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

is chosen with the condition <strong>of</strong> the N/Z-equilibrium in the system, mass and charge evolutions
are described analogously. A diffusion process leads to the exchange <strong>of</strong> nucleons between the
two touching fragments, thus generating a time-dependent distribution in the Z(A) variables <strong>of</strong>
the DNS. This process can be described by a master-equation [33, 44, 73, 119] for the probability
PZ(t) <strong>of</strong> finding the system at the time t in the configuration with the charge number <strong>of</strong> the
light fragment Z. The asymmetric DNS evolves to a compound nucleus or to a symmetric DNS.
The melting <strong>of</strong> the DNS nuclei in variable R is strongly hindered [35, 36, 42, 66]. The decay
in R affects the motion <strong>of</strong> the system in Z. In order to take the effect <strong>of</strong> the DNS decay into
consideration, we can rewrite the known master-equation for PZ(t) [33, 44, 73, 119] as follows
∂PZ(t)
∂t =∆(−) (Z+1) P (Z+1)(t)+∆ (+)
(Z−1) P − (∆ (Z−1)(t) (+)
Z +∆(−) Z
+Λqf
Z ) P (7.1)
Z(t),
where the microscopically calculated transport coefficients ∆ (±)
Λ and qf
Z
Z
given by the expression (4.3)
are
is the rate <strong>of</strong> decay probability in R. In the right side <strong>of</strong> Eq. (7.1), only the transitions
Z ⇀↽ Z + 1and Z ⇀↽ Z − 1are taken into account in the spirit <strong>of</strong> the independent-particle
model.
For decay, the DNS should overcome the potential barrier B qf, which coincides with the
depth <strong>of</strong> the pocket in the double-folding nucleus-nucleus potential as a function <strong>of</strong> R. The
bottom <strong>of</strong> this pocket corresponds to the distance Rm = R1+R2+0.5fm (Ri is the radius <strong>of</strong> the
nuclei). The values <strong>of</strong> the quasifission barriers B qf which depend on Z are mainly responsible
the lifetime t0 <strong>of</strong> the DNS. During this time, the DNS evolves in the variables Z. The decay
for
the DNS in R is treated using the one-dimensional Kramers rate <strong>of</strong> probability Λ <strong>of</strong> qf
Z
(6.9). In
our calculations, the values ¯hω Bqf =1.0 MeV and ¯hω =2.0 MeV are used for the reactions
considered.
The measurable quasi-fission charge (mass) yield is expressed through the formation prob-
PZ(t) <strong>of</strong> the DNS configuration with charge (mass) asymmetry Z and the decay probaability
in R described by the Kramers rate Λ bility qf
Z
Z(t0) =Λ Y qf
Z
95
t0
0
PZ(t)dt. (7.2)