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

following ratio in the limit <strong>of</strong> an irrotational flow was derived in [100]
M irr
/γ ν
irr
= ν
where β is the coefficient <strong>of</strong> the two-body viscosity and r0 =1.2 fm.
3A2/3 1
(5.24)
,
β 1)r0 − +1)(ν 8π(2ν
5.1.3 Derivation from the mean—field cranking formula
Using the single particle spectrum ɛα and the corresponding wave functions |α >, one can
obtain the mass parameter with the cranking formula [94]
M cr =¯h 2 α=β
| |2 n(ɛα) n(ɛβ) −
(5.25)
.
ɛα − ɛβ
In reality the Hamiltonian <strong>of</strong> the system contains a residual two-body interaction between the
nucleons in addition to the mean field. The residual coupling distributes the strength <strong>of</strong> single
particle states over more complicated states. This spectral smoothing has the effect that the
sum over α and β appearing in (5.25) also includes diagonal terms with α = β. Let us prove
this statement.
The Eq.(5.25) can be rewritten as
M cr =¯h 2
α=β
Next we use the following replacements
and the approximation
dɛ1δ(ɛ1
dɛ2 − ɛα) δ(ɛ2 2 n(ɛ1) n(ɛ2) −
(5.26)
.
ɛ1 − ɛ2
Γ
(ɛ − ɛk) 2 +(Γ/2) 2
, (5.27)
(5.28)
D 2 2 k1k2 | ≈|F 2 (5.29)
.
Here, D =1/g is the average energy distance between single particle states. We then express
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