  Lambda- Cold Dark Matter (LambdaCDM) has been successful at explaining the
large-scale structures in the universe but faces severe issues on smaller
scales when compared to observations. Introducing self-interactions between
dark matter particles claims to provide a solution to the small-scale issues in
the LambdaCDM simulations while being consistent with the observations at large
scales. The existence of the energy region in which these self-interactions
between dark matter particles come close to saturating the S-wave unitarity
bound can result in the formation of dark matter bound states called darkonium.
In this scenario, all the low energy scattering properties are determined by a
single parameter, the inverse scattering length gamma. In this work, we set
bounds on gamma by studying the impact of darkonium on the observations at
direct detection experiments using data from CRESST-III and XENON1T. The
exclusion limits on gamma are then subsequently converted to exclusion limits
on the self-interaction cross-section and compared with the constraints from
astrophysics and N-body simulations.
