(1,0) and (1,1) are allowed.

$L$ = $\frac{E}{\bar{\chi}}$ = $E^*(MeV)$\
1 $-58$ 10.07\
2 $-46$ 12.31\
3 $-28$ 15.67\

\(c) \[f\]=\[2,2\] ($\lambda,\mu$)=(0,2) The ($S,T$) combinations (0,0), (0,2), (2,0) and (1,1) are allowed.

$L$ = $\frac{E}{\bar{\chi}}$ = $E^*(MeV)$\
0 $-40$ 13.43\
2 $-22$ 16.78\

\(d) \[f\]=\[2,1,1\] ($\lambda,\mu$)=(1,0) The ($S,T$) combinations (0,1), (1,0), (1,1), (1,2) and (2,1) are allowed.

$L$ = $\frac{E}{\bar{\chi}}$ = $E^*(MeV)$\
1 $-10$ 19.02\

Note that this supermultiplet also has a state with the quantum numbers of the scissors mode $L=1~S=0~T=1$.

Some further comments are in order. The scissors mode state in $^{156}Gd$, as a single band state originally discovered in electron scattering [@bo], was found when finer resolution ($\gamma,\gamma'$) experiments were performed to consist of many states [@berg; @bohle]. This was a beautiful example of intermediate structure. The supermultiplet scheme here affords a concrete example of the origin of the intermediate structure. Our scissors mode state at an energy of $-58~\bar{\chi}$ is degenerate with an $L=1~S=1~T=1$ state. If we introduce spin-dependent interactions the two states will admix and the degeneracy will be removed. We will get intermediate structure.

B. Supermultiplet Scheme in $^{10}Be$
-------------------------------------

We now give the energies and some properties of the states in $^{10}Be$ ($\bar{\chi}=0.1286$): 