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{\large {\bf Experiment Proposals}}\\[2mm]
Suggestions based on recent theory}}\\[7mm]
\makebox[2.5cm][l]{Author:} W.D.M. Rae, A.C. Merchant\\[2mm]
\makebox[2.5cm][l]{Date:} 23 Sep 1994\\[2mm]
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\begin{center} \begin{tabular}{l@{\hspace*{14cm}}l} \hline
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\begin{center}
{\Large {\bf Proposals for new experiments resulting from recent theoretical
work at Oxford.}}\\
\bigskip
{\large Bill Rae and Alan Merchant}
\bigskip
\end{center}
\begin{enumerate}
\item 
Our recent interpretation of the decay of alpha chain states
suggests that the spreading width is larger than the escape (or
fission) width. The implication of this is that the chain state
resonance is strongly mixed with other cluster resonances at the
same excitation energy in $^{24}$Mg. This implies that if the chain
state is observed with high energy resolution it should be seen to
be fragmented into a large number of narrower resonant structures.

We propose that the excitation function and angular distributions
(from 30$^{\circ}$ to 90$^{\circ}$) should be measured with an adequately thin
target and an energy step of 100-200 keV in the centre of mass.
These data should show evidence of the narrower intermediate
structure resonances typical of $^{12}$C+$^{12}$C scattering. We essentially
have found evidence of this effect in the Argonne data where we
had to add random components at each energy to fit the data.
But the energy step was too large to really determine if this
was intermediate structure.

\item Following on from the above, as we know from our own work and
the Strasbourg conference, because of the mixing and the coherence
of the angular distributions at 90$^{\circ}$ evidence of the existence
of a ``shape eigenstate'' can be found in reaction channels other
than the fission channel. Thus the search for other alpha chain
states may be easier if we were to look for 90$^{\circ}$ enhancements in
mismatched 0$^+$--0$^+$ final states---but not necessarily the multi-alpha
fission final state.

Thus for $^{28}$Si we maybe should use the $^{16}$O+$^{12}$C reaction
 but look at
the $^{16}$O(12.05 MeV 0$^+$) + $^{12}$C(7.65 MeV 0$^+$) channel, at 
90$^{\circ}$ in the centre of mass over a wide energy range.

It may be there are effects we do not yet understand about chain states
in odd-alpha nuclei. Possibly the existence of negative parity states
in the entrance channel also creates problems. Thus it may be better
to look in $^{32}$S via $^{16}$O+$^{16}$O looking at the mutual 12.05 MeV 
0$^+$ excitation.

The 12.05 MeV state is observed in $^{16}$O scattering using the RPS
technique (Rae et al. Phys.Rev. {\bf C30} (1984) 158, S Allcock 
D.Phil Thesis 1986).
It is close to the 11.47 MeV 2$^+$ which is strong. But with detectors
placed sufficiently far from the target it should be easily resolved
cleanly. It decays to $^{12}$C$_{\rm gs} + \alpha$ so a hybrid-strip pair is
required to detect each $^{16}$O.

\item Calculations of the D1 band in $^{24}$Mg (Jie Zhang) are beginning to
suggest that the ground state of the D1 is below the 
barrier---possibly starting at around 15 MeV E$_{\rm x}$ in 
$^{24}$Mg (c.f. $^{20}$Ne. The ground state
of $^{20}$Ne is closely related to D1. The 0$^+_2$, 
0$^+_3$ and 0$^+_4$ bands in $^{20}$Ne are
closely spaced bands in $^{20}$Ne two of which are known to be vibrations
of the $^{20}$Ne$_{\rm gs}$. The third we believe is also closely related. 
These bands start at around 6 MeV E$_{\rm x}$ in $^{20}$Ne and are closely 
spaced. These could correspond with the barrier resonances in $^{24}$Mg 
some 6 MeV or so above the D1 ground state.) (See also next section 4.)

To probe this we should use $^{16}$O+$^{12}$C and sit on one of the resonances
observed by S.Fox in the $^{16}$O$_{\rm gs}+^{12}$C(0$^+_2$) 
final channel. Such a resonance
should have an $\alpha$--$^{16}$O--$\alpha$--$\alpha$ structure. 
Thus alpha decay should take
it to the gs of the D1 band in $^{24}$Mg and although this is below the
barrier for $^8$Be or $^{12}$C decay---it can alpha decay. So study the
$^{16}$O($^{12}$C,$\alpha$--$\alpha$)$^{20}$Ne 
reaction (c.f. Rae + Keeling, Nucl.Phys. {\bf A575} (1994)
175). Data should be taken at the strong resonance energies in S.Fox's
data and off resonance to compare the spectra of $^{24}$Mg on and
off resonance. (See also Zhang et al. Phys.Rev. {\bf C48} (1993) 2117 and
Eswaran et al. Phys.Rev. {\bf C47} (1993) 1418.)

\item A new type of shape eigenstate in $^{32}$S and negative parity D1.

We have just modified the BB model to improve the calculations
for the D1 band in $^{24}$Mg. As a result of this we can now predict
a stable negative parity D1 band in $^{24}$Mg some 0.5--1 MeV above the
positive parity band.

The D1 is part of a family starting with $^{12}$C. The family is
$^{12}$C, $^{12}$C--$\alpha$ ($^{16}$O gs), $\alpha$--$^{12}$C--$\alpha$ 
($^{20}$Ne gs), $\alpha$--$^{12}$C--$\alpha$--$\alpha$ (D1),
$\alpha$--$\alpha$--$^{12}$C--$\alpha$--$\alpha$ (see above 3), 
$\alpha$--$\alpha$--$\alpha$--$^{12}$C--$\alpha$--$\alpha$ ($^{32}$S) and
$\ldots$

Alan Merchant is calculating the properties of these states
using the new improved BB code. In $^{32}$S the moment of inertia
of the band may be close to that of the 6--$\alpha$ chain state---and
thus may be a ``Shape Eigenstate''. The entrance channel is
obviously $^{20}$Ne+$^{12}$C---thus an Argonne experiment. We will keep you
posted.

(The improvement to the BB model is essentially a better
parity projection algorithm which generates a better
wavefunction in a variational sense.)

\end{enumerate}
\vfil


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