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\title{Breakup of Lithium Near Threshold}

\author{R.~P.~Ward, N.~M.~Clarke, B.~R.~Fulton and G.~Tungate}
\address{School of Physics and Space Research,
University of Birmingham,\\ Edgbaston, Birmingham~B15~2TT, United~Kingdom}

\author{N.~Keeley and J.~S.~Lilley}
\address{Department of Physics and Astronomy, University of Manchester,\\ 
Manchester~M13~9PL, United~Kingdom}

\author{B.~Bilw\`es}
\address{Centre de Recherches Nucl\'eaires,\\ 23 Rue du Loess B.P. 20 CRO,
F-67037 Strasbourg-Cedex, France}

%\date{\today}

\maketitle

\begin{abstract}

A recent study has demonstrated that the elastic scattering of $^7$Li exhibits
a threshold anomaly, whereas $^6$Li scattering does not. It has been
suggested that this difference is due to differences in the breakup of
the two lithium isotopes. The proposed experiment would investigate this
assertion by measuring the 
$\alpha$-particle yield following the scattering of $^6$Li and
$^7$Li from a $^{208}$Pb target at bombarding energies between 25 
and 60\,MeV. Six days of beam-time are requested.

\end{abstract}

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\section*{}
 
Over the past several years, developments in theoretical techniques for
performing advanced coupled-reaction-channels~(CRC) calculations have led to
significant advances in our understanding of the way the structures of 
colliding nuclei influence the course of the collision process itself.
The overall effect of the couplings can be usefully described in terms of
an energy dependent, complex polarization component to the nuclear
potential, the details of which depend on the nature of the reaction processes
involved. Channel coupling effects appear to be manifested particularly strongly
at energies close to the Coulomb barrier. This is seen most clearly in the
enhancement of near and sub-barrier fusion and in the appearance of a 
threshold anomaly in the optical potential~\cite{satc}.
At energies near threshold, the number of significant contributing channels
becomes relatively small and it becomes possible to examine in some detail
the influences of the various reaction mechanisms arising from differences
in the nuclear structure. It is this fact which makes the interplay of
different nuclear processes at near barrier energies such a fruitful area 
for investigation.  

In a recent analysis~\cite{keel} of the elastic scattering of $^6$Li 
and $^7$Li by
$^{208}$Pb it was found that at energies just above the Coulomb barrier
the polarization contribution to the real potential is of opposite sign for
the two isotopes. The results are consistent with the existence of a 
threshold anomaly for
$^7$Li but not for $^6$Li. The strengths and energy variation of the 
imaginary potentials are also considerably different. This is in contrast to
the results at higher energy, where the double-folded potential (generated
from the M3Y nucleon-nucleon interaction) of either projectile
must be scaled by a factor of about 0.6 in order to describe the
elastic scattering. The energy variations of the real and imaginary parts 
of the surface potentials are summarized in Figure~1. Although there are
differences in the structure and breakup thresholds of $^6$Li and $^7$Li
they were not expected to be sufficiently great to give rise to such marked 
differences in the scattering of the two projectiles. Work has commenced to
try to understand these differences theoretically.

\begin{figure}
\epsfig{file=/usr/export/home/staff/rpw/charissa/fig2n.ps,width=6in,angle=90}
\caption{ Best fit real and imaginary potentials evaluated at 12.4\,fm
for $^7$Li~+~$^{208}$Pb~(left) and $^6$Li~+~$^{208}$Pb~(right). The 
horizontal dot-dash lines mark the values of the unrenormalized double-folded
potential for both cases. The solid and dashed lines on the $^7$Li
potential plot are dispersion relation~\protect\cite{keel}.}
\end{figure}

Certain consequences for some of the unobserved reaction processes are
implied by these findings. The existence of a threshold anomaly for
$^7$Li suggests, for example, that the relative importance of breakup for the
two projectiles, which is similar at high energies, changes dramatically
when the bombarding energy is reduced to near the Coulomb barrier. Indeed,
Keeley {\em et al.}~\cite{keel} suggested that the quasi-elastic
scattering cross-section $\sigma_{qe}$ may be two to three times greater for
$^6$Li at Coulomb barrier energies than for $^7$Li and, if it is the 
case that breakup
dominates $\sigma_{qe}$ for $^6$Li, as expected, the ratio of the breakup
cross-sections would be even greater.

Although many studies of $^6$Li and $^7$Li breakup have been published,
only that by Pfeiffer {\em et al.}~\cite{pfei} compared $^6$Li and $^7$Li
breakup at the same centre-of-mass energies in the vicinity of the Coulomb 
barrier. Figure~2 shows the data measured by Pfeiffer {\em et al.}
for the breakup of $^6$Li and $^7$Li populating channels including an
$\alpha$-particle; the Coulomb barriers for Li incident on $^{118}$Sn and
$^{58}$Ni are approximately 17 and 11\,MeV respectively.
With a $^{118}$Sn target, the breakup cross-section for $^6$Li was 
approximately twice that for $^7$Li, while for breakup from a $^{58}$Ni target,
the cross-sections for $^6$Li and $^7$Li were the same within experimental
uncertainties.

\begin{figure}
\epsfig{figure=/usr/export/home/staff/rpw/stras/graph.ps,width=6in}
\caption{Excitation function for $^6$Li and $^7$Li breakup following
scattering by $^{58}$Ni and $^{118}$Sn. The data are from Pfeiffer
{\em et al.}~\protect\cite{pfei}.}
\end{figure}

We propose an experiment similar to that performed by Pfeiffer {\em et al.},
but measuring the $\alpha$-particle yield from $^6$Li and $^7$Li breakup
following scattering from a $^{208}$Pb target over a range of bombarding
energy similar to that of Keeley {\em et al.}~\cite{keel}. Given a sufficiently
wide angular range, the total (angle integrated) breakup cross-section can 
be obtained as a function of bombarding energy for both $^6$Li and $^7$Li.
If our present models of $^6$Li and $^7$Li are correct the observed 
cross-sections for $^6$Li and $^7$Li breakup will differ dramatically at 
bombarding energies near the Coulomb barrier and be similar at higher energies.
The data obtained in the proposed experiment should be sufficient to confirm 
or refute the picture described above and would be suitable for rapid 
publication. 

However, the proposed experiment would only be the first in a series; 
later experiments would attempt to determine why the breakups of $^6$Li and 
$^7$Li are different by determining which channels the yield goes through.
Analyses of polarized $^6$Li elastic scattering data have suggested that
nonresonant breakup is very important for $^6$Li~\cite{hira,ruse}. Polarized
$^7$Li scattering data has not yet been compared with the results of
calculations including the effects of nonresonant breakup. To provide 
guidance for subsequent experiments we will include additional detector 
telescopes in the set-up for the first experiment
which will enable us to detect the breakup fragments ($\alpha + d$ for $^6$Li
and $\alpha + t$ for $^7$Li) in coincidence (plus any other breakup channels). 
Determination of the relative energy between the two fragments will enable 
us to identify the excited states through which the breakup proceeds. 
This information should enable us to plan the follow-up experiments which 
will address this question in more detail. 

The proposed experiment is part of an on-going European collaboration 
studying heavy ion interactions near the Coulomb barrier. If approved, the 
experiment would utilise the Charissa scattering chamber from the Nuclear 
Structure Facility, which is due to be installed at CRN~Strasbourg towards 
the end of 1994. The experimental set-up would be similar to that used by
Keeley {\em et al.}~\cite{keel}, that is, three $10 \times 50$\,mm$^2$ 
position-sensitive detector telescopes subtending a total solid angle of
18\,msr. Data would be taken at bombarding energies of 25, 27, 29, 31, 33, 
35, 39, 44 and 60\,MeV for both $^6$Li and $^7$Li. Assuming $^{208}$Pb 
target thicknesses of approximately 200\,$\mu$g~cm$^{-2}$, beam currents 
of 10\,nA~(electrical) and integrated breakup cross-sections of 100\,mb, it is 
estimated that a total of 6~days of beam-time are required to obtain data for 
the breakup of $^6$Li and $^7$Li to a statistical accuracy of $\pm 1$\%.

\begin{thebibliography}{A99}

\bibitem{satc} G.R.~Satchler, Phys.\ Rep.\ {\bf 199} (1991)~147.

\bibitem{keel} N.~Keeley, S.J.~Bennett, N.M.~Clarke, B.R.~Fulton, G.~Tungate,
P.V.~Drumm, M.A.~Nagarajan and J.S.~Lilley, Nucl.\ Phys.\ {\bf A571} 
(1994)~326.

\bibitem{pfei} K.O.~Pfeiffer, E.~Speth and K.~Bethge, Nucl.\ Phys.\ {\bf A206}
(1973)~545.

\bibitem{hira} Y.~Hirabayashi, Phys.\ Rev.\ {\bf C44} (1991)~1581.

\bibitem{ruse} K.~Rusek, N.M.~Clarke and R.P.~Ward, Phys.\ Rev.\ {\bf C50} 
(1994)~(in press).

\end{thebibliography}

\end{document}


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