Systematic study of the heavy-ion fusion dynamics at near-barrier energies
2017
In recent decades, the study of capture and fusion dynamics in
heavy-ion collisions has been a subject of intense experimental and
theoretical interests because the heavy-ion capture not only is of
central importance for nucleosynthesis but also can reveal rich interplay
between nuclear structure and reaction dynamics. Theoretically, the
heavy-ion capture and fusion processes at energies near the Coulomb
barrier can be treated as a multidimensional barrier penetration problem.
The multidimensional barrier penetration process can be described
by solving the coupled-channel equations, i.e., the coupled-channel
(CC) model. However, for heavy reaction systems, it is necessary to
take into account a large number of channels which is not easy to
realize in the CC model. Moreover, the structure information of the
interacting nuclei are needed as inputs. Therefore, full CC calculations
become intractable in many cases including many fusion reactions leading
to superheavy nuclei. On the other hand, in the eigenchannel framework,
the couplings to other channels split the single potential barrier
into a set of discrete barriers. Based on the concept of the barrier
distribution, several empirical CC approaches have been developed.
Recently, we have developed an empirical coupled-channel (ECC) model
and performed a systematic study of capture excitation functions for
220 reaction systems. In this ECC model, an asymmetric Gaussian-form
barrier distribution function was used to take effectively into account
the effects of inelastic excitation couplings and neutron transfer
coupling. Based on the interaction potential between the projectile
and the target, empirical formulas were proposed for the parameters
of the barrier distribution according to the static and dynamical
deformations of the two colliding nuclei. For the vibrational coupling
effect and the rotational coupling effect, the parameters of the empirical
formulas were given, respectively. For spherical reaction systems
(vibrational coupling effect), the width of the barrier distribution
increases with the charge product of the reaction system, while for
the deformed reaction systems (rotational coupling effect), besides
the charge product of the reaction system, the width of the barrier
distribution is also related to the static deformation parameters
of the projectile and the target. For some reaction systems, the coupling
effects of the positive Q -value neutron transfer
(PQNT) channels are needed to explain the enhancement of sub-barrier
capture cross sections. In this ECC model, the effects of PQNT are
simulated by broadening the barrier distribution. Moreover, the positive Q value for one neutron pair transfer is used to broaden
the barrier distribution in the present model. Among these 220 reaction
systems, there are 89 systems with positive Q value
for one neutron pair transfer channel. The calculated capture cross
sections of most of these 89 reaction systems are in good agreement
with the experimental values, which implies that the Q value for one neutron pair transfer is very important to understanding
of the coupling to PQNT channels. Generally speaking, the ECC model
together with the empirical formulas for parameters of the barrier
distribution works quite well in the description of the capture cross
sections at near-barrier energies. This model can provide useful information
on capture dynamics and predictions of capture cross sections for
the synthesis of superheavy nuclei. In the present paper, we will
review this ECC model and its applications.
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