A New Region of Superdeformed Nuclei

R.M. Clark^1^, P. Fallon^1^, A. Görgen^1^, M. Cromaz^1^, M.A.
Deleplanque^1^, R.M. Diamond^1^, G.J. Lane^1^, I.Y. Lee^1^,\
A.O. Macchiavelli^1^, R.G. Ramos^1^, F.S. Stephens^1^, C.E. Svensson^1^,
K. Vetter^1^, D. Ward^1^, M.P. Carpenter^2^,\
R.V.F. Janssens^2^, R.Wadsworth^3^

*^1^ Nuclear Science Division, Lawrence Berkeley National Laboratory,
Berkeley, California 94720\
^2^ Physics Division, Argonne National Laboratory, Argonne, Illinois
60439\
^3^ Department of Physics, University of York, Heslington, York, YO1
5DD, UK*

![](media/image1.png){width="3.0in" height="2.095833333333333in"}Within
the framework of the nuclear harmonic--oscillator model one expects the
existence of favorable shell gaps that appear regularly as a function of
deformation and nucleon number. They are predicted to occur for
particular magic numbers and at deformations corresponding to integer
ratios of the lengths of the major--to--minor axes (e.g. for
superdeformed (SD) nuclei, with a quadrupole deformation of ε2=0.6, the
ratio is 2:1). SD structures which have a major--to--minor axis ratio
close to 2:1 have been found in nuclei of the A≈150 (close to 152Dy) and
A≈240 (close to 236U) mass regions. In the A≈190 region the
superdeformed structures have a slightly smaller axis ratio of \~1.7:1.
Lighter mass regions near A\~130, 80, and 60 have also been described as
being regions of superdeformed nuclei but generally one ﬁnds these
structures to have much smaller differences in the deformation from the
normal--deformed states. Many of the models that explain SD nuclei
predict additional minima in the potential energy surfaces at even
larger deformations that correspond to prolate shapes with
major--to--minor axis ratios of about 3:1. These are the
long--sought--for hyperdeformed nuclei and they are generally predicted
to become yrast at very high angular momentum. It is questionable
whether hyperdeformed structures can survive ﬁssion since the
corresponding barriers tend to be very small at these high angular
momentum values. Observation of hyperdeformation would have a profound
impact on our understanding of ﬁssion barriers and shape
parameterizations, and provide a stringent test of theoretical models.

Recent calculations by Chasman \[1, 2\] using the cranked Strutinsky
method and a four--dimensional shape space representing quadrupole,
octupole, hexadecapole, and necking degrees of freedom, predict that a
region of shape minima at deformations with 2:1 axis ratios (or larger)
exist at high angular momentum in nuclei with A\~110. In fact, the
calculations ﬁnd that many nuclei have minima in the potential energy
surfaces corresponding to a variety of extended nuclear shapes. For Cd
the calculations predict a minimum in the potential energy surface
corresponding to a shape with an axis ratio of 2.3:1 which becomes yrast
at I≈60. The very extended minimum results from the large shell
corrections for both protons and neutrons at this deformation, which
lies intermediate between super-- and hyperdeformation. Moreover, the
outer barrier to ﬁssion is calculated to be \>9 MeV at I=60 and \>6 MeV
at 70 implying that the nucleus at this deformation is stable against
ﬁssion and that it should be possible to observe the discrete gamma--ray
decay of states in this minimum over a range of angular momentum.

Motivated by such considerations we have performed an experiment, at the
ATLAS facility of the Argonne National Laboratory, using the Gammasphere
array to search for very extended nuclear shapes with predicted
deformations of ε~2~≥ 0.6. Shown in Fig. 1 is an SD band which has been
assigned to ^108^Cd. Away from band crossings, the mass--scaled moment
of inertia is very similar to that of the yrast SD band in ^152^Dy. A
Doppler Shift Attenuation measurement indicates a lower limit of the
transitional quadrupole moment of Q~t~ ≥9.5 eb. These facts suggest a
very extended quadrupole ellipsoidal shape of the nucleus, with a
major--to--minor axis ratio ≥1.8. This is amongst the most deformed
structures ever seen and it cannot be ruled out that the band may have a
major--to--minor axis ratio ≥2:1 as predicted by Chasman. Moreover,
calculations of very extended minima with low predicted ﬁssion barriers,
as expected in the case of ^108^Cd, present a considerable challenge to
theory and such studies may point the way to ﬁrmer predictions of stable
hyper deformed nuclei accessible to experimental investigation.

FIG. 1: Spectrum of a superdeformed band in ^108^Cd.

References

\[1\] R. R. Chasman, Preprint PHY-9018-TH-98, Argonne National
Laboratory (1998).

\[2\] R. R. Chasman, Phys. Rev. C 64, 024311 (2001).