Effects of diabaticity on fusion of heavy nuclei in the dinuclear model ...

to the dependence <strong>of</strong> the diabatic occupation probabilities n due diab on time expressed by the
α
relaxation equations [51, 52, 57]
dndiab(λ, t)
α
dt
t) τ(λ, [ndiab
α
= − 1
(λ, t) − n adiab
α (λ)], (6.4)
which is known in the relaxation-time approximation. Due to the residual two-body inter-
actions, the diabatic occupation probabilities approach a local (fixed λ) equilibrium with an
average relaxation time
τ(λ, t) =
2¯h
< Γ(λ, t) > . (6.5)
The factor 2 assumes that two subsequent collisions are sufficient to establish equilibrium for
fixed values <strong>of</strong> the collective variable λ (local equilibrium). Here, we use a minimal value <strong>of</strong>
this factor (or minimal possible value <strong>of</strong> τ) in comparison to Refs. [51, 52, 57] where this factor
was chosen as 3—4. From the (6.1) it is clear that the effective time τ necessary to reorganize
the densities <strong>of</strong> the system corresponds to a mean value <strong>of</strong> various relaxation times associated
with the shape degrees <strong>of</strong> freedom <strong>of</strong> the system. This effective relaxation time τ is larger than
average single-particle decay time ( the ¯h ) due to the effect <strong>of</strong> a self-consistency between
collective and intrinsic degrees <strong>of</strong> freedom [86, 107]. The width in Eq. (6.5)
Γ(λ, t) >= <
α
n diab
α (λ, t)Γα(λ)/ an average width <strong>of</strong> the particle-states above the Fermi level (n is diab
α
<strong>of</strong> the hole-states under the Fermi level (n and diab
α
α
n diab
(λ, t) (6.6)
α
ndiab
α =
ndiab
α for ɛ =1− diab ≤ ɛF ).
α
ɛ for diab
α
>ɛ F )
For the widths Γ α, the expression (5.31) is used. In the calculations we take the standard
c=20 MeV and consider the cases with two extreme values <strong>of</strong> Γ value −1
0 : 0.030MeV−1and 0.061MeV −1 . The results depend weakly on the value <strong>of</strong> the parameter c. From (5.31), one
see that for very large free energies ɛ can diab − ɛF the broadening <strong>of</strong> single-particle widths
α
due to intrinsic excitation energy <strong>of</strong> the system plays no essential role in contrast to the case
when the excited system is near the equilibrium state [108]. Although one may define a local
excitation energy during the decay <strong>of</strong> the diabatic potential to the adiabatic one, the concept
<strong>of</strong> temperature is less meaningful as the system is not locally equilibrated or thermalized [109].
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