One of the most striking results obtained in this domain are the recent
publications related to the so-called *nuclear caloric curve*. These
curves result from an independent measurement of both temperature T (via
measurement of ratios of isotopic yields) and excitation energy E^{*}
(via calorimetry) for a nuclear system. The upper part of Figure
shows the first of such measurements. One may notice the following features:
i) at low energy a square root dependence of T on E* as predicted for a
Fermi gas, ii) a indication of a *plateau* possibly corresponding
to a saturation of this temperature above an excitation energy of 3 MeV
per nucleon, followed by iii) a linear rise whose slope is close to the
one associated to an ideal gas. These features and a possible interpretation
of the *plateau* in terms of a *latent heat* could represent
a signal of the long sought *liquid-gas phase transition*. In a similar
measurement (lower part of Figure )
temperatures deduced from a series of isotopic ratios differ among each
other. These differences can be resolved by taking into account effects
such as the population of excited states, secondary decays, and excluded
volume.

The full lines in this figure show the predictions of a quantum statistical model where these effects are taken into account and where one assumes, for each excitation energy, an equilibrated state of given density and temperature. These results do not exhibit the simple features as shown in the upper part of Figure and it is presently investigated to what extent the differences can be attributed to expansion effects, to the time dependence of the temperature of the system, and to the fact that different isotopes freeze out at different times.

**Multifragmentation: Is equilibrium achieved? ...**

One of the most significant and recent breakthroughs
is the understanding that copious multifragmentation can indeed be achieved
if low nuclear densities are reached as indicated in the phase diagram
(Figure ).
Dynamical models show, e.g. for central collisions, that a first phase
of compression is followed by expansion leading to the low density region
where multifragmentation occurs. Using statistical models one finds significant
fragmentation only if the densities decrease well below normal nuclear
densities. Therefore, multifragmentation may be the experimental indicator
that the critical/spinodal region in the phase diagram has been reached.
It is, however, a subject of intense theoretical debate to what extent
the fragmenting systems is really equilibrated or still has a 'memory'
of the earlier phase. The present hypothesis is that the velocity of the
expansion which follows the primary compression depends on the symmetry
of the colliding nuclei, on the incident velocity and on the impact parameter.
If it is too small in order to reach sufficiently low densities the system
reaches a turning point and shrinks back to its initial density (see second
arrow in Figure ).
If the initial expansion velocity is sufficiently large, low densities
will be achieved and the medium will become unstable against *volume*
fragmentation producing a large number of nucleons and fragments. This
is, for such a scenario, the *freeze-out* configuration, comparable
to the *saddle point* in nuclear fission. Before this *freeze-out*
is reached, the dynamics of the expansion allows for the emission of nucleons
and fragments (in small numbers) from the surface, thus cooling the system.
The duration of the expansion, its velocity, the final densities reached
before break-up and the amount of cooling are questions that are addressed
and will be answered in the coming years. A question of special interest
arising from this scenario is *if and when* thermodynamical equilibrium
is reached and to what extent the observed fragment yields (Z,A) and spectra
are consistent with the statistical models applicable to such a situation.
A violent decompression phase or a strong thermal pressure will result
in collective radial flow. Decoupling this flow from the thermal motion,
the analysis of the production of intermediate mass fragments (IMF) by
statistical codes give generally an accurate description as long as the
size, the density and the excitation energy of the system at *freeze-out*
are adjusted freely. This is shown in Figure
and can also be seen in Figure .
Whether the values obtained for this configuration are also consistent
with the dynamics has to be verified for the various circumstances where
multifragmentation is observed. The evolution of the nuclear system formed
depends on the initial condition of the system: impact parameter, relative
velocity, mass asymmetry, total size of the system, etc.. This has led
experimental studies to look at the evolution of systems formed under very
different conditions: central collisions for symmetric systems where compression
effects are important, peripheral collisions (or central collisions of
asymmetric systems) for a more gentle heating of the nucleus. In most of
these cases, copious multifragmentation is found, extending up to the vaporisation
of the system. The large variety of beams accessible in Europe has clearly
been a remarkable asset in these studies.

**...Not necessarily**

The thermodynamical picture for the evolution of
hot nuclear matter is not the only one prevailing: such alleys as dynamical
effects, mechanical instability and percolative phenomena are suggested
and it needs to be studied how they relate to the equilibrium picture.
It is, for example, of importance to point out that the freeze-out configurations
are rather systematically located within the spinodal region (see Figure ).
In this region, any mechanical instabilities will rapidly grow and give
rise to multifragmentation. It is therefore a challenge for future studies
to disentangle which effect, mechanical instability or phase space, is
predominant for the production of the IMFs. The observation of a *power
law* behaviour for the size distribution of the fragments has triggered
a number of studies that have looked for evidence of *critical behaviour*.
These analyses consider nuclear multifragmentation as one example of a
*critical phenomenon* and attempts are made to extract from the data
the related critical exponents. Comparison with percolative and liquid-gas
systems show remarkable similarities. The existence of power law behaviour
in fragment size distributions still has to be fully understood and progress
in this type of critical analysis should eventually relate this nuclear
phenomenon to the various universal classes of fragmentation, including
thermodynamical processes. Not all experimental situations populating a
similar excitation energy range lead to copious multifragmentation: an
example is the heating of nuclear matter with high energy anti-protons.
In this case a strong reduction of IMF production is observed when comparing
to ion beams. Assuming that anti-proton heating leads to a well defined
equilibrated source, the production rates of IMFs observed are reproduced
with statistical codes using as input parameter normal nuclear density.
It is still necessary to understand the particular dynamical path followed
by a system heated with anti-protons, i.e. what initial excitation energy
is reached and how the system evolves to apparent equilibrium and statistical
decay.

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