At even higher spins, nuclear states with hyperdeformed shapes are predicted
by improved mean field calculations. Here we are still in the situation
with regard to superdeformation before 1986, i.e. there are signs of its
presence from some ridge structure but no discrete rotational bands have
been identified. Of course, the first step is to find such discrete bands
and then establish their hyperdeformed character from lifetime measurements.
We expect that they will be populated with an intensity at least one order-of-magnitude
smaller than that of superdeformed bands, which means that they lie at
the limits of sensitivity of the coming generation of large spectrometers.
EUROBALL may provide an answer to the question of the existence of states
with this exotic shape at high spins. Detailed studies of the properties
of such exotic shapes will demand more sophisticated spectrometers of even
greater sensitivity. Very elongated shapes are also predicted in light
nuclei. The most exotic examples involve chains of several
particles. To date their existence is deduced only from the observation
of resonances in light symmetric systems in binary reaction channels. On
the theoretical side, there are efforts to find more adequate microscopic
descriptions of nuclear rotation including three-dimensional cranking models,
generator co-ordinate projection methods, and large scale spherical shell
model calculations. It will also be of primary importance to establish
the role of time-odd components in the effective Hamiltonian/Lagrangian.
At lower angular momentum Coulomb excitation has been the main tool to
probe the collective properties of stable nuclei. A recent example is the
long sought observation of multi-phonon surface vibrations in strongly
deformed nuclei; future investigations will have to concentrate on the
elusiveness of two and higher phonon states and on the question of the
fragmentation of the vibrational strength. Multi-nucleon transfer reactions
with the multiple Coulomb excitation process provide the only promising
tool for populating collective states in heavy transactinide nuclei and
studying their behaviour at high angular momentum, which is important for
our understanding of the shell structure of the heaviest elements. With
the advent of radioactive beams we will also be able to investigate in
detail the collectivity of nuclei with exotic proton/neutron ratios. First
Coulomb excitation studies confirmed definitely the sudden shape change
in n-rich S isotopes and the fact that the semi-magic nucleus ^{32}Mg
is superdeformed. These findings encourage further investigations of the
structure of these nuclei as well as of heavier isotopic chains to study
the effect of the neutron excess on their shell structure (e.g. vanishing
shell gaps). To gain access to higher spin states up to almost 20 ,
peripheral nuclear fragmentation reactions can be employed. Relativistic
Coulomb excitation also leads to the population of the E1 giant dipole
resonance, thus providing an unorthodox approach to the ground state quadrupole
deformation of exotic nuclei via the splitting of the resonance. Alternatively,
Coulomb excitation with low energy radioactive beams may be used to determine
E3 octupole matrix elements of nuclei predicted to exhibit reflection asymmetry.
In addition, one should note that much of the information on the structure
of very neutron-rich nuclei at higher excitations with spins up to 14
have come from the studies, which employ spontaneous fission sources and
large Ge-detector arrays. Most of the examples discussed in this section
are associated with rather low production rates or can only be studied
in reactions with low intensity radioactive projectiles. To overcome these
difficulties, it is clear that a major effort has to be started right now
to develop more sophisticated arrays if we are to make a significant advance
both in efficiency and sensitivity.

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