  We study the $\bar B_s^0 \to J/\psi f_0(980)$ and $\bar B_s^0 \to J/\psi
a_0(980)$ reactions, and pay attention to the different sources of isospin
violation and mixing of $f_0(980)$ and $a_0(980)$ resonances where these
resonances are dynamically generated from meson-meson interaction. We find that
the main cause of isospin violation is the isospin breaking in the meson-meson
transition $T$ matrices, and the other source is that the loops involving kaons
in the production mechanism do not cancel due to the different masses of the
charged and neutral kaons. We obtain a branching ratio for $a_0(980)$
production of the order of $5 \times 10^{-6}$. Future experiments can address
this problem, and the production rate and shape of the $\pi^0 \eta$ mass
distribution will definitely help to better understand the nature of scalar
resonances.
