  Using the polarisation labelling spectroscopy, we performed the detailed
analysis of the level structure of excited electronic states of the $^{39}$KCs
molecule in the excitation energy interval between 17500~cm$^{-1}$ and
18600~cm$^{-1}$ above the $v=0$ level of the $X^1\Sigma^+$ ground state. We
prove that the observed states are strongly coupled by spin-orbit interaction
above 18200~cm$^{-1}$, as manifested by numerous perturbations in the recorded
spectra. The spectra are interpreted with the guidance of accurate electronic
structure calculations on KCs, including potential energy curves, transition
electric dipole moments, and representation of the spin-orbit interaction with
a quasi-diabatic effective Hamiltonian approach. The agreement between theory
and experiment is found remarkable, clearly discriminating among the available
theoretical data. This study confirms the accuracy of the polarisation
labelling spectroscopy to analyse highly-excited electronic molecular states
which present a dense level structure.
