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

γ nondiag (0) [86]. The zero-frequency limit <strong>of</strong> the intrinsic response function defined as [86]
is expressed as follows
where
= lim
χ(0)
ɛ→0
+∞
−∞
dω
π
χ ′′
(ω)
− iɛ ω =lim
ɛ→0
+∞
−∞
dω
¯hπ
tanh( ¯hω
2T0 )ψ′′ (ω)
ω − iɛ
(5.11)
χ(0) = χ diag (0) + χ nondiag (0), (5.12)
χ diag (0) =
k
∂n(ɛ)
∂ɛ
ɛ=ɛk
2 ∂ɛk
∂Q
. (5.13)
With realistic assumptions γ diag (0) ≫ γ nondiag (0) and χ diag (0) ≫ χ nondiag (0) and neglecting
C(0)/χ(0), we can divide the mass parameter (5.2) as
The contribution <strong>of</strong> the diagonal matrix elements <strong>of</strong> ˆF to M are
M diag = (γdiag (0)) 2
χdiag (0)
M = M diag + M nondiag . (5.14)
¯h2
=
Γ2
k
∂n(ɛ)
∂ɛ
∂ɛk
2
ɛ=ɛk
∂Q
. (5.15)
If the single particle widths are properly taken into account, the nondiagonal contributions to
the inertia are [88]
M nondiag = M cr =¯h 2
k=k ′
|Fkk ′ |2
ɛ 2
kk ′ +Γ2 − n(ɛk ′ )
n(ɛk)
(5.16)
.
ɛ k ′ −
ɛ k
The main contribution to M is the diagonal part M diag (e.g., ∼ 102 for
the fission <strong>of</strong> 240 Pu [91]), because it dominates for collective variables which are responsible for
changes <strong>of</strong> the nuclear shape <strong>of</strong> the system [89, 90, 91, 94]. Note that the calculation <strong>of</strong> M diag
is simpler than M nondiag . For the case that the pairing residual interaction is regarded and
only diagonal matrix elements in the cranking formula are taken into account, Eq. (5.16) was
obtained with Γ = ∆ (∆ is the pairing gap) in Ref. [91, 95]. Starting with an equation for the
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