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

For the Fermi occupation numbers n(ɛk), the function
= − fk dnk
dɛk
= 1
cosh
4T0
−2
ɛF − ɛk
has a bell-like shape with a width T0 and is peaked at the Fermi energy ɛ F .
2T0
(5.33)
Various calculations <strong>of</strong> the mass parameter for the motion in λ were carried out with expres-
sions similar to Eq. (5.32), for example in [88, 91, 95]. When the system adiabatically moves
towards the compound nucleus, the value <strong>of</strong> M λλ increases approximately by a factor 10—15
in our and other calculations. In this section, we concentrate on the calculation <strong>of</strong> the mass
parameter M εε for the motion <strong>of</strong> the neck to test whether the DNS exists long enough with
a relatively small neck. The dependence <strong>of</strong> M εε on ε is presented in Fig. 5-1for the system
110 Pd+ 110 Pd at λ =1.6, which corresponds to the touching configuration in this symmetric
reaction. The obtained values <strong>of</strong> M εε have the same order <strong>of</strong> magnitude as in [88], where the
pairing correlations were taken into account. The value <strong>of</strong> M εε increases by a factor 2.5 when
the system falls into the fission-type valley [42]. This valley is observed in the adiabatic poten-
tial energy surface for ε =0− 0.2 andλ =1.6 − 1.7. This increase reflects the decrease <strong>of</strong> the
shell correction δU with ε towards ε → 0. Smaller values <strong>of</strong> δU correspond to larger masses
because the mass parameter is proportional to some effective level density g eff at the Fermi
The expression (5.15) could be written as M energy. diag ≈ ¯h2
Γ2
∂ɛk
∂Q
density g eff is in inverse proportion to the shell correction δU [95].
2
aver
g eff. The effective level
In order to obtain a nuclear shape for the touching configuration <strong>of</strong> the nuclei similar to the
one obtained in the DNS model, the neck parameter ε should be set about 0.75 [42]. With this
value <strong>of</strong> ε, the neck radius and the distance between the centers <strong>of</strong> the nuclei are approximately
equal to the corresponding quantities in the DNS.
For the parameter c in Eq. (5.31), we use the ”standard” value 20 MeV since the masses
depend only weakly on this parameter. Setting the parameter Γ (5.32) −1
0
and comparing our results with M (5.32) WW
ij
=0.045 MeV−1 in
obtained in the Werner-Wheeler approximation
for a touching configuration <strong>of</strong> the nuclei with the excitation energy 30MeV (T0 =1.3MeV ),
find Mλλ = M we WW,
Mεε ≈ (20 − 30)M λλ WW,
Mλε ≈ 0.4M εε WW and Mλε/ λε √ λλMεε ≪ 1,
M
practically independent <strong>of</strong> the mass number <strong>of</strong> the system. Therefore, we can conclude that
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