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?A genuine N-body approach should cover the gap
between mean filed approach and equilibrium
statistical models
?We could characterize the results of the
dynamical model at long time by comparing the
correlations and the fluctuations produced by the
dynamics and by the equilibrium statistical
models.
?Correlations and fluctuations of some quantities
can be observables The mentioned comparison can
give a kind of operative definitions of
Temperature for a dynamical descriptions.
A relatively simple example is given by the study
of the pre-equilibrium GDR ?-ray emission from
hot nuclei and the correlations with the
fragments productions.
In a dynamical approach and in the semi-classical
limit ?-ray dipolar Emission is evaluated through
2 time derivative of the total dipole as
function of time and with the
related Fourier analysis
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CoMD model
N1/Z1?N2/Z2

• Incoherent contribution
• Collective
• Microscopic incoherent

Coherent contribution (ensemble average)
Mean field approach
Statistical models
Fully N-body dynamical approach for 1000 fm/c
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Ensemble average from CoMD calculations for the
40Ca48Ca system at 25 MeV/A
Source of strong anisotropy
b0 fm
b3.5 fm
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b0 fm E/A 25 MeV
Langevin prediction for the total system

• Prediction in the loc. Time
• equil. hypothesis

• Prediction according to a
• full CoMD approach

g12
M.Papa et al, PRC 68(2003) 024612
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35 MeV/A b0 fm
M.Papa et al, PRC 68(2003) 024612
? obtained from the fit procedure
Very small Coherent contribution
or
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High energy results Multi-fragmentation of the
hot source in passing from 25 to 35 MeV/A
Bending of Campi-plot in passing from 25 to 35
MeV/A
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Degree of coherence, degree of collectivity as
function of energy show critical behavior in
multifrag. processes.
M.Papa et al, PRC 68(2003) 024612,
Black rather smooth behaviour
40Ca 48Ca Central Collisions
Redit contains the Ambiguity related to the
experimental selections of 1 equilibrated source
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Greenhigh sensitivity related to the natural
time selection performed by the dynamic through
memory effects.
?c(0,tm)
?c(0,tf)
?ch(0,tf)