  The translation action of $\RR^{d}$ on a translation bounded measure $\omega$
leads to an interesting class of dynamical systems, with a rather rich spectral
theory. In general, the diffraction spectrum of $\omega$, which is the carrier
of the diffraction measure, live on a subset of the dynamical spectrum. It is
known that, under some mild assumptions, a pure point diffraction spectrum
implies a pure point dynamical spectrum (the opposite implication always being
true). For other systems, the diffraction spectrum can be a proper subset of
the dynamical spectrum, as was pointed out for the Thue-Morse sequence (with
singular continuous diffraction) in \cite{EM}. Here, we construct a random
system of close-packed dimers on the line that have some underlying long-range
periodic order as well, and display the same type of phenomenon for a system
with absolutely continuous spectrum. An interpretation in terms of `atomic'
versus `molecular' spectrum suggests a way to come to a more general
correspondence between these two types of spectra.
