We apply the diabatic formalism, an extension of the adiabatic approximation
inherent to the Born-Oppenheimer (BO) approach of atomic physics, to the
problem of mixing between exotic multiquark hadrons and their nearby di-hadron
thresholds. The unperturbed BO eigenstates are obtained using the dynamical
diquark model, while the diabatic calculation introduces a mixing potential
between these states and the threshold states. We solve the resulting coupled
Schr\"{o}dinger equations numerically for hidden-charm tetraquarks of both open
and closed strangeness to obtain physical mass eigenvalues, and explore the
di-hadron state content and spatial extent of the eigenstates. As an explicit
example, X(3872) emerges with a dominant D0DΛβ0 component, but
also contains a considerable diquark-antidiquark component that can contribute
significantly to its radiative decay widths, and this component also generates
a full multiplet of other diquark-based exotic hadrons to be compared with
experiment.Comment: 9 pages - Version accepted to Physical Review