  We calculate the excitation spectrum and spectral weights of the alternating
antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange
couplings $J$ and $-|\lambda|J$ as a power series in $\lambda$. For small
$|\lambda|$, the gapped one-particle spectrum has a maximum at $k=0$ and there
is a rich structure of bound (and anti-bound) states below (and above) the
2-particle continuum. As $|\lambda|$ is increased past unity the spectrum
crosses over to the Haldane regime, where the peak shifts away from $k=0$, the
one particle states merge with the bottom of the continuum near $k=0$, and the
spectral weights associated with the one-particle states become very small.
Extrapolation of the spectrum to large $|\lambda|$ confirms that the ground
state energy and excitation gap map onto those of the spin-one chain.
