The branching ratio of intercombination A1Σ+∼b3Π→a3Σ+/X1Σ+transitions in the RbCs molecule: Measurements and calculations

•The detection of the exremely weak A1Sigma+b˜3Pi→a3Sigmatransitions in laser-induced fluorescence of RbCs.•The scalar- and full-relativistic ab initio calculations of the transition dipole moments.•The comparison of the experimental and theoretical branching ratios of transitions to the triplet and singlet ground states.•The explanation of pecularities in the doublet progressions to the triplet ground state.