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

fusion and quasi-fission processes after the capture stage in the DNS. In these reactions the
quasi-fission channel dominates and leads to a strong reduction <strong>of</strong> the magnitude <strong>of</strong> the fusion
cross-section. The surviving probability Wsur estimates the competition between fission and
neutron evaporation in the excited compound nucleus and may be calculated according to the
statistical model [39] on the basis <strong>of</strong> the Monte Carlo method.
1.2 Goals <strong>of</strong> the present work
The basic microscopical model for the dinuclear system is the two-center shell model (TCSM)
[40] (see Appendix). The usual parametrisation <strong>of</strong> the two-center potential consists <strong>of</strong> the
relative distance between the centers (or elongation), the mass (charge) asymmetry η =(A1 −
A2)/(A1 + A2), the deformations <strong>of</strong> the fragments β i and the neck coordinate ε. The elongation
λ = l/(2R0) measures the length l <strong>of</strong> the system in units <strong>of</strong> the diameter 2R0 <strong>of</strong> the spherical
compound nucleus. This variable can be used to describe the relative motion. The mass ratio
between the fragments and the transition <strong>of</strong> the nucleons through the neck are described by the
mass asymmetry η. The neck parameter ε = E0/E ′ is defined by the ratio <strong>of</strong> the actual barrier
height E0 to the barrier height E ′ <strong>of</strong> the two-center oscillator. The deformations β i = a i/b i
<strong>of</strong> axial symmetric fragments are defined by the ratio <strong>of</strong> their semiaxes. The neck grows with
decreasing ε (Fig.1-3). The potential energy surface (PES) in these coordinates is generally
calculated with the Strutinsky method [41]. This is an adiabatic approach since the nucleons
occupy the single particle states up to the Fermi level in calculating the shell corrections.
The adiabatic potential energy surfaces calculated as functions <strong>of</strong> the elongation <strong>of</strong> the
DNS and <strong>of</strong> the neck parameter were used to study classical trajectories for various heavy ion
reactions by using dissipative forces and mass parameters obtained with the Werner-Wheeler
aproximation [42]. The fusion probabilities in the adiabatic TCSM are much larger than those
obtained from experimental data and show an incorrect isotopic dependence.
The reactions considered were for example the symmetric ones 90 Zr+ 90 Zr, 100 Mo+ 100 Mo,
110 Pd+ 110 Pd, 124 Sn+ 124 Sn and 136 Xe+ 136 Xe and asymmetric ones. Therefore, it is concluded
that a hindrance exists which prohibits the fast growth <strong>of</strong> the neck and the motion to smaller
elongations and allows the DNS to survive a time comparable with the reaction time.
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