Download The Physics of Cu Nuclei with particular reference to magnetic

The physics of Cu nuclei from A = 56 to 78
with particular reference to ground state magnetic
moments.
N.J.Stone
Oxford University and
University of Tennessee, Knoxville
Russbach Workshop 2009
Outline of Talk
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.
(Very) Basic Nuclear Theory
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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 acts between both like and unlike nucleons.
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
interation, 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 - C of M], 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
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 measure of the state wavefunction
Cu isotope magnetic moments close to 68Ni
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 these nuclei are expected to provide
a good laboratory for nuclear theory since the proton states are relatively
simple.
Pre
1998
Known Odd-A Cu Magnetic Moments circa 1998
Nuclear Magnetons
4
Schmidt limit
3.5
3
2.5
2
60
61
62
63
64
65
66
Mass number
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.
Odd-A Cu Magnetic Moments to N = 40
Magnetic moment 69Cu(3/2-)
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 85 1392 (2000)
Nuclear Magnetons
= 2.84(1) n.m.
4
Schmidt limit
3.5
3
2.5
2
60
62
64
66
Mass number
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)]
68
70
Down to shell closure at N = 28
59Cu
measured by Leuven group at NICOLE by NMR/ON
μ(59Cu, 3/2-) = 1.891(9) n.m. [V.V.Golovko et al. PR C70 014312 (2004)]
57Cu
measured by β−NMR at MSU fragment separator
μ(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
Odd-A Cu Magnetic Moments 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
Nuclear Magnetons
4
3.5
Schmidt limit
3
2.5
2
1.5
1
56
58
60
62
64
66
68
Mass number
Major discrepancy with shell model theory. Is 56Ni truly
double magic?
70
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
μ = 2.22(9) n.m. [Ref 2.23]
59Cu
μ = 1.84(3) n.m. [Ref. 1.89]
58Cu
μ = 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.
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, as we have seen, the ground state of Cu
isotopes is 3/2Both 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.
We can see influence of this change by comparing the magnetic
moments of 69Cu and 71Cu.
[N.J. Stone et al. PR C77 014315 (2008)]
There is clearly a difference between 69,71Cu (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.
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 πf5/2 and νg9/2
[N.B. not πf7/2 - νg9/2 as mentioned yesterday from Tensor term]
•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
Magnetic moments A > 70
71Cu
73Cu
NMR/ON
I = 3/2 μ = 2.28(1) n.m.
collinear laser I = 3/2 μ = 1.748(1) n.m.
[Isolde laser group, unpublished]
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 μ = 2.28(1) n.m.
collinear laser I = 3/2 μ = 1.748(1) n.m.
[Isolde laser group, unpublished]
in-source laser I = 5/2 μ = 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) μ = 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 μ = 2.28(1) n.m.
collinear laser I = 3/2 μ = 1.748(1)* n.m.
[Isolde laser group, to be published]
in-source laser I = 5/2 μ = 1.005(1)* n.m.
and collinear laser
[combined group, to be published]
in-source laser I = 5/2 μ = 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
Odd-A Cu Magnetic Moments towards N = 50
Nuclear Magnetons
4
3.5
spin 3/2
Schmidt limit p3/2
spin 5/2
3
2.5
2
1.5
1
60
65
70
Mass number
Schmidt limit for f5/2 is at +0.8 n.m.
75
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 μ = 2.6(1) n.m.
[Cocolios, Van Duppen et al. to be published]
The Final Picture
Odd-A Cu Magnetic Moments towards N = 50
Nuclear Magnetons
4
3.5
spin 3/2
Schmidt limit p3/2
spin 5/2
3
2.5
2
1.5
1
60
65
70
Mass number
75
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.
Thank You