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

with χ(0) and C(0) being the static intrinsic response and stiffness, respectively. Since the
constant k is entirely determined by quasi-static properties, it is no surprise that E is the internal
energy at a given entropy S0 or the free energy at a given temperature T0. The structure <strong>of</strong>
Eq.(B.2) reflects self—consistency between the treatment <strong>of</strong> collective and microscopic dynamics.
It expresses the response <strong>of</strong> the system <strong>of</strong> interacting nucleons in terms <strong>of</strong> the response <strong>of</strong> the
individual nucleons.
In the local harmonic approximation [86], the inverse <strong>of</strong> the collective response function
χ −1
(ω) is considered as the inverse <strong>of</strong> the damped oscillator response function χ−1
osc (ω) which
coll
is expressed as
χ −1
osc (ω) =C F iγ − F − M ω F ω 2 (B.5)
,
where C F , γ F and M F are related to the derivative <strong>of</strong> the effective collective potential, calcu-
lated in linearized form, to a friction force and to an inertial one, respectively. The associated
”transport coefficients” have been marked by a superscript F to indicate that they are asso-
ciated with the quantity δ< ˆ F >. The transport coefficients T¸= M,γ,C <strong>of</strong> the Q-mode are
related to the transport coefficients T¸ F = M F ,γ F ,C F <strong>of</strong> the δ< ˆ F >-mode by the relation
T¸ F k = 2 [86]. An expression like (B.5) may be obtained by expanding χ T¸ −1
(ω) (B.2) to second
coll
order in ω. In this way one gets
C ≈
γ ≈ 1
1
k 2 χ coll (ω)
k 2
M ≈ 1
2k 2
∂χ −1
coll (ω)
| ω=0,
∂ω
∂2χ −1
coll (ω)
117
∂ω 2
|ω=0, (B.6)
|ω=0 .