From spherical 34Si to deformed 32Mg:
ground state magnetic and quadrupole moments of Al-isotopes
Spokespersons: G. Neyens and P. Himpe
Participants:
K.U. Leuven : D. Borremans, P. Himpe, K. Turzo, D. Yordanov, G. Neyens, N.
Vermeulen, S. Mallion
GANIL :
F. de Oliveira Santos, G. Georgiev, I. Matea, C. Stodel, D. Verney
University of Sofia : D. Balabanski (now at University of Camerino, Italy)
Ghent University : N. Smirnova
JINR-Dubna: Yu. E. Penionzhkevich, Yu. Sobolev, S. Lukyanov
Bruyeres le Chatel: J.M. Daugas, V. Meot
Abstract
The ground state properties of odd-mass Al-isotopes (Z=13), are dominated by the unpaired
d5/2 proton. The evolution of the g-factors and quadrupole moments of the odd Al-ground
states allows to probe the influence of core polarization effects as a function of neutron
number. Furthermore, the g-factors are very sensitive to configuration mixing and to M1-core
polarisation, while the quadrupole moments are more sensitive to changes in the nuclear
deformation (E2 core polarization). The moments of the even mass (odd-odd) Al-isotopes will
give information on which orbital is occupied by the unpaired neutron. This changes as a
function of neutron number. The g-factors of the 31,32,33Al isotopes have been measured
successfully during a previous run (E437). We intend to complete the systematic study by
extending it to the neutron and proton rich side, and by measuring also the Q-moments of
these isotopes in order to probe a possible change in deformation as a function of neutron
number.
Introduction
The shell structure around the magic number N=20 is changing very rapidly from a
normal spherical ground state for 34Si (Z=14) to a well deformed ground state for
32
Mg (Z=12). The origin of this deformation in 32Mg is the appearance of intruder
configurations (2p-2h neutron excitations) at very low excitation energy, due to a
decrease of the N=20 shell gap with decreasing proton number (starting at Z=20).
The Al-isotopes, with proton number Z=13, are precisely on the border of this
spherical and deformed regions.
The ground state spin and parity of the odd Al-isotopes is suggested to be 5/2+,
dominated by the unpaired proton in the d5/2 orbital. Theoretical calculations in the
sd-shell model space and in the sd-pf shell model space performed by different
groups, predict a significant different structure for the 5/2+ ground state of 33Al, the
isotope with N=20 neutrons. In particular, the magnetic and quadrupole moments
are predicted to be very different, depending on whether admixtures with 2p-2h
configurations are taken into account or not.
The interest in the even-even Al isotopes is slightly different : the ground state of
these isotopes consists of a coupling between an odd proton (d5/2) and an odd
neutron. The orbital that is occupied by the odd neutron changes as a function of N.
By measuring the g-factor of these even-even Al isotopes, we can probe which
neutron orbital is preferentially occupied, and probe the influence of configuration
mixing. In particular, it will be interesting to see if the 34Al ground state is a normal
coupling of a d5/2 to a f7/2, (to form I=4-) or whether in the neutron rich N=21 Al
isotopes, the ground state is governed by the d3/2 (to form a positive parity state). It
was suggested recently that the ground state of 33Mg, the isotone of 34Al, is indeed
governed by this d3/2 neutron state. A g-factor measurement (subject of another
proposal) will have to confirm that.
Several theoretical calculations have been performed in order to explain the
properties of nuclei around the Island of Inversion. While most of these models are
now able to describe rather accurately the experimentally determined properties of
the even-even nuclei, their predictions about the properties of the odd nuclei are not
always in agreement with each other [Cau02, Uts01]. The reason is because in odd
nuclei the unpaired proton or neutron plays a crucial role in the structure at low
excitation energy. If the single particle levels in the shell model have slightly different
energy gaps, this has an immediate consequence on the low-energy structure of the
odd nuclei. In particular the properties of nuclei at the border of the ‘Island of
inversion’ are crucial ingredients to fix the monopole part of the shell model
Hamiltonian.
Results from previous runs related to this proposal.
In a recent experiment, july 2003, we have been able to measure the g-factor of the
33
Al ground state. The preliminary result from an on-line analysis is shown in the left
of figure 1. The quoted error bars will still be reduced by factor 2 to 5, because a
carefully calibration of the magnetic field needs to be preformed off-line.
Figure 1: g-factor measurements on 31,32,33Al ground states, results from E437, july 2003
The interpretation of this data should allow to determine if the 33Al ground state is
rather a ‘normal’ state, or whether some admixture with 2p-2h excitations of the
neutron core are needed to reproduce the experimental result. The analysis of these
data is still in progress, but from the on-line result is can already be deduced that the
g-factor is smaller than predicted for a pure sd-shell state [Him04]. Some admixture
with neutron 2p-2h excitations into the wave function will be needed to reproduce the
experimental value, as demonstrated in figure 2.
It that same experiment, we have also performed precision measurements on the
31
Al and 32Al ground state g-factors. The 31Al g-factor had been measured a few
years ago by our collaboration [Bor02]. From the good agreement of the measured gfactor with a calculated value from the sd-shell model (using USD interaction), we
could deduce that he ground state spin/parity of 31Al is 5/2+. A g-factor is however
indirectly sensitive to the nuclear spin, by comparing the deduced magnetic moment
with theory prediction. Only for nuclei with a structure that is rather well understood,
this ‘indirect’ determination of the spin via a g-factor measurement is possible (this is
demonstrated e.g. in [Ney03a]. A direct measurement of the spin is possible using
the Level Mixing Resonance (LMR) technique [Ney97]. This technique also allows to
measure the quadrupole moment, provided the magnetic moment is known. The
measured quadrupole moment could further confirm if the 5/2+ ground state is
indeed, as predicted, very little influenced by admixtures of 2p-2h states into the
wave function.
Figure 2: Comparison of experimental magnetic moments with shell model calculations for
5/2+ ground states in odd mass Al-isotopes.
The LMR-method has been used a few years ago, to measure the ground state
moments of 31Mg (E314) [Teu01, Ney01, Ney03]. The result from that experiment
was rather ‘intriguing’, because the number of resonances, as well as the position
between the observed LMR resonances, clearly showed that the spin of the
investigated state was 7/2. Such a state is most likely the 7/2- 1p-1h neutron excited
state. Whether this is the ground state, or an isomeric state, could not be concluded
from this work, neither whether it was a - or  decaying isomer [Teu01]. Earlier
beta-decay work [Klo93] suggested a (3/2)+ for the 31Mg ground state. The presence
of a long-lived 7/2- state, next to a 3/2+ state in 31Mg, would be a clear signature for
shape coexistence in this nucleus. Publication of this result, including a discussion,
has been delayed, until the presence of two beta-decaying states could be confirmed
more firmly. Last week, by measuring the hyperfine structure of an optically
polarized 31Mg beam at ISOLDE-CERN, we could show indeed the presence of two
-decaying states in 31Mg with opposite sign for the g-factors, as expected for a 3/2+
and 7/2- state. The data need still to be analysed more carefully of course. Also
good-quality lifetime curves have been obtained, as well as  coincidence data
from the 31Mg beta-decay (these are data from the april 2003 run, E314b, which are
still under analysis).
Finally, in the july 2003 run, we have been able for the first time, to demonstrate the
presence of spin-polarization in a projectile pick-up reaction: for 34Al (N=21) produced
from a 36S (N=20) beam, we have measured the largest amount of spin-polarization
at the maximum of the yield distribution (figure 3, right).
Furthermore, we have found a method to measured the spin-polarization BEFORE
the moment measurement starts, which was not possible till now. Until now, the spin
orientation was deduced from the amplitude of the measured resonances, while the
position of the resonances gave us information on the nuclear moments. The new
method to deduce the asymmetry, is by measuring the decay-asymmetry with and
without applied magnetic field, which can be done in about 15-30 min. of beamtime.
We have compared the amount of experimental asymmetry measured by both
methods, for the 3 investigated Al isotopes, and very similar values are obtained, as
shown in figure 4, middle. The large difference in -asymmetry measured for the 4
isotopes, reflects partly the difference in the asymmetry parameter of the -decay.
The high asymmetry parameter for 32Al is because its -decay is governed by a
Gamov-Teller transition (32Al, 1+  32Si, 0+), while in the other Al-isotopes the decay
is spread over several transitions.
With a new crystal holder it is now also possible to implant the selected isotope in
different crystals, without breaking the vacuum. That, in combination with a fast
asymmetry measurement, allowed to find the crystal in which the polarization was
maintained the best (figure 4, right).
Figure 4: (Right) Measured asymmetry in the decay of a polarized 34Al beam, selected in
different windows of the longitudinal momentum distribution. The corresponding detected yields are shown below. (Middle) Measured asymmetry for the different Al-isotopes, as
deduced from the new ‘fast’ method and from the NMR resonances. (Left) Measured decay
asymmetry for 29Mg and 31Al in different implantation crystals.
Beamtime Request
(1) g-factor of 34Al
The presence of 2% of asymmetry, and a measured beta-detection yield of 200/s for
the polarized 34Al beam, will allow to measure it’s g-factor by the Nuclear Magnetic
Resonance technique in 3 UT of beam time. Several regions of g-factors need to be
scanned, because the predicted g-factors for an assumed positive or negative partity
ground state are very different. First, rough g-factor scans are made, which are then
refined to determine the g-factor with an accuracy of less than 1%.
(2) Q-moments of Al-isotopes
The quadrupole moments of the Al-isotopes can be measured using the Level Mixing
Resonance method. This method requires a fine scan of a large range of values of
the applied static magnetic field, in order to measure all the resonances induced by
the combined magnetic and quadrupole interactions. As an implantation crystal, we
will use Al2O3, a crystal for which the electric field gradient is known very accurately:
Vzz(Al Al2O3) = 70.7(6)*1015 eV/cm2 [Sun92, Pou50].
The quadrupole moments of the odd-mass Al isotopes close to stability have been
reproduced very well by the sd-shell model calculations using the USD-interaction
[Bor02]. By measuring these moments in the more neutron rich nuclei, we will be
sensitive to possible admixtures of 2p-2h components in the wave functions, which
usually induce an additional deformation.
As it was demonstrated for 31Mg in the Ph. D. thesis of S. Teughels and in a
forthcoming paper, the LMR method is also very sensitive to the spin of the
investigated state. That will allow to determine the ground state spin of 34Al, for
which very little spectroscopic information is available till now.
To measure 1 LMR curve, the time required varies between 3 UT for
32
Al (each), up to 5 UT for 33Al and 9 UT for 34Al.
30
Al,
31
Al and
The experiments will be performed at the LISE beam line, using the -NMR-LMR setup. For these experiments, pure beams of polarized (for NMR) or aligned (for LMR)
fragments are required. A polarized beam requires a deviation of the primary beam
with respect to the secondary beam, which takes about 0.5 UT of time (once).
Highest polarizations are mostly obtained from a projectile fragmentation reaction on
a light target, by a selection in the wing of the momentum distribution (except for the
34
Al case which is produced by a neutron-pick-up reaction). During the previous
experiment, using polarized fragment beams, it was shown that beams with typical
purities between 80 and 98% were obtained for all isotopes at the beam line in D6,
without using the velocity filter.
For aligned beams, the purity of the beam is usually much less because the
alignment is often largest when selecting the center of the momentum distribution. In
this case, it might be needed to use the velocity filter for further purifying the beam.
(3) Summary
We suggest to measure the g-factor of 34Al and the quadrupole moments of all Alisotopes between mass A=30 and A=34.
This can be achieved in three experiments:
The first one, to measure the g-factor (NMR-curves) of 34Al and the quadrupole
moments for the best produced Al-isotopes: 30,31,32Al. This will require:
- 4 UT for selection and tuning of the 4 polarized fragment beams
- 1 UT to measure the g-factor for 31Al to test the experimental set-up and
as a calibration of the magnetic field.
- 3 UT for the g-factor measurement on 34Al
- 1 UT to change between fragment beams (once they are tuned, this can
be done in about 2 hours/change).
- 9 UT for the Q-moment measurements on 30,31,32Al
a total of 18 UT for experiment I.
Once the optimal conditions for the LMR measurements are established, the
quadrupole moments of the more exotic Al-isotopes (33,34Al) can be measured in a
second experiment. For this we will need:
- 3 UT to select 3 isotopes (a test on a previously measured case will be
performed to validate the experimental set-up)
- 3 UT to measure the LMR on a know case (32Al probably, as this has I=1,
so only 1 resonance need to be measured)
- 5 UT to measure LMR on 33Al
- 9 UT to measure the LMR on 34Al.
- 1 UT to change between isotopes (once they are tuned)
a total of 21 UT is requested for this experiment.
References
[Bor02] Physics Letters B 537 (2002) 45 – 50
[CAU02] E.Caurier, F.Nowacki, A.Poves, Eur. Phys. J. A 15, 145-150 (2002)
[KLO93] G.Klotz et all. Phys.Rev.C Vol 47 Number 6 47
[Ney01] G. Neyens, Hyperfine Interactions 136/137 (2001) 171-177
[Ney03] G. Neyens, Reports on Progress in Physics 66 ( 2003) 633-689
[Ney04] G. Neyens et al., in preparation
[OTS02] T.Otsuka et all. Eur. Phys. J. A 15, 151-155 (2002) and private communication.
[Pou50] R.V. Pound Phys. Rev. 79 Vol.4 685 (1950)
[Teu01] S. Teughels, Ph.D. Thesis, K.U. Leuven
[Sun92] D.Sundholm PRL 68, 927-930 (1992)