We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state ($n_A$P) and the other is in the ground state ($n_B$S). The presentation of the general expressions for the interaction energies in the Hund’s case (c) is followed by the calculation of the corresponding $C_6$ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the $C_6$ constants are found to be significantly influenced by the perturber’s fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in $C_6$ constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund’s case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.

We report on the observation of three RbCs satellite bands in the blue and green ranges of the visible spectrum. Absorption measurements are performed using all-sapphire cell filled with a mixture of Rb and Cs. We compare high resolution absorption spectrum of Rb-Cs vapor mixture with pure Rb and Cs vapor spectra from the literature. After detailed analysis, the new satellite bands of RbCs molecule at 418.3 nm, 468.3, and 527.5 nm are identified. The origin of these bands is discussed by direct comparison with difference potentials derived from quantum chemistry calculations of RbCs potential energy curves. These bands originate from the lower Rydberg states of the RbCs molecule. This study thus provides further insight into photoassociation of lower Rydberg molecular states, approximately between Cs(7s) + Rb(5s) and Cs(6s) + Rb(6p) asymptotes, in ultracold gases.

In the paper, several theoretical approaches to the determination of the reduced absorption and emission coefficients under local thermodynamic equilibrium conditions were exposed and discussed. The full quantum-mechanical procedure based on the Fourier grid Hamiltonian method was numerically robust but time consuming. In that method, all transitions between the bound, free, and quasi-bound states were treated as bound–bound transitions. The semi-classical method assumed continuous energies of ro-vibrational states, so it did not give the ro-vibrational structure of the molecular bands. That approach neglected the effects of turning points but agreed with the averaged-out quantum-mechanical spectra and it was computer time efficient. In the semi-quantum approximation, summing over the rotational quantum number J was done analytically using the classical Franck–Condon principle and the stationary–phase approximation and its consumption of computer time was lower by a few orders of magnitude than the case of the full quantum-mechanical approach. The approximation described well the vibrational but not the rotational structure of the molecular bands. All the above methods were compared and discussed in the case of a visible and near infrared spectrum of LiHe, Li₂, and Cs₂ molecules in the high temperature range.

In this study, we analyzed the light absorption by diatomic molecules or colliding atoms in a spectral region dominated by an avoided crossing of adiabatic state levels or crossing of the corresponding diabatic state levels. Our attention was focused on the low-resolution spectrum at a higher gas temperature under local thermodynamic equilibrium conditions. The absorption measurements of mixed vapors of potassium (≈80%) and cesium (≈20%) were made in the temperature range of 542–715 K and the infrared spectral range 900–1250 nm. In this area, the main spectral contributions were the broad $A^1{\Sigma }_{\left(u\right)}^{+}\left(0_{\left(u\right)}^{+}\right)-X^1{\Sigma }_{\left(g\right)}^{+}\left(0_{\left(g\right)}^{+}\right)$ bands of K₂, Cs_2, and KCs molecules. There was a crossing of $A^1{\Sigma }_{\left(u\right)}^{+}\left(0_{\left(u\right)}^{+}\right)$ and $b^3{\Pi }_{\left(u\right)}\left(0_{\left(u\right)}^{+}\right)$ state potential curves and the coupling of this state was due to the matrix element $⟨A^1{\Sigma }_{\left(u\right)}^{+}\left(0_{\left(u\right)}^{+}\right)|H_{so}|b^3{\Pi }_{\left(u\right)}\left(0_{\left(u\right)}^{+}\right)⟩$ of the spin–orbit interaction. Using data for relevant electronic potential curves and transition dipole moments existing in the literature, the spectra of the $A^1{\Sigma }_{\left(u\right)}^{+}\left(0_{\left(u\right)}^{+}\right)-X^1{\Sigma }_{\left(g\right)}^{+}\left(0_{\left(g\right)}^{+}\right)$ molecular bands of K₂, Cs_2, and KCs molecules were calculated. Full quantum mechanical and semi-quantum coupled channel calculations were done and compared with their non-coherent adiabatic or diabatic approximations. Through the comparison of our theoretical and experimental spectra, we identified all observed spectral features and determined the atoms’ number density and gas temperature.

To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g., the atom–atom and atom–surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of “elementary catastrophes” with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points (“cusp” catastrophe) and four saddle points (“swallow-tail” catastrophe).