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The Physics of Cu Nuclei - with particular
reference to magnetic moment
measurements - from A = 56 to 78.
N.J.Stone
Oxford University and
University of Tennessee, Knoxville
ISOLDE Seminar August 4th 2009
Outline
Relevance of topic
Elements of Nuclear Theory - brief!
Nuclear magnetic moments
Moments close to 68Ni shell closure
Moments close to 56Ni shell closure
Towards 78Ni shell closure
Nuclear astrophysics concerns, among other things, the physics of
nuclei which lie along the several paths towards formation of the
elements of the universe.
For the r-process in particular, experimental access to the isotopes of
importance is difficult. Discussion of the details of the sequence, in
particular of the 'waiting point' nuclei, requires specific knowledge of the
properties of the relevant isotopes which often cannot be measured
experimentally.
Thus we depend upon extrapolations from accessible nuclei, using
methods or models which incorporate whatever degree of understanding
we have.
Extrapolations from 'known' territory is notoriously unreliable in nuclear
physics - mass models are a well known example.
One of the interesting 'waiting points' in the r-process is the region of
78Ni.
This talk explores what we know of nuclei of Cu isotopes, far from and
closer to, 78Ni, to see how well we can say we understand them and thus
how reliably we may hope to make the necessary extrapolations to
describe detailed properties of nuclei in the region of 78Ni.
(Very) Basic Nuclear Theory
• Nucleons move in an average potential produced by interaction
with the other nucleons.
• This leads to a sequence of single particle levels with quantum
numbers associated with their orbital and spin angular
momenta and parity.
• The strongest term in their interaction after this is the spin-orbit
which produces splitting between levels of j = l + s and gives
quantum labels e.g 1f5/2, 1f7/2 with the higher j lying lower.
• The larger energy gaps between states of higher l produce the
magic numbers and the idea of closed shell nuclei.
• The next strongest term is the pairing interaction which acts
between like nucleons and leads to pairs in the same j state
coupling to zero angular momentum in their ground states.
• What remains after these terms is called the 'residual
interaction' and is considered to act between both like and
unlike nucleons with varying properties
• Evidence for its nature is elusive…..
The Residual Interaction
We do not have an analytic understanding, or form, for the
interaction between nucleons in nuclei.
Simple effective potentials are used to construct a general
scheme of energies of nucleon states in terms of their
(spherical) quantum numbers, with an additional spin-orbit
interaction, e.g. 1f5/2.
Then there is the pairing interaction between like nucleons
All other parts of the interaction are called 'residual' and
described by a multipole expansion with monopole,
[no dipole], quadrupole etc terms, connected to the shape of
the nucleus.
This is merely a DESCRIPTION, not an UNDERSTANDING of
the origin or magnitude of the terms in the residual
interaction. It is a LANGUAGE to describe what is observed.
In the absence of the residual interaction
Energies of single nucleons are independent of the occupation numbers of
the same or other nucleon states, with the clear exception of the
phenomenon of Pairing, whereby two nucleons with the same (spherical)
potential quantum numbers combine to form a state of total angular
momentum zero.
As early as the 1960's examples were known where this situation
did not apply:
Example:
Proton ground states in Sb isotopes
As the neutron h11/2 shell fills the single proton ground state
changes from d5/2 [in lighter] to g7/2 [in heavier] Sb's.
Since these nuclei are not deformed, i.e. their potentials have little or no
quadrupole or higher terms, the effect which was seen as responsible for
the dependence of the occupancy of the neutron h11/2 orbital was called the
'monopole' shift term in the residual interaction.
Kisslinger and Sorensen, Pairing + Quadrupole Model [RMP 35 853 1963]
Knowledge of local behaviour of the residual interaction
is needed to give nuclear models predictive power.
Nuclear states
• Extreme single particle.
• Extreme collective: vibrations and rotations of the
nucleus as a single entity.
• Limited 'collective': states associated with excitations of
'valence' nucleons outside a close shell 'core'.
• Clearly a complex system!
Nuclear magnetic moments.
Nuclear magnetism has contributions from all angular motion
carrying charge
unit: the nuclear magneton (n.m.)
Orbital angular momentum:
Single particle
-
proton charge 1
neutron charge 0
Collective
-
whole nucleus - average charge Z/A
valence nucleons - average variable
Spin angular momentum
Single particle
-
proton s1/2 moment + 2.79 n.m.
neutron s1/2 moment -1.91 n.m.
A sensitive measure of the state wavefunction
Cu isotopes
In the range between N,Z = 28
and 40 both protons and
neutrons are filling states p3/2, f5/2
and p1/2 (all negative parity).
Cu isotopes have a single
proton outside the Z = 28 shell
closure
Between N = 28 (57Cu) and N = 40 (69Cu) the ground state
spin/parity of the odd-A copper isotopes is 3/2- the p3/2 state
The ground states and excitations of
copper isotopes are expected to provide
a good laboratory for nuclear theory
since the proton states are relatively
simple.
Magnetic moments of Copper isotopes
Pre
1998
Only three, mid-shell N, values known: isotopes 63,65Cu are stable.
Experimental methods of magnetic moment measurement
Outline only
Low temperature nuclear orientation with NMR [NMR/ON]
Fragmentation b/NMR
Laser spectroscopy - In Source and Collinear
The NICOLE On-Line Low Temperature
Nuclear Orientation facility, ISOLDE, CERN
On-Line NMR/ON
Nuclear Magnetic Resonance on Oriented Nuclei is done at ~10 mK temperatures.
Polarised radioactive nuclei are exposed to an RF field of variable frequency.
When the Zeeman splitting frequency is found
resonant absorption changes the
sublevel populations and hence also the observed anisotropy
a resonance in the
anisotropy versus frequency plot.
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.
Measured magnetic moment 69Cu(3/2-)
2.84(1) n.m.
Starting from extreme single particle
(Schmidtetlimit),
full
treatment
of
J. Rikovska-Stone
al. PRL 85
1392
(2000)
moment operator, including meson
exchange, gave calculated value
2.85 n.m.
At 28,40 double shell closure: Full agreement with best
shell model theory calculations [Ian Towner]
[J.Rikovska et al. PRL 85 1392 (2000)]
The NSCL Fragment Separator, MSU
Fragmentation b-NMR
Fragments are polarised in their creation.
Implanted in cubic materials, their polarisation can be detected by
measurement of the asymmetry of their beta decay. Application of a
magnetic field creates a Zeeman splitting which is deduced from
resonant destruction of the asymmetry, yielding the nuclear gfactor.
Effects are small.
Down to shell closure at N = 28
59Cu
measured by Leuven group at NICOLE by 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 the MSU fragment separator
m(57Cu, 3/2-) = 2.00(5) n.m [K.Minamisono et al. PRL 98 103508 (2006)]
N.B. Narrow resonance
Small effect
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:
Atomic Hyperfine Structure splitting
In Source, Doppler width resolution ~ 250 MHz
68Cu
Collinear Concept - add constant energy to ions
ΔE=const=δ(1/2mv2)≈mvδv
Resolution ~1 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.
- poor resolution (In Source) only for the A (large magnetic dipole) splitting
- good resolution (Collinear) for both A and B (smaller 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.
In Source 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.
NJS et al Phys Rev C77 067302 (2008)
Situation at 28,28
double shell
closure
Failure of experimental magnetic moment of 57Cu to
move strongly towards value found for 59Cu suggests
a serious problem for detailed shell model
calculations
M. Honma et al. PR C69 034335 (2004)
Cu isotopes across the N = 40 shell closure.
Between N = 28 and N = 40 the ground state of Cu isotopes is 3/2-
Both the proton and neutron subshells in this range are p3/2, f5/2 and
p1/2 [with increasing energy - all negative parity]
Above N = 40, the neutron filling subshell becomes positive parity g9/2.
Influence of this change:
compare the magnetic moments of 67Cu and 71Cu
two neutron holes
vs
two neutron particles [g9/2]
[N.J. Stone et al. PR C77 014315 (2008)]
There is clearly a difference between 67,71Cu (results joined by
solid line), which is to be associated with the fact that residual
interactions exist between the unlike nucleons which are not
fully described by the Honma et al. shell model calculations.
This is a ghostly sign of the residual interaction
Configuration mixing depends upon the states available.
Spectroscopic study of decay of Ni isotopes above 68Ni.
Work of Leuven group at LISOL
S. Franchoo et al. PRL 81 3100 (1998)
S. Franchoo et al. Phys. Rev. C64 054308 (2001)
Odd neutron ground states g9/2 - no allowed beta decay to p3/2 or f5/2.
Decay of beta fed states revealed a state at 534 keV in 71Cu and at 166 keV in 73Cu
- no electron conversion or angular correlation information
- identified as likely (5/2-)
SOME model calculations gave support to this assignment
Sinatkas et al - shell model with S3V' interaction - J.Phys.G18 1377 (1992)
Ji and Wildenthal Phys Rev C40 389 (1989)
Both placed f5/2 below p3/2 in context of 79Cu
Oros-Peusquens and Mantica Nucl Phys A669 81 (2000)
Placed f5/2 2 MeV below p3/2 in 78Ni in PCM
Suggestive of monopole interaction between pf5/2 and ng9/2
I=5/2- level:
•5/2- level associated with the π(f5/2) orbital
E(keV)
•Remains static between 57-69Cu at
1/25/2-
1000
~1MeV
•Systematically drops in energy
as the ν(g9/2) shell begins to fill
?
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
From Kieren Flanagan
•Leads to expectation that the
inversion of the ground state lies
between 73Cu and 79Cu
•Seek experimental
evidence for this
inversion.
Magnetic moments A > 70
Isotope
Method
71Cu
NMR/ON
Spin and Moment
I = 3/2 m = 2.28(1) n.m.
[Phys Rev C77 014315 (2008)]
73Cu
collinear laser I = 3/2 m = 1.7426(8) n.m.
[Isolde laser group, to be published]
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) of
the different level populations, hence transition intensities.
77Cu
Fitting data with I = 3/2 and I = 5/'2 - peak ratio clearly favours 5/2.
N.B. peaks well resolved
Magnetic moments A > 70
Isotope
71Cu
73Cu
77Cu
Method
NMR/ON
Spin and moment
I = 3/2 m = 2.28(1) n.m.
collinear laser I = 3/2 m = 1.748(1) n.m.
[Isolde collinear laser group]
in-source laser I = 5/2 m = 1.75(5) n.m.
[Isolde in-source laser group]
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
Isotope
Method
71Cu
NMR/ON
Resulting spin and moment
I = 3/2 m = 2.28(1) n.m.
73Cu
collinear laser I = 3/2 m = 1.7426(8) n.m.
[submitted to PRL as below]
75Cu
in-source laser I = 5/2 m = 1.0062(13) n.m.
and collinear laser [combined group, submitted
to PRL last week: Flanagan
et al]
77Cu
in-source laser I = 5/2 m = 1.75(5)* n.m.
[in-source laser group, to be published]
* preliminary value
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 Meeting, Feb 16th (priv. comm. Gerda Neyens)
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. PRL to be published]
The Final Picture
The very latest word ---- last week
78Cu
Isomers??
From Bill Walters, U. of Maryland
In-Source 78Cu
Unpublished data
No sign of isomers or
well resolved hyperfine
splitting
Assuming spin 6:
magnetic moment
small ~ 0.40(4) n.m.
- sign not determined
(no asymmetry to data)
The Final-Final Picture
with 78Cu added!
Communication
from Kamila
Sieja and
Frederic
Nowacki
[GSI and
Strasbourg]
Calculation of
ground state
copper nuclear
magnetic dipole
moments using
their shell model
code
(ANTOINE) with
up to 6 particlehole pair
excitations.
0p+0h
2p+2h
4p+4h
6p+6h
p3/2
f5/2
p3/2
Consistently good agreement with
experiment with 4p+4h.
f5/2
Conclusions
1. Best shell model calculations have yielded odd-A Cu magnetic moments at
N = 28, 40 very close to experiment and adequately described the variation
between these shell closures.
2. Now that the shift of the f5/2 state has been identified, magnetic moments of
71-78Cu can be calculated reasonably well. The residual interaction monopole
shift of this level has been established by spectroscopy and direct moment
and spin measurements.
3. Models which give these results successfully may be expected to
give useful predictions concerning the A = 78 shell closure and
related r-process properties. Models which fail to reproduce them may
not be trusted in other predictions.
Magnetic moments provide an aid to
development, and a stringent test of the reliability,
of nuclear model calculations.
Thank You