\documentstyle [12pt,inch,psfig]{article}
\begin{document}

\begin{center}

\Large{\bf Target Dependence in Breakup Reactions}

\vspace{7.0mm}

\large{Neil Curtis}

\vspace{7.0mm}

\end{center}

\normalsize


This report outlines some of the preliminary results of an experiment
performed at ANU in June 1996. The aim of this experiment was to search for
the breakup of $^{24}$Mg, $^{28}$Si and $^{32}$S from carbon, lithium, oxygen and beryllium targets. This was in an attempt to help establish the reaction
mechanism populating the breakup states seen previously in the
$^{12}$C($^{24}$Mg,$^{12}$C $^{12}$C)$^{12}$C, 
$^{12}$C($^{24}$Mg,$^{12}$C $^{16}$O)$^{8}$Be and
$^{12}$C($^{24}$Mg,$^{16}$O $^{16}$O)$^{4}$He channels.

The experiment was performed using a 170~MeV $^{24}$Mg beam and targets of
380~$\mu$g/cm$^{2}$ carbon, 300~$\mu$g/cm$^{2}$ lithium oxide (Li$_{2}$O)
and 350~$\mu$g/cm$^{2}$ beryllium ($^{9}$Be). Additional calibration beams of
54.4~MeV and 85.0~MeV $^{12}$C and 63.8~MeV
and 91.8~MeV $^{16}$O were used. The breakup fragments were detected by two 
gas-silicon-scintillator hybrid telescopes, this being the first time that these
detectors have been used in an experiment. The telescopes were placed at arm angles
of 16$^{\circ}$/16$^{\circ}$ for the majority of the running, and at
a distance of 170~mm from the target (as measured from the front face
of the silicon strip detectors). The gas 
$\Delta$E detectors were held at 60~torr of propane, and 3.5~$\mu$m
mylar windows were used.


\vspace{10.0mm}

\noindent \large{\bf The $^{\mathbf 12}$C + $^{\mathbf 12}$C Breakup of $^{\mathbf 24}$Mg}

\vspace{6.0mm}

\normalsize


\begin{figure}
\begin{center}
\ 
\psfig{figure=cc.figs/cmgccc.etot.ex.ps,width=130mm}
\end{center}
\caption{(a) Total energy (including predicted $Q_{ggg}$ peak position) and (b)
excitation energy spectra for the $^{12}$C($^{24}$Mg,$^{12}$C~$^{12}$C)$^{12}$C
reaction.}  \label{cmgccc}
\end{figure}


In Figure~\ref{cmgccc} the reconstructed total and excitation energy spectra
are shown for the $^{12}$C($^{24}$Mg,$^{12}$C~$^{12}$C)$^{12}$C reaction.
Both of these spectra agree well with previous results. The $Q_{ggg}$ peak
in the total energy spectrum lies at a measured energy of
(155.06~$\pm$~0.01)~MeV, the predicted position being 155.07~MeV (using the
average of the energy lost in the target calculated by the codes
DEDX~\cite{dedx} and TARGET~\cite{target}). The excitation energy spectrum 
is in good agreement with that obtained in a previous
experiment by Curtis~{\em et al.}~\cite{ncthesis}, and when overlaid upon
this earlier data agrees to within one channel (100~keV). 
Both the total energy and excitation energy spectra therefore indicate that
the energy and position calibrations and the $\Delta$E reconstruction have
been performed correctly in the sort code used to analyse the data. Data were
taken from the carbon target to allow the above check with previous results
to be made.

The value of the double differential cross-section obtained for this
reaction channel is $\frac{d^{2}\sigma}{d\Omega_{1}d\Omega_{2}}$ = 
(0.22~$\pm$~0.02)~mb~sr$^{-2}$. This compares well to the range of values found
in previous measurements of this channel of (0.12~$\pm$~0.01)~mb~sr$^{-2}$
\cite{leddy} to (1.21~$\pm$~0.18)~mb~sr$^{-2}$~\cite{ncthesis}. This order
of magnitude variation is due to the range of breakup angles
sampled and
$\theta^{\ast}/\psi$ coverage of the various experiments, and makes direct comparisons 
of cross-sections between different measurements very difficult. A second reason for taking data on a carbon target was therefore to provide a normalisation 
for the cross-sections obtained from other breakup channels
measured in the experiment.




\begin{figure}
\begin{center}
\ 
\psfig{figure=cc.figs/limgccli.etot.ps,width=130mm}
\end{center}
\caption{Total energy spectra for the 
Li$_{2}$O($^{24}$Mg,$^{12}$C~$^{12}$C) reaction, assuming a recoil of
(a) $^{16}$O, (b) $^{7}$Li and (c) $^{12}$C. The predicted $Q_{ggg}$ peak positions are indicated.}  \label{limgccx}
\end{figure}



In Figure~\ref{limgccx} the reconstructed total energy spectra for the
Li$_{2}$O($^{24}$Mg,$^{12}$C~$^{12}$C) channel are shown. In
Figure~\ref{limgccx}(a) the data has been analysed assuming that the breakup
occurred following an interaction with an $^{16}$O target nucleus. In Figure~\ref{limgccx}(b)
the recoil has been assumed to be $^{7}$Li, and in 
Figure~\ref{limgccx}(c) a recoiling $^{12}$C nucleus has been used (the
Li$_{2}$O target used had a nominal 10~$\mu$g/cm$^{2}$ carbon backing).
Clear $Q_{ggg}$ peaks can be observed in both Figures~\ref{limgccx}(a) and
\ref{limgccx}(c), and both appear at energies in good agreement with the 
predicted $Q_{ggg}$ energies. There is no evidence for a $Q_{ggg}$ peak in 
Figure~\ref{limgccx}(b), the data reconstructed assuming a $^{7}$Li recoil.



\begin{figure}
\begin{center}
\ 
\psfig{figure=cc.figs/lio.cc.cat.ps,width=110mm}
\end{center}
\caption{Catania plot for the Li$_{2}$O($^{24}$Mg,$^{12}$C~$^{12}$C) reaction.
The predicted slopes for $^{7}$Li, $^{12}$C and $^{16}$O recoils are indicated.}  \label{limgcccat}
\end{figure}


In order to try to distinguish between the two different target possibilities
of $^{12}$C and $^{16}$O a Catania plot has been produced for the data.
This is shown in Figure~\ref{limgcccat}.
Overlaid upon the data are the predicted slopes for recoils of mass 7, 12
and 16. It can be seen that both the predicted slopes for mass 12 and 16
recoils lie over the broad band of data running from 20~MeV (x axis) and 15~MeV
(y axis) to 60~MeV (x axis) and 18~MeV (y axis). Therefore it is not possible
to distinguish which of the two possible target/recoil masses is more likely.

By gating on the $Q_{ggg}$ band in the Catania plot shown in Figure~\ref{limgcccat}
an excitation spectrum has been obtained for the 
$^{12}$C~+~$^{12}$C breakup of $^{24}$Mg from the Li$_{2}$O target, and this
is shown in Figure~\ref{limgccex}. This spectrum appears remarkably similar
to that shown in Figure~\ref{cmgccc}(b) for the $^{12}$C($^{24}$Mg,$^{12}$C~$^{12}$C)$^{12}$C channel, suggesting that the
breakup may be arising from reactions with the carbon backing on the
Li$_{2}$O target. However, a comparison of the double differential 
cross-section for the $^{12}$C($^{24}$Mg,$^{12}$C~$^{12}$C)$^{12}$C reaction
($\frac{d^{2}\sigma}{d\Omega_{1}d\Omega_{2}}$ = 
(0.22~$\pm$~0.02)~mb~sr$^{-2}$) with that obtained from the data shown in
Figure~\ref{limgccex} suggests otherwise. Assuming all of the data
appearing in Figure~\ref{limgccex} is due to interactions with carbon
target nuclei it is found that the total thickness of carbon in the
target would need to be (235~$\pm$~25)~$\mu$g/cm$^{2}$ in order to
produce the statistics seen in the excitation spectrum (Figure~\ref{limgccex}).
The nominal thickness of the carbon backing on the Li$_{2}$O target
was 10~$\mu$g/cm$^{2}$, and the remaining $\sim$~225~$\mu$g/cm$^{2}$
required seems to be too great an amount to be due to carbon build up
on the target during the $\sim$~39 hours of beam exposure for this
target (at an average beam current of only 5 enA). It therefore
appears that the additional statistics may be arising from breakup from
the oxygen in the target, and it is clear that this result
merits further attention in the analysis. The next stage into the investigation
of possible breakup from the $^{16}$O target will be to determine the cross-section
for the breakup for each data run in turn, in an attempt to observe any
change in cross-section value (and therefore carbon build up) with time.




\begin{figure}
\begin{center}
\ 
\psfig{figure=cc.figs/limgccli.ex.ps,width=130mm}
\end{center}
\caption{Excitation energy spectrum for the
Li$_{2}$O($^{24}$Mg,$^{12}$C~$^{12}$C) reaction, gated on the 
$^{12}$C and $^{16}$O recoil line in the Catania plot.}  \label{limgccex}
\end{figure}



The total energy spectrum for the $^{9}$Be($^{24}$Mg,$^{12}$C~$^{12}$C)$^{9}$Be
reaction is shown in Figure~\ref{bemgccbe}, as is the theoretical
$Q_{ggg}$ peak position. There appears to be no evidence for structure in
this spectrum. The Catania plot produced for this channel, shown in
Figure~\ref{bemgcccat}, also lacks
structure, indicating that $^{12}$C~+~$^{12}$C breakup of $^{24}$Mg is not
seen from the $^{9}$Be target. 
Interestingly, the absence of any structure in either the total energy spectrum
or the Catania plot indicates that carbon build up on the
$^{9}$Be target was minimal during the experiment, as significant
build up would be expected to give rise to $Q_{ggg}$, $Q_{gg}$ and $Q_{g}$
peaks as seen in the carbon target data shown in Figure~\ref{cmgccc}(a). This
in turn suggests that
carbon build up on the Li$_{2}$O target may also be minimal, although
it is noted that the different physical characteristics of $^{9}$Be and
Li$_{2}$O are likely to effect the rate of
carbon build up
on these two target materials. If the rate of carbon build up on the Li$_{2}$O target was low, however, then the $^{12}$C~+~$^{12}$C breakup of $^{24}$Mg
seen from this target may indeed arise from the oxygen content, as 
previously mentioned.



\begin{figure}
\begin{center}
\ 
\psfig{figure=cc.figs/bemgccbe.etot.ps,width=130mm}
\end{center}
\caption{Total energy spectrum for the
$^{9}$Be($^{24}$Mg,$^{12}$C~$^{12}$C)$^{9}$Be reaction. The predicted $Q_{ggg}$ peak position is indicated.}  \label{bemgccbe}
\end{figure}


\begin{figure}
\begin{center}
\ 
\psfig{figure=cc.figs/be.cc.cat.ps,width=110mm}
\end{center}
\caption{Catania plot for the $^{9}$Be($^{24}$Mg,$^{12}$C~$^{12}$C)$^{9}$Be
reaction. The predicted slope for a $^{9}$Be recoil is indicated.}  \label{bemgcccat}
\end{figure}





\newpage

\noindent \large{\bf The $^{\mathbf 12}$C + $^{\mathbf 16}$O Breakup of $^{\mathbf 28}$Si}

\vspace{6.0mm}

\normalsize

The reconstructed total and excitation energy spectra
for the $^{12}$C($^{24}$Mg,$^{12}$C~$^{16}$O)$^{8}$Be reaction are shown in
Figure~\ref{cmgcobe}. As for the $^{12}$C~+~$^{12}$C breakup data shown
in Figure~\ref{cmgccc}, both of the spectra shown in Figure~\ref{cmgcobe}
agree well with previous results~\cite{ncthesis}. This is again seen as
an indication that the calibrations and sort codes used are correct.
The value of the double differential cross-section obtained for this
channel is $\frac{d^{2}\sigma}{d\Omega_{1}d\Omega_{2}}$ = 
(0.61~$\pm$~0.06)~mb~sr$^{-2}$.



\begin{figure}
\begin{center}
\ 
\psfig{figure=co.figs/cmgcobe.etot.ex.ps,width=130mm}
\end{center}
\caption{(a) Total energy (including predicted $Q_{ggg}$ peak position) and (b)
excitation energy spectra for the 
$^{12}$C($^{24}$Mg,$^{12}$C~$^{16}$O)$^{8}$Be reaction.}  \label{cmgcobe}
\end{figure}


In Figure~\ref{limgcox} the total energy spectra for the $^{12}$C~+~$^{16}$O
breakup from the Li$_{2}$O target are shown. In Figure~\ref{limgcox}(a) the
data have been analysed assuming a $^{12}$C recoil, in Figure~\ref{limgcox}(b)
assuming a $^{3}$H (triton) recoil and in Figure~\ref{limgcox}(c) a
$^{8}$Be recoil. In Figures~\ref{limgcox}(a) and (c) peaks can be
observed at $\sim$~159~MeV, but in both cases these are
approximately 5~MeV higher than the predicted $Q_{ggg}$ peak position.
However, in Figure~\ref{limgcox}(b) the peak seen in the total energy spectrum
does appear at the expected energy, suggesting that the breakup is occurring
from the $^{7}$Li in the target. This is supported by the Catania plot,
which is shown in Figure~\ref{limgcocat}. In this spectrum there is no
evidence for structure along the lines predicted for mass 8 and 12 recoil
nuclei, but there is a band of data ranging from 0~MeV (x axis) and 
9~MeV (y axis) to 10~MeV (x axis) and 12~MeV (y axis). This lies along
the line predicted for a mass 3 recoil, indicating that the breakup is
occurring from the $^{7}$Li within the target.



\begin{figure}
\begin{center}
\ 
\psfig{figure=co.figs/limgcot.etot.ps,width=130mm}
\end{center}
\caption{Total energy spectra for the 
Li$_{2}$O($^{24}$Mg,$^{12}$C~$^{16}$O) reaction, assuming a recoil of
(a) $^{12}$C, (b) $^{3}$H ($t$) and (c) $^{8}$Be. The predicted $Q_{ggg}$ peak positions are indicated.}  \label{limgcox}
\end{figure}


\begin{figure}
\begin{center}
\ 
\psfig{figure=co.figs/lio.co.cat.ps,width=110mm}
\end{center}
\caption{Catania plot for the Li$_{2}$O($^{24}$Mg,$^{12}$C~$^{16}$O) reaction.
The predicted slopes for $^{3}$H ($t$), $^{8}$Be and $^{12}$C recoils are indicated.}  \label{limgcocat}
\end{figure}


\begin{figure}
\begin{center}
\ 
\psfig{figure=co.figs/limgcot.ex.ps,width=130mm}
\end{center}
\caption{Excitation energy spectrum for the
$^{7}$Li($^{24}$Mg,$^{12}$C~$^{16}$O)t reaction, gated on the 
$^{7}$Li recoil line in the Catania plot.}  \label{limgcoex}
\end{figure}



Gating on the data along the predicted 1/3 slope in the Catania plot
(Figure~\ref{limgcocat})
allowed the excitation energy spectrum for the
$^{7}$Li($^{24}$Mg,$^{12}$C~$^{16}$O)t reaction to be obtained. This is shown in
Figure~\ref{limgcoex}. In this spectrum 3 distinct states may be seen,
appearing at energies of 28.1~MeV, 29.8~MeV and 33.6~MeV. These
energies agree well with those for the states seen in the
$^{12}$C($^{24}$Mg,$^{12}$C~$^{16}$O)$^{8}$Be channel (Figure~\ref{cmgcobe}(b)),
these being 28.0~MeV, 29.8~MeV and 33.2~MeV. This suggests that the same
states are being populated in the reactions off both the $^{12}$C and
$^{7}$Li targets. The measured centroids and widths of the states observed
are listed in Table~\ref{table}.
The measured double differential cross-section for the
$^{7}$Li($^{24}$Mg,$^{12}$C~$^{16}$O)t reaction is
$\frac{d^{2}\sigma}{d\Omega_{1}d\Omega_{2}}$ = 
(0.91~$\pm$~0.09)~mb~sr$^{-2}$.


\begin{figure}
\begin{center}
\ 
\psfig{figure=co.figs/bemgcohe.etot.ex.ps,width=130mm}
\end{center}
\caption{(a) Total energy (including predicted $Q_{ggg}$ peak position) and (b)
excitation energy spectra for the $^{9}$Be($^{24}$Mg,$^{12}$C~$^{16}$O)$^{5}$He
reaction.}  \label{bemgcohe}
\end{figure}




\begin{table}
\begin{center}
\begin{tabular}{|cc|cc|cc|}
\hline
\multicolumn{2}{|c|}{$^{12}$C target} &\multicolumn{2}{|c|}{$^{7}$Li target} &\multicolumn{2}{|c|}{$^{9}$Be target}  \\
\hline
$E_{x}$ & $\Delta$E & $E_{x}$ & $\Delta$E & $E_{x}$ & $\Delta$E \\
 (MeV)  &   (keV)   &  (MeV)  &    (keV)  &  (MeV)  &   (keV)   \\
\hline
27.98 $\pm$ 0.05 & 840 $\pm$ 132 & 28.12 $\pm$ 0.02 & ~516 $\pm$ 40~ & 28.12 $\pm$ 0.01 & ~512 $\pm$ 26 \\
\hline
29.81 $\pm$ 0.03 & 814 $\pm$ 84~ & 29.78 $\pm$ 0.02 & 1234 $\pm$ 72~ & 29.84 $\pm$ 0.02 & 1340 $\pm$ 54 \\
\hline
33.23 $\pm$ 0.03 & 838 $\pm$ 74~ & 33.63 $\pm$ 0.04 & 2366 $\pm$ 152 & 33.54 $\pm$ 0.03 & 1702 $\pm$ 98 \\
\hline
\end{tabular}
\caption{Energies and widths for the states observed 
in the $^{12}$C + $^{16}$O breakup of $^{28}$Si. \label{table}}
\end{center}
\end{table}



The total energy and excitation energy spectra for the $^{12}$C + $^{16}$O
breakup of $^{28}$Si from the $^{9}$Be target are shown in
Figure~\ref{bemgcohe}. Gating on the peak seen in the total energy
spectrum just below the predicted $Q_{ggg}$ peak position allowed
the excitation energy spectrum seen in Figure~\ref{bemgcohe}(b) to be
obtained. Additional gating was also applied to the Catania plot produced
for this channel. In the excitation energy spectrum several distinct
peaks may be
observed, and the energies of these states agree well with those observed in both the $^{12}$C and $^{7}$Li target data sets. The
measured energies and widths of the states are given in Table~\ref{table}.
The $\sim$ 2~MeV shift in the position of the
experimental $Q_{ggg}$ peak from the predicted energy has yet to be 
explored in the analysis, but may be due to the use of an inaccurate
target thickness in the reconstruction of the events.
It is noted that the $^{9}$Be target used in the experiment was split,
which caused the central portion of the foil to roll up. It is therefore
likely that the beam particles and breakup fragments passed through a significantly
greater amount of material than the 350~$\mu$g/cm$^{2}$ assumed in the analysis.
This will be investigated by studying the position of the $Q_{ggg}$ peak as a function
of the target thickness used in the event reconstruction.
The measured double differential cross-section for the
$^{9}$Be($^{24}$Mg,$^{12}$C~$^{16}$O)$^{5}$He reaction (assuming a target
thickness of 350~$\mu$g/cm$^{2}$) is
$\frac{d^{2}\sigma}{d\Omega_{1}d\Omega_{2}}$ = 
(2.40~$\pm$~0.24)~mb~sr$^{-2}$.

The excitation energy spectra for the $^{12}$C + $^{16}$O
breakup of $^{28}$Si obtained from the $^{9}$Be, $^{7}$Li and
$^{12}$C targets are shown for comparison in Figure~\ref{coex}.
It can be seen that the positions of the observed peaks are nearly
identical for the three different channels shown. Although spin
assignments have not been made for the states, the clear
resemblance between the spectra indicates that the $^{12}$C + $^{16}$O
breakup of the $^{28}$Si nuclei is occurring from the same states in all three
reaction channels studied. This suggests that the reaction
mechanism populating the resonant $^{28}$Si nuclei is alpha
transfer. Future work will include analysis of the breakup angular 
correlations to investigate possible spin information.



\begin{figure}
\begin{center}
\ 
\psfig{figure=co.figs/be.c.li.co.ex.ps,width=130mm}
\end{center}
\caption{Excitation energy spectra for the $^{12}$C~+~$^{16}$O breakup
of $^{28}$Si, obtained from targets of (a) $^{9}$Be, (b) $^{7}$Li and
(c) $^{12}$C.}  \label{coex}
\end{figure}


\vspace{1.0cm}

\noindent \large{\bf The $^{\mathbf 16}$O + $^{\mathbf 16}$O Breakup of $^{\mathbf 32}$S}

\vspace{6.0mm}

\normalsize


In Figure~\ref{cmgooa} the total energy and excitation energy spectra for
$^{12}$C($^{24}$Mg,$^{16}$O~$^{16}$O)$^{4}$He breakup are shown. These 
spectra agree well with the previous measurement of this
channel~\cite{ncthesis,oopaper}, again indicating that the calibrations used in the
analysis are correct. The total energy spectrum for the 
$^{16}$O~+~$^{16}$O breakup of $^{32}$S from the $^{9}$Be target is shown
in Figure~\ref{bemgoon}(a). There is no evidence for a $Q_{ggg}$ peak in
either this spectrum or the Catania plot produced from the data. It is
seen in Figure~\ref{bemgoon}(a) that the data extend above the beam energy
(170~MeV). This is due to the large energy range (up to 200~MeV) of the
reconstructed recoil neutrons (the summed energy spectrum of the two $^{16}$O 
fragments has no significant yield above 150~MeV, suggesting that the problem
does not lie with the energy calibrations). The reason for the large range
of recoil energies has yet to be determined in the analysis.

The data extending above the beam energy in the total energy
spectrum has been removed by software gating, in an
attempt to observe any evidence for a $Q_{ggg}$ peak that may be hidden in
Figure~\ref{bemgoon}(a). The gating was applied by rejecting recoil energies
outside the range predicted by a Monte Carlo simulation of the reaction.
The resulting total energy spectrum produced following this gating is shown
in Figure~\ref{bemgoon}(b). No evidence for a $Q_{ggg}$ peak has emerged
following this process, and it is clear that the problem of the large
range of recoil energies must be studied in more detail.



\begin{figure}
\begin{center}
\ 
\psfig{figure=oo.figs/cmgooa.etot.ex.ps,width=130mm}
\end{center}
\caption{(a) Total energy (including predicted $Q_{ggg}$ peak position) and (b) excitation energy (gated on a Dalitz plot) spectra for the
$^{12}$C($^{24}$Mg,$^{16}$O~$^{16}$O)$^{4}$He reaction.}  \label{cmgooa}
\end{figure}

\begin{figure}
\begin{center}
\ 
\psfig{figure=oo.figs/bemgoon.etot.ps,width=130mm}
\end{center}
\caption{Total energy (including predicted $Q_{ggg}$ peak position) for the
$^{9}$Be($^{24}$Mg,$^{16}$O~$^{16}$O)n reaction. The data shown in (a)
includes all reconstructed recoil energies. The data shown in (b) have had 
gates calculated from a Monte Carlo simulation applied to the recoil energy.}  \label{bemgoon}
\end{figure}


\vspace{1.0cm}

\noindent \large{\bf Summary}

\vspace{6.0mm}

\normalsize


The $^{12}$C($^{24}$Mg,$^{12}$C $^{12}$C)$^{12}$C, 
$^{12}$C($^{24}$Mg,$^{12}$C $^{16}$O)$^{8}$Be and
$^{12}$C($^{24}$Mg,$^{16}$O $^{16}$O)$^{4}$He channels have been analysed,
and the results are seen to agree closely with previous measurements. This gives confidence
in the calibrations used in the event reconstruction.

There is evidence for $^{12}$C~+~$^{12}$C breakup of $^{24}$Mg
from the $^{16}$O content of the Li$_{2}$O target used in the experiment. Further detailed analysis is needed to confirm this idea. There is no
evidence for $^{12}$C~+~$^{12}$C breakup from the $^{9}$Be target.

Breakup of 
$^{28}$Si to $^{12}$C~+~$^{16}$O has been observed from all three targets used
in the experiment, $^{12}$C, $^{7}$Li and $^{9}$Be. The proposed reaction
mechanism populating the states seen in the reconstructed
$^{28}$Si excitation energy spectrum is alpha transfer.

An investigation of the $^{9}$Be($^{24}$Mg,$^{16}$O~$^{16}$O)n reaction
has produced no evidence for the breakup of $^{32}$S. Further analysis of this
channel, as well as the $^{16}$O($^{24}$Mg,$^{16}$O~$^{16}$O)$^{8}$Be
reaction from the Li$_{2}$O target data, is planned.

Following the analysis of the $^{12}$C~+~$^{12}$C breakup of $^{24}$Mg,
the $^{12}$C~+~$^{16}$O breakup of $^{28}$Si and the
$^{16}$O~+~$^{16}$O breakup of $^{32}$S a search will be made for breakup
to various other exit channels. As the experimental trigger was set to allow
alpha~+~heavy ion, $^{8}$Be~+~heavy ion and (3~$\times$~$\alpha$)~+~heavy ion
coincidences to be passed to tape,
there are many reactions that may be investigated in the data set.
These include $^{16}$O~+~$^{8}$Be and $^{20}$Ne~+~$\alpha$ breakup of $^{24}$Mg,
and $^{20}$Ne~+~$^{8}$Be breakup of $^{28}$Si (data being taken at arm
angles chosen specifically for this channel).

\vspace{0.9cm}


\begin{thebibliography}{A99}

\bibitem{dedx} Computer code DEDX, (Daresbury Laboratory), unpublished.

\bibitem{target} N. Curtis, Computer code TARGET, (University of Birmingham), unpublished.

\bibitem{ncthesis} N. Curtis, PhD Thesis, (University of Birmingham, 1995),
unpublished.

\bibitem{leddy} M.J. Leddy, PhD Thesis, (University of Birmingham, 1994),
unpublished.

\bibitem{oopaper} N.~Curtis, A.St.J.~Murphy, N.M.~Clarke, M.~Freer,
B.R.~Fulton, S.J.~Hall, M.J.~Leddy, J.S.~Pople, G.~Tungate, R.P.~Ward,
W.N.~Catford, G.J.~Gyapong, S.M.~Singer, S.P.G.~Chappell, S.P.~Fox,
C.D.~Jones, D.L.~Watson, W.D.M.~Rae, P.M.~Simmons and P.H.~Regan,
Phys. Rev. C {\bf 53}, 1804 (1996).


\end{thebibliography}



\end{document}








