**Breakup/Transfer
Channel
Couplings in Sub-barrier Fusion Reactions**,
C. Beck, *Institut
Pluridisciplinaire Hubert Curien
IN2P3/CNRS and University of Strasbourg, FRANCE* −
Heavy-ion fusion
reactions with colliding stable and/or weakly bound nuclei at
bombarding
energies at the vicinity and below the Coulomb barrier have been
widely studied
[1-9]. The specific
role of multi-step
neutron-transfers and/or breakup in sub-barrier fusion
enhancement still needs
to be investigated in detail both experimentally [2,3,7,8] and
theoretically
[4-6]. In a
complete description of the
fusion dynamics the transfer channels in standard
coupled-channel (CC)
calculations [1,5,9] have to be taken into account accurately in
reactions
induced by stable nuclei. Similarly, the breakup channel is
included in the
Continuum-Discretized Coupled Channel (CDCC) approach [4,6]
applied for weakly
bound and/or halo nuclei.

It
is
known that neutron transfers may induce a neck region of nuclear
matter
in-between the interacting nuclei favoring the fusion process to
occur. In
low-energy fusion reactions, the very
simple one-dimensional barrier-penetration model (1D-BPM) is
based upon a real
potential barrier resulting from the attractive nuclear and
repulsive Coulomb
interactions. For
light- and medium-mass
nuclei, one only assumes that the di-nuclear system fuses as
soon as it has
reached the region inside the barrier i.e. within the potential
pocket. If the
system can evolve with a bombarding
energy high enough to pass through the barrier and to reach this
pocket with a
reasonable amount of energy, the fusion process will occur after
a complete
amalgation of the colliding nuclei forming the compound nucleus.
On the other hand,
for sub-barrier energies
the di-nuclear system has not enough energy to pass through the
barrier. In
this case, neutron pick-up processes can occur when the nuclei
are close enough
to interact each other significantly, if the Q-values of neutron
transfers are
positive. It was shown that sequential transfers can lead to the
broad
distributions characteristic of many experimental fusion cross
sections. Finite
Q-value effects can lead to neutron
flow and a buildup of a neck between the target and projectile.
The situation of
this neck formation of neutron matter between the two colliding
nuclei could be
considered as a ”doorway state" to fusion. In a basic view, this
intermediate state induced a barrier lowering. As a consequence,
it will favor
the fusion process at sub-barrier energies and enhance
significantly the fusion
cross sections. Experimental results have already shown such
enhancement of the
sub-barrier fusion cross sections due to neutron transfer with
positive Q-values
[2].

In
order
to investigate the role of neutron transfers we studied ^{32}S+^{90,96}Zr
as
benchmark reactions. The analysis of the quasi-elastic barrier
distributions
[7] showed the significant role played by neutron transfers in
the fusion
processes. We
present the analysis of
fusion excitation functions recently measured for these
reactions [10]. For
this purpose we develop a new computer code named NTFus [11] by
taking the
neutron transfer channels into account within the model of
Zagrebaev [5]. The
effect of neutron transfers yield a fair
agreement with the present data of sub-barrier fusion for ^{32}S+^{96}Zr
[10].
This was
initially expected from
the positive Q-values of the neutron transfers as well as from
the failure of
previous CC calculation of quasi-elastic barrier distributions
without coupling
of the neutron transfers [7]. With
the
agreement obtained by fitting the present experimental fusion
excitation
function and the CC calculation at sub-barrier energies, we
conclude that the
effect of the neutron transfers produces a significant
enhancement of the
sub-barrier fusion cross sections for ^{32}S+^{96}Zr
as
compared to ^{32}S+^{90}Zr.

Finally.
an
experimental overview of reactions induced by the stable, but
weakly-bound
nuclei ^{6}Li, ^{7}Li and ^{9}Be, and
by the exotic,
halo nuclei ^{6}He,
^{8}B,
^{11}Be and ^{17}F on medium-mass targets, such
as ^{58}Ni,
^{59}Co or ^{64}Zn, is presented. Existing data on elastic
scattering, total
reaction cross sections, fusion, breakup and transfer channels
will be
discussed in the framework of a CDCC approach taking into
account the breakup
degree of freedom.

[1]
M.
Dasgupta *et al*., Annu. Rev. Nucl. Part. Sci. **48**, 401 (1998).

[2]
H.
Timmers *et al*., Nucl.
Phys. **A633**, 421
(1998).

[3]
C.
Beck *et al*., Phys.
Rev. C **67**, 054602
(2003).

[4]
A.
Diaz-Torres, I. J. Thompson and C. Beck, Phys. Rev. C **68**, 044607 (2003).

[5]
V.
I. Zagrebaev, Phys. Rev. C **67**,
061601 (2003).

[6]
C.
Beck, N. Keeley and A. Diaz-Torres, Phys. Rev. C **75**, 054605 (2007).

[7]
F.
Yang *et al*., Phys.
Rev. C **77**, 014601
(2008).

[8]
F.
A. Souza *et al.*, Eur.
Phys.J. A **44**, 181
(2010).

[9]
Sunil
Kalkal *et al.*, Phys.
Rev. C **81**, 044610
(2010).

[10]
H.
Q. Zhang it *et al.*,
Phys. Rev. C **82**,
054609 (2010).

[11]
A.
Richard *et al.*, EPJ
Web of Conf. **17**,
08005 (2011).