Horizontal evaluation:
Nuclear Magnetic Dipole and
Electric Quadrupole Moments
Recent activity
Nick Stone
Kuwait February 2013
Outline
Update of the General Table – involvement now more than 15 years.
Done for 2010/11 and 2011/12 ongoing for 2012/13
6192 line spreadsheet – new entries ~ 80/year 03-09 – more 2010 (fewer 2011)
Magnetic Moments
Results of interest since 2011
Sc isotopes across the f7/2 neutron shell and f7/2 proton shell filling
Sn and Te: 2+ state g-factors
Ti 9/2+ hyperfine anomaly corrections
New methods
HVTF on 72Zn
Paul trap laser spectroscopy in 229Th
A problem case
Reported -4 nm moment in 72As 8+ state
Quadrupole Moments
Status of the new Recommended Value Table
Major changes
Problem elements
New moment results 1.
Scandium Ground States
M. Avgoulea et al J Phys G 38 025104 (2011)
43,45Sc
2011Av01
7/2- ground states, 44,46Sc odd-odd ground states and isomers in 44,45Sc
Standard laser spectroscopy at Jyvaskylla with improved Sc yields from
IGISOL system
T.Ohtsubo et al PRL 109 032504 (2012)
2012Oh01
NMR on-line at Nicole Facility
Isolde CERN 49Sc ground state
Shows complete sequence of single
f7/2 proton configurations
from zero f7/2 neutrons (41Sc)
to the full 8 f7/2 neutrons (49Sc)
Demonstrating variation of
configuration mixing across
neutron subshell filling
with respect to Schmidt limit.
Also completes sequence of odd
numbers of f7/2 protons all with
full f7/2 neutron subshell from
49Sc to 55Co.
f7/2 neutrons
f7/2 protons
Red triangles show best available theory : Towner at 49Sc and Honma et al . for
Sc – Co sequence.
New moment results 2.
Sn First 2+ g-factors
Sn 2+ (Walker TF), Kumbartski (TF) and Allmond (RIV)] to be published.
Old measurements (Hass 1980) suggested some of the first negative g’s for 2+
states in heavier Sn even-A isotopes
Recent work (TF and RIV) have reached
some kind of consensus, showing a
steady fall as A increases
Walker et al PR C84 014319 (2011) 2011Wa15
112,114,116,122,124Sn claim high precision
Kumbartski et al PR C86 034319 (2012)
2012Ku14 RIB TF method
124,126Sn 126 definitely negative
Allmond et al – in preparation for PR 2013
smaller errors at 124,126,128Sn by RIV
complex composition of the 2+ states clearly neutron dominated at higher N – as
expected for major closed-shell Z=50 at Sn.
New moment results 3. g-factor of 2+ at closed n shell 134Te
Second radioactive beam measurement
at HRIBF, Oak Ridge National Lab
following 132Te.
Stuchbery et al in preparation –
preliminary result - shows
sharp rise in g-factor in 134Te
as compared to sequence
of lower even-even Te isotopes.
Several theoretical predictions
what will be measured in 136Te ???
New Moment results 4.
Tl Isomers Hyperfine anomaly
Barzakh et al. Gatchina PR C86 014311 (2012)
2012Ba32
One of few papers to make serious hyperfine anomaly corrections based on
fully resolved hfs.
Previously only S states measured.
New data A parameters for p1/2 and s1/2 atomic states
(p - no anomaly s – contact term anomaly)
found differences in ratios for two isotopes
at the 1.3 – 2.0% level with error about
0.6 – 1.0%.
Revised values have larger errors but are
corrected e.g. 191m was 3.903(5) now 3.78(2)
New methods 1.
HVTF on RIB
Fiori 72Zn PR C85 034334 (2012) 2012Fi02
TF on fragmentation reaction products at the GANIL accelerator, Caen France using thick
Gd both as reaction target and precession medium.
High Velocity Transient Field.
Radioactive 72Zn beam
Wide range of velocity as ions slow in
target (vout/vin ~ 0.7).
Assumed precession due to k shell e’s
although average field found was much
less than this would give.
Calibrated dependence (Fig shown) was used
to extract Is probability result: ~ 0.001
– which limits method.
Found also that RIV reduced anisotropy
so precession angle measurement
was made harder by factor 3 (G2 ~ 0.6).
despite problems, found g(2+) 72Zn +0.18(17)
New methods 2.
Laser Spectroscopy in Paul Trap
Laser spec in Paul trap – C.J.Campbell et al PRL 106 223001 (2011)
2011Ca17
Included since it’s a fantastic experiment! Ions held in a Paul trap are
laser cooled so that the ions ‘crystallise’ in a regular layout.
Can be held like this for ~ 1 hour.
Further cooled to tens of mK temperatures
to reduce Doppler broadening.
Fully resolved laser HFI measurements
ON A SINGLE ION WITHIN THE LINEAR CHAIN
gave A and B hfs coefficients.
Existing calculations of electronic B
give Q 229Th 3.11(16) eb
– compare previous 3.15(3) eb.
Lowest panel RHS shows line of 4 229Th ions
Real interest of experiment is precise study of the 7.6(5) eV isomer
for atomic clock purposes.
Oddball result
8+ isomer 72As D. Pantelica et al PR C82 044313 (2010)
2010Pa29
Integral PAD experiment on As implanted into iron. Rotation of angular distribution
observed and as a result, a moment of -4.3(3) nm suggested for the 8+ 982 keV state in
72As.
Suggested configuration is p and n both g9/2 but gives large +ve g 0.46 using empirical
local g9/2 g’s.
The problem is that NO SUCH LARGE negative nuclear magnetic dipole moment has even
been found and the simple reason for that is that no such large negative value can be
constructed from ANY proton and ANY neutron configuration.
Likely explanation is error in formula for precession frequency, which is quoted as
 = - 2pgmNB/h. This to be found in some early papers by well known authors
including Steffen and Fraunfelder, but is not correct.
If positive sign is taken, moment is acceptably close to +3.8 nm predictable using
empirical g9/2 proton and neutron g-factors.
In correspondence with the authors!
New Table of Recommended Values of Electric Quadrupole Moments
As outlined in 2011 the time is ripe to take advantage of advances in computational
ability to make high precision calculations in multi-electron systems, atoms, ions and
compounds, yielding reliable values of electric field gradients acting at nuclei
Since nuclear Q’s are always measured combined with a field gradient, such input is
necessary for extraction of all Q values and over the years for any element it is both
likely and true that a range of efg values have been used.
Pekka Pyykko is an acknowledged expert in such efg calculations and he has issued a
set of recommended efg values for the majority of elements.
In 2011 the new Table of Q values was started, reviewing all Q measurments and
correcting the results using the adopted Pyykko recommended efg’s and ratios
derived from them. The Table progressed as far as Sb in 2011-12 and will be
completed for publication in 2013
Whilst many quadrupole moments are not changed, since the adopted efg’s were
used previously, many have been adjusted in light of new adopted efg best values
The most notable changes to standard results are listed below
Element change%
N
F
Ca
Ge
Se
Sr
In
Sn
+2.2
-22
-26.1
+15.3
-30.9
-7.6
-5.1
+25.7
error(factor)
0.33
0.25
1.22
0.03
0.14
0.1
0.4
0.7
ref isotope
14N
19F
41,41Ca
73Ge
77Se 250 keV
87Sr
113,115In
119Sn 24 keV
References Pyykko Z. Naturforsch. 47a 189 (1992),
Mol Phys 99 1617 (2001),
Mol Phys 106 1965 (2008) and private communication 2011
Format of Quadrupole Reference Value Table
Rhodium
Calculation of the quadrupole coupling constants in Rh intermettalic compounds
Reference isotope
45 Rh 100
74
214 ns
(2)+
0.153 (18)
PAC
2008Py02/1996Bl15
45 Rh 103
295
6.7 ps
3/2-
-0.3(2)
CERP
1976Ge19
357
73 ps
5/2-
-0.4(2)
CERP
1976Ge19
Palladium
Reference isotope
Muonic atom X-ray hyperfine structure
46 Pd 102
556
11.3 ps
2+
-0.20(15)
CERP
1977Fa11
46 Pd 104
556
9.7 ps
2+
-0.46(11)
CERP
1977Fa11
46 Pd 105
0
stable
5/2+
+0.660(11)
Mu-X
2008Py02/1978Vu01
46 Pd 106
512
12 ps
2+
-0.51(7)
ES
1973Ho05
46 Pd 108
434
23 ps
2+
-0.58(4)
ES
1978Ar07
46 Pd 110
374
46 ps
2+
-0.47(3)
ES
1976Li19
2013 will see completion of this Table, but there are some disappointing features
Pyykko’s best efg’s are for some elements still disappointingly inaccurate. These include
Pm 27%, Pb 61% and Rn 10%
For others Pyykko makes no recommendation and he and I are in correspondence as to
the best way ahead. Setting up a new a-priori calculation can take months or more and
is not undertaken unless there is a proven need – usually NOT to establish nuclear Q
values!
The difficulty is not only the absence of a high quality efg estimation, but also the
problem of setting an error on whatever has been used
The problem elements are Te, Ce, Tm , W, Pt, Tl, Po, At, Ra, Cm, Bk
Conclusions (2011)
Plan of action:
1. Continue to update comprehensive all results table with new entries at 12 month
intervals. Publish update frequency ---- 3 to 5 years?
Latest published version is INDC(NDS)-0594 April 2011:
more up to date available from NJS on application
2.
Attack need for recommended mu and Q 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’.
2013 Item 1
Item 2
done as proposed
on track for Q’s and planned to follow
for mu’s
NJS available for direct consultation:
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