  We allow up to $4 \hbar\omega$ excitations in $^8Be$ relative to the basic
configuration $(0s)^4(0p)^4$ in order to see if there are low-lying intruder
states in $^8Be$. We use three interactions $-\chi Q \cdot Q, -\chi Q \cdot Q$
+ spin-orbit, and a realistic (x,y) interaction, where for $x=1,y=1$ one gets
values for the spin-orbit and tensor interactions which correspond closely to
those of a non-relativistic $G$ matrix such as Bonn A. For the three
interactions considered, if we allow up to $2 \hbar \omega$ excitations we get
the energy of the lowest $J=0^+$ intruder state to be at 32.1 MeV, 30.1 MeV and
33.8 MeV, respectively. If we allow up to $4 \hbar\omega$ excitations the
corresponding values are 26.5 MeV, 26.5 MeV and 28.7 MeV. We thus support the
statement made by E. Warburton in his 1986 $R$ matrix analysis of the
$\beta^{\mp}$-delayed alpha spectra from the decay of $^8Li$ and $^8B$ that
``satisfactory fits are obtained without introducing intruder states below
26-MeV excitations'' (Phys. Rev. C 33, 303(1986)). In $^{10}Be$ however, with
the first two ``$Q \cdot Q$'' interactions, we get (with up to $2 \hbar \omega$
excitations) low-lying intruder states at 9.7 MeV and 11.9 MeV respectively.
Thus the presence of low-lying intruder states in $^{10}Be$ (the $0^+_2$ state
at 6.179 MeV may or may not be an intruder) does not imply that there are
low-lying intruder states in $^8Be$.

Nuclear Theory