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

The half-decay width is obtained from Eq.(5.18) as
=¯h
Γn
m
w(n → m +¯hω). (5.19)
With the fluctuation-dissipation theorem for small temperatures we have [99]
< ¯hω| | ˆ > | F|0 2 = ρqs(¯hω)d(¯hω) 2 ¯hω
(5.20)
R(ω)dω
with the relaxation function defined as R(ω) =χ ′′
χ function ′′
[86] and a Taylor expansion
(ω)
= R(ω) χ′′ (ω)
ω
1
=
ω
χ ′′
=0)+ (ω ∂χ′′
(ω)
∂ω
ω=0
π
2
(ω)/ω. Using the properties <strong>of</strong> the response
+ ω 1
2
(ω)
∂ω2 ∂ 2 χ ′′
ω=0
ω 2 + ...
, (5.21)
we calculate the integral in (5.18). We then replace w(n → m +¯hω) in (5.19) by (5.18).
Considering the standard formula for mass Mn (En = Em)
Mn = ¯h2
2 ( m | | 2 [En − Em ])
−1 , (5.22)
which is obtained from the relation Mn =¯h 2 () −1 [94], we obtain by setting
Γ=Γn and M = Mn
= M ¯h ∂χ
Γ
′′
(ω)
∂ω | = ω=0 ¯h
γ(0). (5.23)
Γ
Large temperatures in (5.20) effectively lead to a temperature dependence <strong>of</strong> Γ in (5.23). Since
γ(0) in Eq. (5.9) contains the terms with the diagonal matrix elements <strong>of</strong> the operator ˆ F,the
mass parameter M also has the diagonal component M diag (5.15). So, the contributions to the
mass parameter can be again classified as those with diagonal and nondiagonal matrix elements,
respectively.
That the mass parameter is proportional to the friction coefficient (see Eq. (5.23)), has an
analogy in the hydrodynamic model. For multipole moments ν <strong>of</strong> the nucleus with ν>1,the
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