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

As a result <strong>of</strong> Fig. 5-2, we find that the microscopical mass parameters keep the system
near the entrance configuration for a sufficient long time comparable with the time <strong>of</strong> reaction
even in an adiabatic potential. Therefore, this situation justifies the assumption <strong>of</strong> a fixed neck
as we assume it in the DNS model [34]. When the DNS configuration exists a long time, then
thermal fluctuations in the mass asymmetry coordinate play the essential role in the fusion
process. Indeed, these fluctuations are responsible for the fusion in the DNS model. Thus, the
dynamical restriction for the growth <strong>of</strong> the neck can be caused partly by a large microscopical
mass parameter for the neck motion, partly by the potential energy surface intermediate between
diabatic and adiabatic limits.
In the adiabatic two-center shell model, the mass parameter M εε slightly increases with the
deformation parameters β i <strong>of</strong> the two nuclei in the symmetric system 110 Pd+ 110 Pd as shown in
Fig. 5-3. The small variation <strong>of</strong> Mεε is due to the shell structure. Therefore, the relatively large
value <strong>of</strong> M εε is a general result for collisions <strong>of</strong> both spherical and deformed nuclei. Fig. 5-4
shows the mass parameter M εε at the touching configuration <strong>of</strong> symmetric systems η = 0 with
βi = 1as a function <strong>of</strong> the mass number A = A1 + A2 =2A1. The mass Mεε increases with
the mass <strong>of</strong> the system. It slightly decreases with increasing mass asymmetry <strong>of</strong> the DNS.
5.2.2 The diabatic two-center shell model
Let us now consider the calculation <strong>of</strong> the mass parameters (5.32) with the diabatic single
particle energies obtained with the method <strong>of</strong> maximum-symmetry in the diabatic two-center
shell model [35, 57]. In the diabatic motion, the nucleons do not occupy the lowest single
particle states as in the adiabatic case, but remain in their diabatic states. In comparison to
the calculations with the adiabatic single particle levels, the numerical procedure with diabatic
single particle levels is much easier because each level has a complete set <strong>of</strong> quantum numbers
and the drawing <strong>of</strong> the levels as a function <strong>of</strong> a collective variable is simpler and unique.
Due to the nonzero width <strong>of</strong> the single particle states, the distribution <strong>of</strong> single parti-
cle strength over more complicated states is a Lorentzian distribution ρk(ɛ) as introduced in
(5.28) instead <strong>of</strong> the δ-function δ(ɛ − ɛk) [86]. The occupation number n(ɛ k)<strong>of</strong>astatek
Eq.
energy ɛk and the corresponding value <strong>of</strong> fk with
71
are obtained, respectively, from functions