Fusion of ^{32}S+^{48}Ca
at deep
sub-barrier energies, G.
Montagnoli, University of
Padova and INFN, Italy − In
the interesting energy region below the Coulomb barrier, heavy-ion
fusion cross
sections result from a balance between the enhancement produced by
couplings to
internal degrees of freedom of the colliding nuclei and to nucleon
transfers,
and the limitation ("fusion hindrance") generally observed at very
low energies. This
hindrance is
conveniently represented by using the logarithmic derivative L(E)
=
dln(E*sigma)/dE (slope) which is very sensitive to the trend of
the low-energy
excitation function. This phenomenon is receiving much attention
also from the theoretical
side.It has
frequently been observed
that hindrance is so strong that a maximum of the astrophysical
S-factor
develops as a function of the energy, as required by energy
conservation for
systems having negative Q-values for fusion.In our recent study of the sub-barrier fusion excitation
function of ^{40}Ca
+ ^{48}Ca an indication of an S-factor maximum in a
system with a
positive Q value has been observed for the first time. As a matter of fact,
it is known that for
systems having Q>0 the presence of a maximum of the S-factor
vs. energy is
not needed. If
confirmed in other
systems with positive Q values, this effect will play an important
role in
nuclear astrophysics where fusion reactions of light heavy-ion
systems occur at
very low energies which are presently unaccessible to laboratory
studies and
thus require extrapolations to estimate the reaction rates in
stars.The fusion
excitation function of ^{32}S+^{48}Ca
(Q=+7.66 MeV) has been experimentally studied in a wide energy
range, from
above the Coulomb barrier down to cross sections in the
sub-microbarn region. The
measurements were done at Legnaro Naz.
Laboratory of INFN, using the high-quality and intense ^{32}S
beam from
the XTU Tandem accelerator.The
excitation
function has a smooth behavior below the barrier, with a rather
flat
slope. This slope
does not reach the
value expected for a constant S factor, which implies that no
maximum of S vs.
energy shows up in the measured energy range. Of course it could be
present at still lower
energies.However
other interesting
features of the dynamics of this system have shown up. In particular, its barrier
distribution has an
unusual shape with two peaks of similar height on either side of
the
Akyuz-Winther (AW) barrier. Preliminary
coupled-channels
calculations have been performed, including the lowest 2+ and
3- states of both projectile and target, and, additionally, the
two-phonon
quadrupole excitation of ^{32}S. The calculations employed
a standard AW
ion-ion potential. The
results strongly under
predict the sub-barrier cross sections, although the slope of the
excitation
function is quite well reproduced. Even
the
predicted barrier distribution is very different from experiment,
in
particular the high-energy peak is completely missing.Since ^{32}S+^{48}Ca
has
several neutron pickup transfer channels with positive Q-values,
further
schematic calculations have been carried out including also a
transfer coupling
simulating the +2n pick up channel.This
produces a fusion excitation function and a barrier distribution
in close
agreement with the data.