  We examine the spectrum of 2-colour lattice QCD with 4 continuum flavours at
a finite chemical potential ($\mu$) for quark-number, on a $12^3 \times 24$
lattice. First we present evidence that the system undergoes a transition to a
state with a diquark condensate, which spontaneously breaks quark number at
$\mu=m_\pi/2$, and that this transition is mean field in nature. We then
examine the 3 states that would be Goldstone bosons at $\mu=0$ for zero Dirac
and Majorana quark masses. The predictions of chiral effective Lagrangians give
a good description of the behaviour of these masses for $\mu < m_\pi/2$. Except
for the heaviest of these states, these predictions diverge from our
measurements, once $\mu$ is significantly greater than $m_\pi/2$. However, the
qualitative behaviour of these masses, indicates that the physics is very
similar to that predicted by these effective Lagrangians, and there is some
indication that at least part of these discrepancies is due to saturation, a
lattice artifact.
