The Shape of the 216Rn Nucleus Close to the Fission Limit
M. Kmiecik1, A. Maj1, B. Million2, M. Brekiesz1, W. Królas1, W. Męczyński1, J. Styczeń2, M. Ziębliński1,
A. Bracco2, F. Camera2, G. Benzoni2, S. Leoni2, O. Wieland2, S. Brambilla2, B. Herskind3, M. Kicińska-Habior4,
N. Dubray5, J. Dudek5, N. Schunck6
1 The Henryk Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland, 2 Dipartimento di Fisica and
INFN, Milano, Italy, 3 The Niels Bohr Institute, Copenhagen, Denmark, 4 Warsaw University, Warsaw, Poland, 5 Institut de Recherches
Subatomiques, Strasbourg, France, 6 Department of Physics, University of Surrey, Guildford, UK
II. THE EXPERIMENT
The experiment was performed at LNL in Legnaro
using 96 MeV 18O beam bombarding the self-supported
target 198Pt of 1 mg/cm2. This bombarding energy was
chosen to lead to the angular momentum distribution with
lmax ≈ 42 , which is slightly larger than the critical spin for
fission (≈ 40 ) and therefore allows for a good population
of the isomeric states. The high-energy -rays were
measured in 8 large BaF2 detectors of the HECTOR array
[4] while the prompt, low-energy transitions, were detected
in 38 small BaF2 detectors arranged in honey-comb mode
above and below the target location and providing the sumenergy and the ray fold. The residual nuclei, ejected
from the target, were stopped in a 8 m thin Mylar catcher,
having central 6 mm hole for the beam. The catcher was
positioned in the forward direction at a distance of 40 cm,
reached by the recoiling nuclei in about 150 ns. The
delayed radiation emitted by the stopped residues was
detected in a cylindrical eight-segmented BGO shield,
which was put on the beam pipe to surround the catcher. A
Ge-detector was installed near to the reaction chamber at
146o for discrete -radiation measurement. In order to be
able to measure the delayed transitions, we used a pulsed
beam providing pulse with the width of 10 ns every 400 ns.
To study the shape of 216Rn we analyzed the highenergy -rays in coincidence with the multiplicity filter or
-rays in coincidence with the multiplicity filter and the
total fold 9-30
MC casc.
total fold 5-8
MC casc.
6
10
5
10
4
10
3
10
2
10
1
10
6
10
14
18
6
10
14
18
E [MeV]
Fig. 1) The high-energy experimental spectra (points)
corresponding to selected low- and high-fold regions and the best
fit Monte-Carlo calculations (lines).
4
10
isomer gated
MC casc.
212
Rn, I>=35
MC casc.
fold 5-30
3
10
Y [a. u.]
The nuclear shape evolution of rotating and hot 216Rn
nucleus has been studied up to the fission limit by
measuring the high-energy -rays coming from Giant
Dipole Resonance (GDR), after the fusion-evaporation
reaction 18O+198Pt.
The decaying 216Rn compound nucleus strongly feeds
the long-lived, high-spin (close to the fission limit)
isomeric states of I=30+ (T1/2=154 ns) in 212Rn and
I=63/2- (T1/2=201 ns) in 211Rn. Therefore the selection of
the GDR decay in coincidence with delayed -ray
transitions are expected to probe mainly the compound
nuclei which survive fission, yet with angular momentum
close to the fission limit.
BGO detector (gated with the time of flight).
Y [a. u.]
I. INTRODUCTION
2
10
1
10
6
10
14
18
E [MeV]
Fig. 2) The experimental high-energy spectrum gated by the
isomer decay is shown with the filled circles. The dashed line is
the statistical model Mont-Carlo calculation corresponding to the
fold interval 5-30. The calculation presented with solid line has
the same GDR parameters as for the dashed line, but includes the
gates on the 212Rn residual nucleus and on the high spin part of
the spin distribution (I≥35).
IV. COMPARISON WITH THEORY
The measured values of the resonance width are found
not to depend on spin. They are larger as compared to the
zero-temperature width (0 ≈ 4 MeV) in some other nuclei
in the mass range of interest. The fact that the width is not
changing indicates that the effective deformation is not
changing significantly with the spin, too. This observation
was investigated further using the calculated potential
energy surfaces and the Boltzmann factor distributions
with on the newest version of the Lublin-Strasbourg Drop
(LSD) model [5,6].
The theoretical GDR line-shape was obtained as a sum
of all possible line-shapes (for all deformation values)
weighted with the Boltzmann factor. From it the theoretical
GDR width was achieved and reported with the dashed line
in upper panel of Fig. 3. In the bottom part of the figure are
shown the equilibrium deformation (eq), average
deformation (<>) and the standard deviation of the 
distribution (<>). The equilibrium deformation is 0 up
to spin 30  and then slightly increases, while the standard
9
exp. fold gated
exp. isomer gated
calc. LSD
8
 [MeV]
The experimental high-energy -ray spectra were
compared with the statistical model predictions in order to
extract the GDR parameters. All the calculations were
performed using the Monte-Carlo version of the
CASCADE code.
The first step of the analysis was to obtain the
information on the GDR from the high-energy spectra
corresponding to the selection of the -fold in the
multiplicity filter. The GDR parameters (centroid and
width) were deduced from the chi-square minimization of
the calculation results to the experimental data. The spectra
and the results of the fit are shown in Fig. 1 for two fold
regions (corresponding to average spin 23 and 29). The
best fitting GDR line-shape parameterization was a
superposition of 3 Lorentzians. For all investigated spectra
best fitting GDR parameters were the same and the overall
GDR width was 7 MeV.
The isomer gated spectrum is shown in Fig. 2 in
comparison with the best-fit calculation result for the total
spectrum. It is seen that isomer gated spectrum has a
different shape in the region of Eγ>6 MeV, but this is only
due to the fact that the data correspond to a different spin
distribution (with average value of 37 ) as compared to
the total spectrum (26 ) and therefore it is related to a
different region of the phase space of the nuclear decay.
Indeed, the Monte-Carlo calculations using the same GDR
parameters as those of the total spectrum but selecting only
the cascades leading to the 212Rn nucleus and having the
entry spin larger than 34 , gives a good fit. This means
that the GDR width in this very high spin region, close to
the fission limit, is almost the same as for lower spins.
deviation is almost constant with angular momentum. Both
quantities determine the average deformation of
investigated nucleus, which is basically constant with spin,
similarly to the calculated GDR width.
7
6
0.5
eq
0.4
fission
<>
<>
0.3

III. STATISTICAL MODEL ANALYSIS
0.2
0.1
0.0
0
10
20
30
40
50
I [ ]
Fig. 3) Top panel: The GDR width as a function of spin obtained
for experimental data (points) in comparison with the GDR
width calculated using the LSD model (line). Bottom panel: The
LSD model predictions for the quadrupole deformation.
V. SUMMARY AND CONCLUSIONS
The present work has shown the possibility to study the
nuclear shape around the fission limit through the GDR decay in exclusive measurements selecting spins and using
the isomer tagging technique. The present study is the first
investigation of the GDR width in the fusion-evaporation
decay channel in this nuclear mass range. The hot 216Rn
nucleus investigated here was found to be almost spherical
up to the fission limit, in contrast to other studied cases
where high spins induce either a Jacobi shape transition or
a super-deformation. The obtained results are in an
excellent quantitative agreement of the newest LSD model.
This work has been supported by the Polish Committee
for Scientific Research (KBN Grant No. 2 P03B 118 22),
the Italian INFN, the LNL Legnaro and the Danish Science
Foundation.
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[2] T.S. Tveter et al., Phys. Rev. Lett. 76 (1996) 1035.
[3] G.D. Dracoulis et al., Phys. Lett. B246 (1990) 31.
[4] A. Maj et al., Nucl. Phys. A571 (1994) 185.
[5] K. Pomorski et al., Phys. Rev. C67 (2003) 044316.
[6] J. Dudek et al., Eur. Phys. J. A, in press (nucl-th/0205011).