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

where the lifetime t 0 <strong>of</strong> the DNS is obtained with the condition
t0
0
[Λλ fus (t)+Λη fus (t)+Λλ (t)]dt =1. (6.8)
qf
rate <strong>of</strong> probability Λ The λ (t) through the external barrier in λ determines the quasi-fission
qf
(the decay <strong>of</strong> the system). The height B process λ
qf
<strong>of</strong> this barrier monotonically decreases
with the mass asymmetry <strong>of</strong> the DNS because the Coulomb repulsion increases with decreasing
η and leads to very shallow pockets in the nucleus-nucleus potential for the near symmetric
configurations. Therefore, the quasi-fission probability for a symmetric and near symmetric
DNS is much larger than for an asymmetric one. The reactions considered in this chapter are
symmetrical or near symmetrical and, correspondingly, their initial DNS configurations are in
or near the minimum <strong>of</strong> the potential energy <strong>of</strong> the systems as a function <strong>of</strong> λ and η. In this
case the main contribution to the quasi-fission channel comes from the initial or near initial
which have approximately the same quasi-fission barrier B configurations λ . Indeed, in reactions
qf
with heavy nuclei the experimental data do not show relaxation in η and have their maximal
yields <strong>of</strong> the quasi-fission products near the initial DNS [112, 113]. All these facts allow us
to calculate the quasi-fission rate for the initial DNS with a Kramers-type expression. It was
proved in calculations with the multidimensional Fokker-Planck equation that the use <strong>of</strong> the
B value λ
qf
for the initial DNS is a good approximation even for asymmetric reactions [34]. The
quasi-fission decay process in λ determines the lifetime <strong>of</strong> the DNS mainly because the barrier
B λ
qf
smaller than the barrier Bη
fus is in η. The lifetimes t0 for the reactions considered
obtained
are comparable with the experimentally extracted characteristic fusion times <strong>of</strong> 10 −21 − 10 −20 s
[114]. Since the effect <strong>of</strong> the transient times for stationary rates <strong>of</strong> probability over the fusion
quasi-fission barriers is weak [34] and their contribution is <strong>of</strong> the order <strong>of</strong> the accuracy <strong>of</strong> the
and
<strong>of</strong> the barrier heights, we use the one-dimensional Kramers expression [115] ( calculation Kr Λ j
i =”fus”or”qf ”andj =”λ” or”η”) which is a quasi—stationary solution <strong>of</strong> the Fokker-Planck
equation for the corresponding rate <strong>of</strong> probability
j Kr
i Λ =
ωj
j
i B 2πω
⎛
( ⎝ Γ
2¯h )2 +(ω
86
j
i ) B
2 − Γ
2¯h
⎞
exp(− ⎠ Bj
i
i ,
T (λ t) ). (6.9)