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

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 s1/2 moment + 2.79 n.m.

neutron s1/2 moment -1.91 n.m.

A sensitive, non-quantised, measure of state wavefunctions

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 - b2/a2))] is given by

Q0 = 2/5 ZRm2(1 + 2/3) where the mean radius is Rm

3 = ab2

And the largest measurable value of this is

the Spectroscopic quadrupole moment.

Qs = Q0[2I + 1)/(2I + 2)]

For a PROLATE ellipsoid (a > b, football shape) Q0 is positive

For an OBLATE ellipsoid (a < b, cushion shape) Q0 is negative

A sensitive, non-quantised, measure of nuclear shape

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 2005. Succeeded Raghavan 1989.• 2005 Table is out-of-date.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

Updated Table

Summary of additions and regions of recent activity

Excel spreadsheet for late 2005 5701 lines[ 6 months after published version]

Update to end 2010 6133 lines

Entries last isotope in 2010 line entry of same new entriesin this range isotope in 2005 total this region

1-500 40Ar 431 69 69501-1000 63Zn 831 169 1001001-1500 87Rb 1283 217 481501-2000 95Ru 1696 304 872001-2500 113Sn 2164 336 322501-3000 141Xe 2627 373 373001-3500 151Pm 3123 377 43501-4000 160Dy 3620 380 24001-4500 174Hf 4115 385 54501-5000 191Pt 4597 403 185001-5500 196Pb 5069 431 285500-6133 254Es 5701 432 1

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

At least 80% of new results are for ground states:

Techniques

beta – NMR originally only below about A ~ 20, now up to A ~ 70with fragmentation accelerators [e.g MSU]

Laser spectroscopy ever more efficient for weaker beams, new ion sourcesallow 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 beamsLimited applicability of old methods

half-life, count rate, angular distribution needed.

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 beamscalibration is a problemapplicable to states of lower spin [2, max ~ 4?]

RIV only gives magnitude – whereknowncan it be calibrated without previous examples?

Tough Innovation required!!

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.

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 D66 010001

(02)]

Principle secondary standards are:

23Na, 203,205Tl From these other standards are derived

165Ho, 207Pb by ratio to give a complete reference structure

185,187Re, 209Bi throughout the periodic table.

199Hg,

Gustavsson and Martensson-Pendrill reviewed the status of knowledge of these secondary standards [PR A58 3611 (1998)] - little change since but the more precise older moments based on earlier values will require adjustment.

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 28 333 (83)]

b) any chemical shift caused by action of the applied field on the surrounding molecules. Hard to calculate, estimated uncertainty 1 in 103. [Gustavsson and Martensson-Pendrill PRA 58 3611 (98)][Recent work of Jaszunski et al. to be published]

These provide the basic standards for nuclear magnetic moments

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.

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 theconduction electrons and the field they produce at the nucleus.

Such measurements are NOT the basic standards of nuclear momentdetermination but require correction for the latest field value.

Electric Quadrupole Moments: The Standards

The basic standards have long been accepted as those from muonic atoms.

Reason: Measure product Qs 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.

Examples related to recent (since ~ 2000) atomic efg calculations

Table entries Atomic efg results

14N +0.02001(10) +0.02044(3)

+2%, error down

19F (197 keV) -0.121(5) [also -0.072(4) -0.0942(9) -21 or +31%

27Al Mu-X +0.150(6) +0.146.6(10) error down

49Ti +0.24(1) and +0.324(3) +0.247(11) -31%

63Cu Mu-X -0.220(15) -0.211(4) -4% error down

69Ga +0.1650(8) and +0.171(11) +173(3) +1 or 5%, error down

73Ge -0.17(3) -0.196(6) +15%

81Br +0.254(6) and +0.276(4) +0.261.5(2.5) +3% or -5.5%

91Zr -0.206(10) and -0.257(13) -0.176(3) -15% or -32%

121Sb -0.360(40) -0.556(24) +54% N.B.also ‘solid state’ calc -0.669(15) even larger

131Xe -0.120(12) and better -0.117(6) good

Pb No muonic data: Q’s related to B(E2) in 4027 keV trans in 206Pb.[1979-2004]

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!

Conclusions

Plan of action:

1. Continue to update new entries at 12 monthintervals. Publish update frequency ---- 3 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’.

Thank you

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.

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

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.

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. NPA215 617 (1973)].

7

g-factor [g = magnetic moment / spin I ]

Recoil in Vacuum

Beam

Target FoilTotal 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

UNATTENUATED Distribution for 126Te stopped in Cu.

Brief description of the recent RIB 132Te RIV measurement at HRIBF

[N.J.Stone et al PRL 94 192501 (2005)]

RIV ATTENUATED distributions from 2+1 states

in 122,126,130Te [known g-factors and lifetimes].

*

.

( , ) ( , ,0)kk kq k k q

k q

W G A Q D Gk are the g-factor dependent attenuation coefficients.

For the RIV method we need to extract g from the Gk.

Compared unattenuated with attenuated to obtain G2, G4 from isotopes with known g-factors and lifetimes to form calibration for their g dependence.

Result: |g-factor| 2+1 132Te = 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.

New Opportunities and challenges for the study of ps state g-factors:

RIB's having beam intensity < 108 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 problemIn 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?

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

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

Pre 1998

J. Rikovska-Stone et al. PRL 85 1392 (2000)

Magnetic moment 69Cu(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.

1999 Cu Laser ion source at ISOLDE : 67,69Cu 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 85 1392 (2000)]

Down to shell closure at N = 28

59Cu measured by Leuven group at NICOLE by On-Line NMR/ON

(59Cu, 3/2-) = 1.891(9) n.m. [V.V.Golovko et al. PR C70 014312 (2004)]

57Cu measured by NMR at MSU fragment separator

(57Cu, 3/2-) = 2.00(5) n.m [K.Minamisono et al. PRL 98 103508 (2006)]

N.B. Narrow resonance

p3/2 proton moments across full sub-shell N = 28 - 40

First complete shell - shell sequence BUT

57Cu result shows little sign of predicted return to close to the value found for 69Cu

Major discrepancy with shell model theory. Is 56Ni truly double magic?

68Cu

ΔE=const=δ(1/2mv2)≈mvδvResolution ~ 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 s1/2 and p1/2.

63Cu 59Cu 58Cu

= 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 58Cu (I = 1) at ISOLDE:

Established fitting parameters using data on 63Cu, confirmed by 59 Cu fit agreement with previous NMR/ON result.

58Cu [odd-odd] predictions - based on shell model 57Cu 0.68(1) n.m. - based on MSU 57Cu result 0.40(2) n.m.

Nature not kind: experimental result 0.52(8) n.m. no decisive answer.

PR C77 067302 (2008)

57 59 61 63 65 67 69 71 73

1000

E(keV)

Mass number

1/2-

5/2-

I=5/2- level:•Remains static between 57-69Cu 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 73Cu and 79Cu.•Experimental evidence for the inversion to occur at 75Cu.

A.F. Lisetskiy et al. Eur. Phys. J. A, 25:95, 2005N.A. Smirnova et al. Phys. Rev. C, 69:044306, 2004

S. Franchoo et al. Phys. Rev. C 64 054308

•5/2- level associated with the π(f5/2) orbital

I. Stefanescu Phys. Rev. Lett 100 (2008)

75

?

From Kieren Flanagan

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

Magnetic moments A > 70

Cu NMR/ON I = 3/2 = 2.28(1) n.m.

73Cu collinear laser I = 3/2 = 1.748(1) n.m.[Isolde laser group, unpublished]

77Cu in-source laser I = 5/2 = 1.75(5) n.m.

[in-source laser group, unpublished]

In source laser data, 75Cu, fits for I = 3/2,5/2

Peaks barely resolved, but clear preference for spin 5/2

Moment of 75Cu(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.

A > 71

Cu NMR/ON I = 3/2 = 2.28(1) n.m.

73Cu collinear laser I = 3/2 = 1.748(1)* n.m.[Isolde laser group, to be published]

75Cu in-source laser I = 5/2 = 1.005(1)* n.m. and collinear laser

[combined group, to be published]

77Cu in-source laser I = 5/2 = 1.75(5)* n.m.

[in-source laser group, to be published]

* preliminary values

Overall situation: ground state spin change positively identified at A = 75

Schmidt limit for f5/2 is at +0.8 n.m.

STOP PRESS UPDATE!!!

Isolde Feb 16th

MSU result for 57Cu is WRONG. New data from Leuven show resonance at higher frequency.

New [est N.J.S.] value 57Cu = 2.6(1) n.m.

[Cocolios, Van Duppen et al. to be published]

The Final Picture

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 f5/2 state has been identified, magnetic moments of 75,77Cu 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.

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 252Cf sample

Huge data sets > 1011 multifold coincidences

Table of Magnetic Dipole and Electric Quadrupole Static Nuclear Moments

• History: Gladys Fuller ~ 1975 - very comprehensivePramila 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 90 75 [2005].

• Contains all reported nuclear magnetic dipole moments and electric quadrupole moments of ground and excited states total ~ 4000 entries

• available from n.stone@physics.ox.ac.uk to late 2005.

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.

skyscrapers

178Hf (109 s = 31 y) 2.4 MeV, 16ħ

178Hf 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..

177Hf levels [Mullins et al., PRC58 (1998) 831]

combination of measurements of and => gK and gR

g-factors for deformed nucleicombination of both measurements => gK and gR

single-particle properties collective properties

see, for example:Purry et al., NPA632 (1998) 229El-Masri et al., PRC72 (2005) 054306

=> configurations and admixtures

=> neutron and proton pair quenching

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 momentMagnetic moment

gR values: 178HfK=0 gR= 0.240(14)K=6 π2 gR= 0.35(5)K=16 π2ν2 gR= 0.28(4)

[K=6, 16: Mullins et al., Phys. Lett. B393 (1997) 279]

more data needed, more-accurate data needed

New Result 177Hf

K=37/2 23 gR=0.22(3)[K = 23/2 21 accessible when moment measured.]