  With the accumulation of experimental data, more and more exotic hadrons are
observed. Among the interpretations of these exotic hadrons, molecular state
and compact multiquark are two of the most popular pictures. However, it is
still difficult to determine the structure of an exotic hadron. In this work,
we propose a possible way to detect the internal structure of an exotic state.
When a molecular state composed of two consistent hadrons is attacked by
another particle, one of the constituents should be kicked out while another
quasifree constituent stays almost unaffected. It is different from a compact
multiquark which has no obvious subcluster. In this work, taking the $X(3872)$
as an example, we perform a Dalitz plot analysis of such reaction to find the
effect of the different internal structures. Under the assumption of the
$X(3872)$ as a molecular state or a compact tetraquark state, with the help of
the effective Lagrangians, the Dalitz plot and the invariant mass spectrum are
estimated with different total invariant mass of three final particles, and the
effect of different binding energies is also discussed. Obvious event
concentration can be observed as strips in the Dalitz plot and sharp peaks in
the invariant mass spectrum for the $X(3872)$ with a small binding energy under
the molecular state picture, while such concentration cannot be observed under
the compact tetraquark picture. Such phenomenon can be applied to identify the
internal structure of a new hadron state.
