 
3. Recent HRIBF Research  The
^{132}Sn + ^{96}Zr Reaction: A Study of Fusion
Enhancement/Hindrance
(W. Loveland, spokesperson)
In fusion reactions induced by neutronrich radioactive nuclei, one
expects to observe a lowering of the fusion barrier, relative to that
observed in reactions induced by stable nuclei with smaller neutron to
proton ratios. This is simply a geometrical effect due to the greater
size of the nrich projectile. In addition, in the synthesis of heavy
nuclei with nrich projectiles, one expects a higher survival
probability of the completely fused system due to its lower fissility
and the lower excitation energies.
In the systems investigated to date, one does not generally expect
significant fusion hindrance because Z_{p}Z_{t}
< 1600. For Z_{p}Z_{t} > 1600,
it is believed that fusion hindrance effects
become prominent. Fusion hindrance generally takes the form of an
extra energy that must be supplied to the fusing system to drive it
from the contact point inside the fission saddle point. This energy
is loosely referred to as the "extrapush" energy although the formal
definition of this energy is that it is the "extraextra push
energy". Evaporation residue (ER) cross section measurements with
massive projectiles (A ~ 100) have clearly established the
occurrence of fusion hindrance with an extra energy needed to cause
fusion. This fusion hindrance was explained successfully by the extra
push model developed by Swiatecki et al. [1].
Studies by Sahm et al. for the ^{9096}Zr + ^{124}Sn
reactions showed an unexpected result. As the fusing system became
more neutronrich (decreasing fissility), the fusion hindrance, as
measured by the extra push energy, increased in contradiction to
predictions of most theoretical models. (See Fig. 31) If this trend
were confirmed, it would reduce the attractiveness of fusion using
very nrich projectiles as a pathway to the heaviest elements. We
have carried out, over a period of several years, a set of
measurements of the capturefission excitation functions for the
^{124,132}Sn + ^{96}Zr system to try to define this effect. The
results of these investigations have been published [2,3].
Figure 31: Extra push as determined from the mean fusion barrier height
E_{B} and the barrier height calculated with the Bass potential,
V_{B}, versus the
effective entrance channel fissility.
The experimental points are
taken from Sahm, et al., with ^{124}Sn+^{96,94,92,90}Zr
systems selected.
The theoretical prediction by Bjornholm and Swiatecki is
shown by a line.
Figure 32: Comparison of the capture fission excitation functions for
the ^{132}Sn+^{96}Zr (solid squares and line) and
^{124}Sn+^{96}Zr reactions (open circles and dashed line).
The lines are to
guide the eye through the data points.
The measured capturefission excitation functions for the two systems
are shown in Fig.32. Clearly the interaction barrier is shifted to
lower energies for the more nrich system.
We have measured capture cross sections in this work. The direct
measurement of fusion cross sections requires the separation of the
quasifission and fusionfission components of the capture cross
sections, which is not feasible with the current generation of
radioactive beam facilities. However, for many purposes, such as
heavy element syntheses, we need to know the properties of the fusion
cross sections in these collisions. What should we do?
We have chosen to extrapolate from the capture cross sections to the
fusion cross sections, which, at least, involves cross sections of
similar magnitude. We do this extrapolation using the dinuclear
system (DNS) model. This model was successful in reproducing
evaporation residue cross sections for ^{16}O+^{204}Pb and
^{124}Sn+^{96}Zr systems.
Figure 33: Excitation function
for ^{132}Sn+^{96}Zr capturefission reaction. The one
dimensional barrier penetration model prediction is shown as a dashed line.
The predicted capture, and fusion cross sections predicted by the DNS model
are shown by solid, and dotted lines, respectively. See text for details.
Calculations by Giardina et al. using the DNS model for capture
cross sections in the ^{132}Sn+^{96}Zr reaction are shown in
Fig. 33 as a solid red line. The predictions of this model for the
fusion cross sections for this reaction are shown as a dotted line.
Since the DNS model calculations agree reasonably well with the
observed capture cross sections for the
^{132}Sn+^{96}Zr and
^{124}Sn+^{96}Zr
reactions [2] and the evaporation
residue cross sections for the ^{124}Sn+^{96}Zr reaction, it is
reasonable to speculate that the interaction and fusion barrier
heights for these reactions are those predicted by the DNS model. For
the ^{132}Sn+^{96}Zr reaction, the deduced (DNS) interaction
barrier height is 192.3 MeV while the fusion barrier height is 201.8
MeV. Similarly, for the ^{124}Sn+^{96}Zr reaction [2],
the deduced interaction barrier height is 204.4 MeV while the fusion
barrier height is 208.9 MeV. The Bass barrier heights for these
reactions are 213.8 and 216.3 MeV, respectively.
One immediately comes to several conclusions. The deduced fusion
barrier heights from the DNS model for the reactions induced by
neutronrich radioactive beams (201.8 and 208.9 MeV) are substantially
below the Bass barrier heights. We take the definition that
"extrapush" energy is the difference between the interaction barrier
height and the fusion barrier height. Both the
^{124}Sn+^{96}Zr
and ^{132}Sn+^{96}Zr reactions show positive
extra push energies
(fusion hindrance) of 4.5 and 9.5 MeV, respectively, as deduced from
the DNS model. (Refs. [2,4] would have estimated these
energies as 10 and 7 MeV, respectively). Some but not all of the
advantage of using neutronrich radioactive beams is predicted by the
DNS model to be lost due to fusion hindrance in the Sn + Zr system.
[1]W. J. Swiatecki, Physica Scripta 24, 113 (1981); Nucl. Phys. A
376, 275 (1982).
[2]A. M. Vinodkumar, W. Loveland, P.H. Sprunger, D. Peterson, J. F. Liang, D. Shapira, R. L. Varner, C. J. Gross and J. J. Kolata,
Phy. Rev. C 74, 064612 (2006).
[3]A.M. Vinodkumar, et al., Phys. Rev. C 78, 054608 (2008).
[4]S. Bjoernholm and W. J. Swiatecki,
Nucl. Phys. A 391, 471 (1982).
