We combined high-resolution Fourier-transform spectroscopy and large-scale electronic structure calculation to study energy and radiative properties of the high-lying (3)1{Pi} and (5)1{Sigma}+ states of the RbCs molecule. The laser-induced (5)1{Sigma}+(4)1{Sigma}+(3)1{Pi}-A(2)1{Sigma}+ b(1)3{Pi} fluorescence (LIF) spectra were recorded by the Bruker IFS-125(HR) spectrometer in the frequency range { u} 5500 to 10000cm-1 with the instrumental resolution of 0.03 cm-1. The rotational assignment of the observed LIF progressions, which exhibit irregular vibrational-rotational spacing due to strong spin-orbit interaction between A1{Sigma}+ and b3(Pi) states was based on the coincidences between observed and calculated energy differences. The required rovibronic term values of the strongly perturbed A-b complex have been calculated by a coupled-channels approach for both 85Rb133Cs and 87Rb133Cs isotopologs with accuracy of about 0.01 cm-1, as demonstrated in A. Kruzins et al. [J. Chem. Phys. 141, 184309 (2014)]. The experimental energies of the upper (3)1(Pi) and (5)1{Sigma}+ states were involved in a direct-potential-fit analysis performed in the framework of inverted perturbation approach. Quasirelativistic ab initio calculations of the spin-allowed (3)1{Pi},(5)1{Sigma}+- (1-4)1{Sigma}+(1-3)1{Pi} transition dipole moments were performed. Radiative lifetimes and vibronic branching ratios of radiative transitions from the (3)1{Pi} and (5)1{Sigma}+ states were evaluated. To elucidate the origin of the {Lambda}-doubling effect in the (3)1{Pi} state, the angular coupling (3)1{Pi}-(1-5)1{Sigma}+ electronic matrix elements were calculated and applied for the relevant q-factors estimate. The intensity distributions simulated for the particular (5)1{Sigma}+(3)1{Pi}-A-b LIF progressions have been found to be remarkably close to their experimental counterparts.
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