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

to the DNS concept [18, 34], cross sections for the synthesis <strong>of</strong> the heaviest elements in nearly
symmetric reactions are very small due to large fusion barriers in mass asymmetry and, corre-
spondingly, due to small fusion probabilities, for example in the reactions 128 Sn+ 126 Sn→254 Fm
and 132 Sn+ 132 Sn→264 Fm.
4-1shows the fusion barriers B Table TCSM
η
in η calculated with the TCSM-method for the
reactions which produce the systems <strong>of</strong> the Figs. 4-1to 4-5. These barriers are compared with
the experimental surplus <strong>of</strong> energy ∆B exp = B exp −
above the Bass barrier BBass [76].
BBass
value <strong>of</strong> B The exp defined [4] as the value <strong>of</strong> the bombarding energy for a fusion probability
is
0.5. The Bass potential [77] is an empirical nucleus-nucleus potential derived from a geometric
interpretation <strong>of</strong> fusion data above the Coulomb barrier for systems with Z 1 ×
2 =64−850. Z
shown in Table 4-1, the isotopic trends <strong>of</strong> the fusion barrier, calculated with the TCSM-
As
method, agree with the experimental data. The experimentally observed hindrance <strong>of</strong> the
fusion roughly increases with a growing Coulomb repulsion between the colliding nuclei, but
also their shell structure and isotopic composition play a major role [78, 79, 80]. The energy
thresholds for fusion increase and, correspondingly, the fusion probabilities decrease [79, 80]
when the neutron number <strong>of</strong> projectile or target increasingly deviates from a magic number in
the reactions 90,96 Zr + 90,96 Zr, 90,96 Zr + 100 Mo, 94,100 Mo+ 100 Mo and 90,96 Zr + 124 Sn. This
effect is simply explained by the deformation <strong>of</strong> the nuclei in the initial DNS and in the DNS at
the top <strong>of</strong> the barrier in η and by the shell effects in dependence <strong>of</strong> the DNS potential energy on
η [34, 67]. In these calculations, we did not average the inner fusion barrier in mass asymmetry
over all possible orientations <strong>of</strong> colliding nuclei as we usually do in the calculations <strong>of</strong> fusion and
evaporation residue cross sections, taking the half <strong>of</strong> the deformation parameters <strong>of</strong> the nuclei
in the entrance channel. They are not always in good agreement with ∆B exp because these
data are not directly measurable but are obtained with model assumptions about the fusion,
the surviving probabilities and the Bass barrier.
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