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
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 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
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2005 Table is out-of-date.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
Entries last isotope in 2010
in this range
1-500
501-1000
1001-1500
1501-2000
2001-2500
2501-3000
3001-3500
3501-4000
4001-4500
4501-5000
5001-5500
5500-6133
40Ar
63Zn
87Rb
95Ru
113Sn
141Xe
151Pm
160Dy
174Hf
191Pt
196Pb
254Es
6133 lines
line entry of same
isotope in 2005
431
831
1283
1696
2164
2627
3123
3620
4115
4597
5069
5701
new entries
total this region
69
169
217
304
336
373
377
380
385
403
431
432
69
100
48
87
32
37
4
2
5
18
28
1
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
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
Techniques
longer lifetime [ms, ms, ns]
shorter lifetime [ps]
Why?
PAC, TDPAD, etc
Transient Field, RIV
Loss of accelerators for stable beams
Limited 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, 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!!
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,
165Ho,
185,187Re,
203,205Tl
207Pb
209Bi
From these other standards are derived
by ratio to give a complete reference structure
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 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.
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.
Examples related to recent (since ~ 2000) atomic efg calculations
14N
19F
(197 keV)
Table entries
Atomic efg results
+0.02001(10)
+0.02044(3)
+2%, error down
-0.121(5) [also -0.072(4)
-0.0942(9)
-21 or +31%
+0.150(6)
+0.146.6(10)
error down
27Al
Mu-X
49Ti
+0.24(1) and +0.324(3)
+0.247(11)
-31%
63Cu
Mu-X
-0.211(4)
-4% error down
69Ga
+0.1650(8) and +0.171(11)
73Ge
-0.220(15)
+173(3)
-0.17(3)
+15%
+3% or -5.5%
+0.254(6) and +0.276(4)
+0.261.5(2.5)
91Zr
-0.206(10) and -0.257(13)
-0.176(3)
131Xe
Pb
-0.360(40)
-0.556(24)
N.B.also ‘solid state’ calc -0.669(15)
-0.120(12) and better
error down
-0.196(6)
81Br
121Sb
+1 or 5%,
-0.117(6)
-15% or -32%
+54%
even larger
good
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 month
intervals. 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 m / spin I ]
of the decaying nuclear state.
This is the basis of the Recoil In Vacuum [RIV] method of gfactor determination [see e.g. Broude, Goldring et. al. NPA215 617 (1973)].
Recoil in Vacuum
Target Foil
Total angular
momentum F
Target recoil
Beam
Coulex Recoil
Nuclear spin
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
Brief description of the recent RIB 132Te RIV measurement at HRIBF
[N.J.Stone et al PRL 94 192501 (2005)]
UNATTENUATED Distribution for 126Te stopped in Cu. RIV ATTENUATED distributions from 2+1 states
in 122,126,130Te [known g-factors and lifetimes].
W ( ,  )   Gk kq Ak Qk D ( , ,0)
k*
q
k .q
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 t to form calibration for
their gt 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.
Can we hope to provide a sound theoretical grounding
for the CALIBRATION OF RIV ATTENUATIONS?
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.
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
Pre
1998
Only three, mid-shell, values known: isotopes 63,65Cu are stable
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
J. Rikovska-Stone et al. PRL 85 1392 (2000)
(Schmidt limit) and based on full
treatment of moment operator, including
meson exchange, gave value 2.85 n.m.
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
m(59Cu, 3/2-) = 1.891(9) n.m. [V.V.Golovko et al. PR C70 014312 (2004)]
57Cu
measured by b-NMR at MSU fragment separator
m(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?
On-Line Laser spectroscopy
Collinear and In-Source Methods
In Source, Doppler width resolution ~ 250 MHz
68Cu
Collinear Concept - add constant energy to ions
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)
PR C77 067302 (2008)
63Cu
m = 2.22(9) n.m. [Ref 2.23]
59Cu
m = 1.84(3) n.m. [Ref. 1.89]
58Cu
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.
•5/2- level associated with the π(f5/2) orbital
E(keV)
1000
1/25/2-
?
57 59 61 63 65 67 69 71 73 75
Mass number
S. Franchoo et al. Phys. Rev. C 64 054308
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
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.
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
71Cu
73Cu
77Cu
NMR/ON
I = 3/2 m = 2.28(1) n.m.
collinear laser I = 3/2 m = 1.748(1) n.m.
[Isolde laser group, unpublished]
in-source laser I = 5/2 m = 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) 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.
A > 71
71Cu
73Cu
75Cu
77Cu
NMR/ON
I = 3/2 m = 2.28(1) n.m.
collinear laser I = 3/2 m = 1.748(1)* n.m.
[Isolde laser group, to be published]
in-source laser I = 5/2 m = 1.005(1)* n.m.
and collinear laser
[combined group, to be published]
in-source laser I = 5/2 m = 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 m = 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 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 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.
178Hf
is at the centre of the multi-quasiparticle K-isomer region
skyscrapers
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..
177Hf
levels
[Mullins et al., PRC58 (1998) 831]
combination of measurements of m and d
=> gK and gR
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) 054306
=> neutron and proton
pair quenching
Magnetic moment
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.)
gR values: 178Hf
K=0
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]