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

2. 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 n.m.
neutron s1/2 moment n.m.
A sensitive, non-quantised, measure of state wavefunctions

3. 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 e = (1 - b2/a2))] is given by
Q0 = 2/5 ZRm2e(1 + 2e/3) where the mean radius is Rm3 = 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

4. 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 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2005 Table is out-of-date.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

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

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

7. At least 80% of new results are for ground states:
Techniques
beta – NMR originally only below about A ~ 20, now up to A ~ 70
with fragmentation accelerators [e.g MSU]
Laser spectroscopy ever 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
longer lifetime [ms, ms, 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.

8. Tough Innovation required!!
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, ms, 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?]
RIV only gives magnitude – where t known
can it be calibrated without previous examples?
Tough Innovation required!!

9. 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.

10. 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:
23Na, ,205Tl From these other standards are derived
165Ho, Pb by ratio to give a complete reference structure
185,187Re, Bi throughout the periodic table.
199Hg,
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.

11. 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 103. [Gustavsson and Martensson-Pendrill PRA (98)]
[Recent work of Jaszunski et al. to be published]
These provide the basic standards for nuclear magnetic moments

12. When are these small corrections important?
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?
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.

13. 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.

14. 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 elements Na, 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.

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

16. The time is clearly ripe
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!

17. Conclusions Plan of action:
1. Continue to update new entries at 12 month
intervals. Publish update frequency to 5 years?
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’.

18. Thank you

19. Why are these small corrections important?
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.

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

21. Why are these small corrections important?
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.

22. 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 m / 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 m / spin I ]

23. Recoil in Vacuum Target Foil Total angular momentum F 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
Total angular momentum F
Target recoil
Beam
Coulex Recoil
Nuclear spin

24. Brief description of the recent RIB 132Te RIV measurement at HRIBF
[N.J.Stone et al PRL (2005)]
UNATTENUATED Distribution for 126Te stopped in Cu.
RIV ATTENUATED distributions from 2+1 states in 122,126,130Te [known g-factors and lifetimes].
Gk are the g-factor dependent attenuation coefficients.
For the RIV method we need to extract g from the Gk.

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

26. 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 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?

27. 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 = N = 40 for single proton beyond Z = 28
Towards establishing reliable nuclear models for the region of N = 50 [A = 78] - R process importance

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

29. Magnetic moment 69Cu(3/2-) = 2.84(1) 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.
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.
J. Rikovska-Stone et al. PRL (2000)
At 28,40 double shell closure: Full agreement with best shell model theory [calculations by Ian Towner]
[J.Rikovska et al. PRL (2000)]

30. Down to shell closure at N = 28
59Cu measured by Leuven group at NICOLE by On-Line NMR/ON
m(59Cu, 3/2-) = 1.891(9) n.m. [V.V.Golovko et al. PR C (2004)]
57Cu measured by b-NMR at MSU fragment separator
m(57Cu, 3/2-) = 2.00(5) n.m [K.Minamisono et al. PRL (2006)]
N.B. Narrow resonance

31. 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?

32. On-Line Laser spectroscopy Collinear and In-Source Methods
In Source, Doppler width resolution ~ 250 MHz
Collinear Concept - add constant energy to ions
68Cu
ΔE=const=δ(1/2mv2)≈mvδv
Resolution ~ MHz, resulting from the velocity compression of the line shape through energy increase.
In Cu+ ion, electron states involved are s1/2 and p1/2.
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)

33. Measurement of moment of 58Cu (I = 1) at ISOLDE:
PR C (2008)
63Cu Cu Cu
m = 2.22(9) n.m. [Ref 2.23] m = 1.84(3) n.m. [Ref. 1.89] m = 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.

34. 5/2- level associated with the π(f5/2) orbital
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.
5/2- level associated with the π(f5/2) orbital
E(keV)
1000
1/2-
5/2- ? 57 59 61 63 65 67 69 71 73 75
Mass number
S. Franchoo et al. Phys. Rev. C
I. Stefanescu Phys. Rev. Lett 100 (2008)
A.F. Lisetskiy et al. Eur. Phys. J. A, 25:95, 2005
N.A. Smirnova et al. Phys. Rev. C, 69:044306, 2004
From Kieren Flanagan

35. 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

36. Magnetic moments A > 70
71Cu NMR/ON I = 3/2 m = 2.28(1) n.m.
73Cu collinear laser I = 3/2 m = 1.748(1) n.m.
[Isolde laser group, unpublished]
77Cu in-source laser I = 5/2 m = 1.75(5) n.m.
[in-source laser group, unpublished]

37. 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) m = 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.

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

39. Overall situation: ground state spin change positively identified at A = 75
Schmidt limit for f5/2 is at +0.8 n.m.

40. 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 m = 2.6(1) n.m.
[Cocolios, Van Duppen et al. to be published]

41. The Final Picture

42. 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.

43. 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

48. 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.

49. 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:
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.

52. skyscrapers
178Hf is at the centre of the multi-quasiparticle K-isomer region
178Hf (109 s = 31 y)
2.4 MeV, 16ħ
[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..

53. 177Hf levels combination of measurements of m and d => gK and gR
[Mullins et al., PRC58 (1998) 831]
combination of measurements of m and d
=> gK and gR

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

55. Moment value: 7.33(7) n.m. (est. 8.14(17) n.m.)
Magnetic moment
This graph shows the 177 Hf 37/2- isomer resonance centred at MHz. The y axis represents the combined signal from several transitions in the decay of this isomer.
The central frequency v0 together with the known hyperfine field of Hf in Fe was used to determine the magnetic moment of the 37/2 isomer.
It is lower than the estimated value, showing the limitation of the method used to obtain the estimates and the importance to exact measurement.
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.) 55

56. gR values: 178Hf New Result 177Hf K=37/2 p2n3 gR=0.22(3)
K= gR= 0.240(14)
K=6 π2 gR= 0.35(5)
K=16 π2ν2 gR= 0.28(4)
more data needed, more-accurate data needed
New Result 177Hf
K=37/2 p2n3 gR=0.22(3)
[K = 23/2 p2n1 accessible when moment measured.]
[K=6, 16: Mullins et al., Phys. Lett. B393 (1997) 279]