Sternheimer correction –Best 'standards' discrepant at ~ 1% level It will take a considerable time to set up a matrix of interrelated standards throughout the nuclear chart.

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skyscrapers 178 Hf (10 9 s = 31 y) 2.4 MeV, 16ħ 178 Hf is at the centre of the multi-quasiparticle K-isomer region [Walker and Dracoulis, Hyp. Int. 135 (2001) 83] Isomers in 177,179,180,182,[184] Hf are long-enough lived to be accessible to Low Temperature On-Line Nuclear Orientation at the NICOLE facility..

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177 Hf levels [Mullins et al., PRC58 (1998) 831] combination of measurements of and => g K and g R

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g -factors for deformed nuclei combination of both measurements => g K and g R single-particle propertiescollective properties see, for example: Purry et al., NPA632 (1998) 229 El-Masri et al., PRC72 (2005) => configurations and admixtures => neutron and proton pair quenching

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NMR/ON observed in a combined signal from several transitions from the upper, 37/2 − isomer. Moment value: 7.33(7) n.m. (est. 8.14(17) n.m.) Magnetic moment

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g R values: 178 Hf K=0 g R = 0.240(14) K=6 π 2 g R = 0.35(5) K=16 π 2 ν 2 g R = 0.28(4) [K=6, 16: Mullins et al., Phys. Lett. B393 (1997) 279] more data needed, more-accurate data needed New Result 177 Hf K=37/2 2 3 g R =0.22(3) [K = 23/2 2 1 accessible when moment measured.]

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