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

the mass (5.26) as
M cr = ¯h2 Γ 2
4π 2
α=β,k1,k2
|Fk1k2 |2
[ɛ 2 αk1 +(Γ/2)2 ][ɛ 2 βk2 +(Γ/2)2 ]
n(ɛk1
− n(ɛk2 )
)
(5.30)
.
ɛk2 − ɛk1
The energy spreading <strong>of</strong> the single particle states is taken into account in Eq.(5.30). A line
broadening happens if collisions <strong>of</strong> particles and holes with the background result in single
particle and single hole strength functions that are concentrated around the original single
particle energies. The quantity Dρk determines the average strength function for a particle in
state k [101]. In the limit ɛk1 = ɛk2 = ɛk, for ɛα ≈ ɛk and ɛβ ≈ ɛα, i.e. when two neighboring
levels near the level k are considered, and 8/π 2 ≈ 1, Eq.(5.30) leads to Eq.(5.15). Thus, diagonal
terms in the mass parameters appear because <strong>of</strong> the finite width <strong>of</strong> the single particle levels
due to the residual interaction.
5.2 Results <strong>of</strong> the calculations
5.2.1 The adiabatic two-center shell model
Since collisions above the Coulomb barrier are discussed, we firstly consider spherical nuclei
with βi = 1and then analyse the deformation effects.
In order to calculate the width <strong>of</strong> the single particle states, we use the expression [86, 102]
= Γk 1
Γ0
(ɛk − ɛ F ) 2 +(πT0) 2
1+[(ɛ k − ɛ F ) 2 +(πT0) 2 ]/c 2 . (5.31)
Here, ɛ F is the Fermi energy. Both parameters Γ0 and c are known from experience with the
optical model potential and the effective masses [86]. Their values are in the following ranges:
0.030 MeV −1 ≤ Γ0 −1 ≤ 0.061MeV −1 , 15 MeV≤ c ≤ 30 MeV. The quadratic dependence <strong>of</strong> the
numerator can be obtained from the collision term in the Landau theory <strong>of</strong> Fermi liquid [103]
and has been also verified within a microscopic approach based on an effective interaction <strong>of</strong>
Skyrme type [104]. Since each single particle state has its own width, Eq. (5.15) is generalised
as (Q i = λ, η, η Z,ε,β1,β2):
M diag
ij
=¯h2 k
65
k f
Γ2 ∂ɛ k
∂Qi k
∂ɛ k
∂Q j
. (5.32)