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\title{\bf~~Fusion of lithium -6 and lithium-7
 }
\author{B R Fulton, N M Clarke, J S Lilley and G Tungate \\
School of Physics and Space Research, University of Birmingham, \\
Birmingham 
B15 2TT, England
\and
N J Davis, G R Kelly and R P Ward \\
School of Sciences, Staffordshire University, College Road, \\
Stoke-on-Trent, ST4 
2DE, England
\and
D L Watson \\
Physics Department, University of York, York Y01 5DD, England
\and
K Rusek \\
Soltan Institute for Nuclear Studies, Zaklad 1, Hoz 69, 00 681 Warsaw, Poland}
\date{}
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\section*{Abstract}
A series of measurements are proposed to investigate the energy dependence of 
the fusion of $^{6}$Li and $^{7}$Li on nuclei in the lead region at energies 
from below to well above the 
Coulomb barrier.  The data will be analysed in conjunction with existing 
elastic scattering data in terms of phenomenological and 
coupled-reaction-channels models.
\section*{Scientific case}

For a number of years, it has been known that nuclear fusion is greatly 
enhanced at near and sub-Coulomb barrier energies due to coupling to different 
reaction channels.
These are mainly the inelastic excitation of collective vibrational and 
rotational modes, but nucleon transfer can also be important.
Details of these coupling effects are seen in barrier distributions derived 
from accurate fusion data and striking examples, exhibiting strong coupling 
to rotational and to single- and multi-phonon excitation modes have been 
reported [1].

The consequences of these couplings are seen most sensitively at and near 
to threshold (barrier region) where the local energy is limited and 
non-elastic channels open up or are closed as the bombarding energy is 
increased or decreased. 
The qualitative behaviour, therefore, changes with energy.
Well above the barrier, the main effect of the couplings is simply to remove 
flux from the entrance channel which leads to an increase in the imaginary 
component W of the interaction.
In most cases, the real part V is given to a good approximation by a 
double-folded potential (bare potential) derived from an effective 
nucleon-nucleon 
force acting between the nucleons in the target and projectile [2].
It is only for bombarding energies near the barrier that there is a substantial 
real polarization potential contribution due to channel coupling.
This is generally attractive and so leads to an increase in fusion compared 
with that due to the bare potential alone.

These variations in the heavy-ion nuclear interaction have been seen in 
analyses of elastic scattering data.
The variation in V corresponding to the rise in W as a function of bombarding 
energy near the barrier has been seen in many systems and is referred to as 
the threshold anomaly [3].

So far, virtually all systematic investigations have focussed on collisions 
between stable, tightly-bound nuclei. 
Relatively little work has been done on systems involving a weakly-bound 
target or projectile.
In their original paper on the heavy-ion potential, Satchler and Love [2] 
noted three projectiles:  $^{6}$Li, $^{7}$Li and $^{9}$Be, which behave 
anomalously in that the double-folded potential is a poor approximation for
V even at energies well above the barrier and that it had to be normalised 
by factors between 0.6 and 0.6 in order to fit the elastic scattering data.
Subsequent work [4] has shown that this behaviour derives from the relatively 
weak binding of these projectiles and consequent large breakup contribution 
to the total cross section.
Evidently, the low breakup threshold will have an effect on other reaction 
channels and, in particular, on fusion.

With the advent of beams of unstable, radioactive nuclear beams the effect 
of breakup modes on the dynamics of the collision will become more important 
as the threshold for populating these channels is reduced.
However, as one considers the use of projectiles further and further from 
stability, the net effect on the effective interaction and on fusion in 
particular is by no means evident.
While there is evidence that  breakup modes contribute a repulsive term 
which would inhibit fusion, the existence of a possible halo of weakly-bound 
nucleons or nucleon clusters could increase the attractive force at large 
distances.
Also, it has been suggested [5] that the possibility of a soft dipole 
vibrational mode between the core and the halo could lead to increases 
in both breakup and fusion.
Moreover, with heavier systems, where the atomic numbers of both target and 
projectile are large, the effects of Coulomb polarizability could produce  
additional, radical changes likely to affect the onset of fusion.

Understanding the nature and origin of the nuclear interaction is one of the 
main objectives of nuclear research and the possible availability for 
experimental work of intense beams of nuclei far from stability promises to 
yield an unprecedented wealth of new information leading to major advances 
in the field. 
However, our understanding of the interplay of the most familiar reaction 
processes via channel coupling is still far from complete and a great deal 
more selective work needs to be done with stable beams, not only to improve 
our theoretical representation of the basic processes, but also to provide 
a sound basis for dealing with the potentially more complex dynamics 
involving exotic beams.
Technically, stable beams have enormous advantages over radioactive beams 
the main one being that they can be produced with sufficient intensity that 
one can obtain accurate, comprehensive data which is vital for nuclear 
reaction studies. 

The main objective of the present proposal is to focus on the specific effect 
on fusion of the breakup mode using two of the anomalous projectiles: $^{6}$Li 
and $^{7}$Li.
These are light, stable nuclei with no nucleon halos.
However, both have low breakup thresholds and represent the best examples 
we have of obtaining specific information on the energy dependence of the 
breakup mode on the nuclear interaction using stable beams.

An initial study of the way the polarization potentials of these ions vary 
with energy near threshold was recently reported [6].
An analysis of accurate elastic scattering data for $^{6}$Li and $^{7}$Li 
on $^{208}$Pb unexpectedly showed markedly different behaviour for the two 
isotopes.
For $^{6}$Li, the required real part was consistently maintained at 0.5 to 
0.6 of the bare potential and the imaginary term showed no tendency to 
decrease with lower energies at threshold.
$^{7}$Li, on the other hand, exhibited a near normal threshold anomaly with 
W decreasing with reducing energy and V showing a peak due to an attractive 
real polarization potential.

A consequence of this interpretation of the scattering data is that the 
low-energy fusion should be very different for the two isotopes.
A comparison of these two cases would be a sensitive indicator of the 
differences in channel coupling due to the differences in the structure 
of $^{6}$Li and $^{7}$Li.

It is proposed, therefore to measure the fusion of $^{6}$Li and $^{7}$Li 
on nuclei in the lead region at several energies: at and near threshold, 
where the polarization potentials of the two isotopes appear to be of 
opposite sign; just 
above threshold - above the $^{7}$Li threshold anomaly; and, finally, well 
above threshold, where the two polarization potentials appear to have the 
same sign.

The lead region is chosen because the scattering data were carried out on 
$^{208}$Pb and also because fusion is dominated by fusion evaporation and leads 
to alpha active products which generally can be measured straightforwardly.
Use of a lighter target would require the availability of a well-tested, 
evaporation residue detector and could be the subject of a future proposal.

Measurements would be made of $^{6}$Li and $^{7}$Li on $^{209}$Bi and of 
$^{7}$Li on $^{207}$Pb and $^{6}$Li on $^{208}$Pb. 
With the Bi target, the Q-values for the two cases differ by 0.61 MeV and 
the dominant residues 
for a given bombarding energy, which can all be measured, differ by one 
neutron. At the higher energies, calculations indicate that fission begins 
to be significant.
The $^{7}$Li + $^{207}$Pb and $^{6}$Li + $^{208}$Pb systems have the 
advantage that the Q-values are very similar (0.11MeV) and fusion leads 
to the same compound nucleus and the same residues for a given energy. 
However at the higher energies, one of the products, $^{209}$At, is difficult 
to measure.
Nevertheless, it is felt that a comparison of the channels which can be 
measured would be direct and, therefore, instructive.
Long-lived products would be measured out-of-beam.  
Shorter-lived products, with half lives down to 25ms would be measured
in-beam and will require a chopped beam from the 
accelerator with variable on-off periods.  Their activities would be 
detected in alpha detectors placed at backward angles in the scattering 
chamber.
Any fusion/fission yield would be measured in beam by detecting the fission 
fragments also at large angles.

All these measurements would require continuous or chopped beams of 15 nA 
or greater and about 1
to 5 hours of beam time per energy depending on the cross section.
Initially, it is proposed to take measurements at least three energies for 
each case requiring a total of about 10 shifts of beam time but not necessarily 
all together because of the need for extensive out of beam counting.
\begin{thebibliography}{9}
\bibitem{1}N Rowley et al...
\bibitem{2}G.R.Satchler and W.G.Love, Phys. Rep.  {\bf 55} (1979)183.
\bibitem{3}G.R.Satchler, Phys. Rep.  {\bf 199} (1991) 147.
\bibitem{4}Y.Sakuragi, M.Yahiro and M.Kamimura, Prog. Theor. Phys. Suppl.  
{\bf 89} (1986) 136.
\bibitem{5}N Takigawa  and H Sagawa, Phys. Lett. {\bf B265} (1991) 23,
C H Dasso et al. preprint (1996). 
\bibitem{6}N Keeley et al. Nucl. Phys. {\bf A571} (1994) 326.
\end{thebibliography}
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