Shape coexistence in light
krypton isotopes
E. Bouchez, E. Clément, A. Chatillon, A. Görgen, A. Hürstel, W. Korten,
Y. LeCoz, C. Theisen
Collaboration:
CEN Bordeaux, GANIL Caen, Grenoble, IPN Lyon, Copenhagen (Denmark), Jyväskylä (Finland),
GSI (Germany), Warsaw (Poland), Bucharest (Romania), Liverpool, Surrey (UK).
Shape coexistence in light Kr isotopes has been studied through conversion-electron spectroscopy after fragmentation
reactions and a new shape isomer has been identified as the first excited state in the N=Z nucleus 72Kr. The results
support the interpretation of an oblate ground state in 72Kr, a strongly mixed ground state in 74Kr, and prolate ground
states in the heavier isotopes. To test this interpretation, electromagnetic transition probabilities and static moments
have been measured in 74Kr and 76Kr via Coulomb excitation of low-energy beams from SPIRAL.
Introduction
In the Se and Kr nuclei near the N=Z line states of
large prolate and oblate deformation are predicted
within a very small energy range. This coexistence of
shapes is caused by the competition of shell gaps in
the single-particle level scheme found at both prolate
and oblate deformation for the proton and neutron
numbers involved. Deformed shell model calculations
predict the N=Z nuclei 68Se and 72Kr to be rare cases
with an oblate ground state with a low-lying state of
prolate configuration. A reversed situation with a prolate
ground state and an excited oblate configuration is
predicted for the heavier isotopes. An experimental
fingerprint of the shape coexistence is a low-lying 0+
state that can be interpreted as the “ground state” of
a different shape. If the excited 0+ state comes close
in energy to the first 2+ state (or even below), it will
predominantly (or exclusively) decay via a E0 transition
to the ground state. The strength of the E0 decay,
which is non-radiative and proceeds only via internal
conversion, contains information about the mixing
amplitude and the difference in size of the deformations.
On the other hand, static moments (and therefore
intrinsic shapes) can be measured using the reorientation
effect in Coulomb excitation.
New Shape Isomer in
72
Kr
A search for isomeric states in the nuclei around A=70
close to the N=Z line was performed by combined
conversion-electron and gamma spectroscopy of
nuclei produced in a fragmentation reaction [1]. A
73 MeV/A 78Kr beam delivered by the GANIL facility
was fragmented on a 9Be target and the fully stripped
fragments were separated in flight using the LISE3
spectrometer. The 74Kr (72Kr) ions were produced at a
rate of ~240 (~3) particles/s with a purity of 18% (0.4%)
and identified event-by-event through time-of-flight
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and energy loss in a stack of Si detetctors, before
being implanted in a 25µm thick Kapton foil. The
detection setup surrounding the catcher foil comprised
two segmented EXOGAM Clover detectors, a
low-energy photon detector, and a Si(Li) detector for
the conversion electrons at 90° to the beam axis.
Since the ions are fully stripped while passing
through the LISE spectrometer, the decay of isomers
proceeding predominantly through internal conversion
is partially blocked and isomers with a lifetime much
shorter than the time of flight through the spectrometer
can be observed. The conversion-electron spectrum
of 72Kr is shown in Fig. 1. The two lines correspond
to the K and L conversion of a 671 (2) keV transition.
No corresponding γ transition was observed as
expected for a E0 transition. This observation
establishes a new 0+ state as the first excited state
in 72Kr. The lifetime was measured to be 38 (3) ns,
which results in an electric monopole strength of
ρ2 = (72±6) 10-3. The excited 0+ state at 508 keV in
74
Kr was confirmed in the same experiment and
the strength of the E0 transition measured to be
ρ2 = (85±19) 10-3.
The low-spin level schemes of neutron-deficient
Kr isotopes are also shown in Fig. 1. The energies of
the excited 0+ states show a parabolic behavior with
a minimum at 74Kr. The energies of the unperturbed
states can be extrapolated from the regular rotational
bands observed at higher spins. The mixing amplitudes
for the prolate and oblate configurations can be derived
from the energy difference of the perturbed and
unperturbed states. This analysis shows a transition
from an almost pure prolate ground state in 78Kr to a
maximum mixing in 74Kr to an oblate ground state in
72
Kr. This scenario is also supported by the measured E0 strengths.
Nuclear structure
Fig. 1: Top left: Systematics of excited 0+ states in neutron-deficient Kr isotopes and other low-spin states.
Bottom left: Conversion-electron spectrum obtained in coincidence with 72Kr ions. Top right: Gamma-ray spectrum from
Coulomb excitation of 76Kr on 208Pb at large impact parameter; bottom right: same for small impact parameter.
Coulomb Excitation of 74Kr and 76Kr
Electromagnetic matrix elements can be directly
determined measuring Coulomb excitation cross
sections. In favourable cases also static moments
(including the sign) can be obtained using the reorientation effect, allowing thus a direct measurement of
the shape of a nucleus. Neutron-deficient β-unstable Kr
isotopes were produced by fragmentation of a
~70 MeV/A 78Kr beam on a C target. The fragmentation
products were extracted using the ISOL technique
and re-accelerated in the CIME cyclotron of the
SPIRAL facility at GANIL. High-quality beams of 76Kr
and 74Kr with intensities of 5 105 and 104 ions/s,
respectively, were Coulomb excited on thin 208Pb and
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Ti targets at energies well below the Coulomb
barrier [2]. Gamma rays were detected in the EXOGAM
array of segmented Clover Ge detectors. Scattered
beam particles and recoiling target nuclei were
detected in a double-sided segmented annular Si
detector, allowing a precise Doppler correction and a
measurement of the differential Coulomb-excitation
cross sections. By measuring both scattered projectiles
and recoiling target nuclei, a large angular range
in was covered in the center-of-mass frame. The
coincidence requirement between particles and γ-rays
eliminated the background from the radioactive
beam almost completely. Gamma-ray spectra obtained
from the 76Kr experiment are shown in Fig. 1. Matrix
elements have been extracted from the measured
excitation probabilities using the code GOSIA. The
transition matrix elements for the ground-state band
in 76Kr result in a constant quadrupole moment of
Q0 = 2.8 eb. The principal new result concerns the
static quadrupole moment of the first 2+ state deduced
from the diagonal matrix element to be Q0 = 2.6 (3) eb.
The positive sign indicates that the deformation is
indeed prolate as expected from the high-spin
structure. This measurement is the first determination
of a static quadrupole moment from a radioactive-beam
Coulomb excitation experiment. The data for
higher-lying states and those for 74Kr are still under
evaluation.
[1] E. Bouchez et al., Phys. Rev. Lett. 90 (2003) 082502.
[2] E. Bouchez et al., Proceedings RNB6 conference,
Argonne 2003, to be published.
Contact: Andreas Görgen
[email protected]
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