  We study the spin-half Heisenberg chain with alternating nearest neighbor
interactions $J_1(1+\delta)$ and $J_1(1-\delta)$ and a uniform second neighbor
interaction $J_2=y (1-\delta)$ by series expansions around the limit of
decoupled dimers ($\delta=1$). By extrapolating to $\delta=0$ and tuning $y$,
we study the critical point separating the power-law and spontaneously
dimerized phases of the spin-half antiferromagnet. We then focus on the
disorder line $y=0.5$, $0\le \delta\le 1$, where the ground states are known
exactly. We calculate the triplet excitation spectrum, their spectral weights
and wavevector dependent static susceptibility along this line. It is well
known that as $\delta \to 0$, the spin-gap is still non-zero but the triplets
are replaced by spinons as the elementary excitations. We study this dynamical
transition by analyzing the series for the spectral weight and the static
susceptibility. In particular, we show that the spectral weight for the
triplets vanishes and the static spin-susceptibility changes from a simple pole
at imaginary wavevectors to a branch cut at the transition.
