  We present a scheme well-suited to investigate quantitatively the angular
momentum coherence of molecular fragments. Assuming that the dissociated
molecule has a null total angular momentum, we investigate the propagation of
the corresponding atomic fragments in the apparatus. We show that the
envisioned interferometer enables one to distinguish unambiguously a
spin-coherent from a spin-incoherent dissociation, as well as to estimate the
purity of the angular momentum density matrix associated with the fragments.
This setup, which may be seen as an atomic analogue of a twin-photon
interferometer, can be used to investigate the suitability of molecule
dissociation processes -- such as the metastable hydrogen atoms H($2^2
S$)-H($2^2 S$) dissociation - for coherent twin-atom optics.
