  In this work we evaluate the $X(3872)$ to $ \psi (2S) $ yield ratio
($N_X/N_{\psi(2S)}$) in Pb Pb collisions, taking into account the interactions
of the $\psi (2S) $ and $ X(3872)$ states with light mesons in the hadron gas
formed at the late stages of these collisions. We employ an effective
Lagrangian approach to estimate the thermally-averaged cross sections for the
production and absorption of the $\psi(2S)$ and use them in the rate equation
to determine the time evolution of $N_{\psi(2S)}$. The multiplicity of these
states at the end of mixed phase is obtained from the coalescence model. The
multiplicity of $X(3872)$, treated as a bound state of $(D\bar D^{*} + c.c.)$
and also as a compact tetraquark, was already calculated in previous works.
Knowing these yields, we derive predictions for the ratio ($N_X/N_{\psi(2S)}$)
as a function of the centrality, of the center-of-mass energy and of the
charged hadron multiplicity measured at midrapidity $[dN_{ch}/d\eta
\,(\eta<0.5)]$. Finally, we make predictions for this ratio in Pb Pb collisions
at $\sqrt{s_{NN}} = 5.02$ TeV to be measured by the ALICE Collaboration in the
Run 3.
