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

B Here, j
i
the height <strong>of</strong> the fusion barriers Bλ
fus (t) andBη fus , and quasi-fission barrier
denotes
B λ . The values <strong>of</strong> Bη
fus qf
Bλ
qf and
are practically independent <strong>of</strong> time. The initial DNS <strong>of</strong>
the reactions considered here are in or near the minimum <strong>of</strong> the total potential energy <strong>of</strong> the
system as a function <strong>of</strong> λ and η. Moreover, they are in thermodynamic equilibrium because
the diabatic and adiabatic potentials practically coincide. The temperature T (λ t) is calculated
using the expression T (λ t)= E ∗ (λ t)/a where λ t is the elongation <strong>of</strong> the touching nuclei, i.e.
<strong>of</strong> the initial DNS. In the calculations we assume that the excitation energy <strong>of</strong> the initial DNS
is E ∗ (λ t)=30 MeV in all reactions considered. In (6.9), ω B j
i is the frequency <strong>of</strong> the inverted
harmonic oscillator approximating the potential in the variable j on the top <strong>of</strong> the fusion or
barriers B quasifission j
i ,andω is the frequency <strong>of</strong> the harmonic oscillator approximating the
j
j
the variable j for the initial DNS. The frequencies ωB i and ωj are calculated using
in potential
the absolute values <strong>of</strong> the second derivative <strong>of</strong> the potential with respect to the variable j (on
top <strong>of</strong> the barrier B the j
i
j
Mjj (e.g, ωB i = mass parameter |∂2V/∂j2 i B |
and for the initial DNS, respectively) as well as the corresponding
j
/Mjj ). The method <strong>of</strong> calculation <strong>of</strong> the mass
parameters Mηη and M λλ is presented in chapter 5 [43]. The microscopical values <strong>of</strong> Mηη and
Mλλ are close to the corresponding hydrodynamical values [84] at the touching configuration <strong>of</strong>
the nuclei (see chapter 5). In our calculations <strong>of</strong> the fusion probabilities, the following values
B λ
η
qf ≈ B
0.8—1.0 MeV, ¯hω fus ≈ 1.5—2.0 MeV, ¯hωλ ≈ 1.5—2.0 MeV and ¯hωη ≈ 0.8—1.0
¯hω used are
B
λ
reactions considered. The value <strong>of</strong> ¯hω fus at the inner fusion barrier in λ is about
the for MeV
0.5—0.6 MeV and agrees with the one obtained in the calculations <strong>of</strong> fission [116] at the saddle
point. The friction coefficients ((5.9) and (5.23)) in λ and in η obtained with Γ=2 MeV at
the touching configuration λt have the same order <strong>of</strong> magnitude as the ones calculated within
the one-body dissipation models [34]. The values obtained for P λ(η)
fus
rather weakly on
depend
Γ in (6.9)[34]. The possibility to apply the Kramers expression to relatively small barriers
(B j
/T > 0.5) was demonstrated in [117].
i
6.1 Results and discussion
The time-dependent diabatic potentials for the reactions 110 Pd+ 110 Pd and 124 Sn+ 124 Sn are
in Figs. 6-2a and 6-2b. The time-dependent inner fusion barrier B presented λ
fus
87
in λ appears