Simple and efficient lambda-method and lambda/2-method (lambda is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium are implemented to study the splitting of hyperfine transitions of 85Rb and 87Rb D_1
line in an external magnetic field in the range of B = 0.5 - 0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in 85Rb (87Rb) spectra in the case of sigma+ polarized laser radiation, only 6 (4) remain at B > 0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen-Back regime). The expressions derived in the frame of completely uncoupled basis (J, m_J ; I, m_I) describe very well the experimental results for 85Rb transitions at $B > 0.6 T (that is a manifestation of hyperfine Paschen-Back regime). A remarkable result is that the calculations based on the eigenstates of coupled (F, m_F) basis, which adequately describe the system for low magnetic field, also predict reduction of number of transition components from 20 to 6 for 85Rb, and from 12 to 4 for 87Rb spectrum at B > 0.5 T. Also, the Zeeman transitions frequency shift, frequency interval between the components and their slope versus $B$ are in agreement with the experiment.
We have implemented the so-called $lambda$-Zeeman technique (LZT) to investigate individual hyperfine transitions between Zeeman sublevels of the Rb atoms in a strong external magnetic field $B$ in the range of $2500 - 5000$ G (recently it was establ
ished that LZT is very convenient for the range of $10 - 2500$ G). Atoms are confined in a nanometric thin cell (NTC) with the thickness $L = lambda$, where $lambda$ is the resonant wavelength 794 nm for Rb $D_1$ line. Narrow velocity selective optical pumping (VSOP) resonances in the transmission spectrum of the NTC are split into several components in a magnetic field with the frequency positions and transition probabilities depending on the $B$-field. Possible applications are described, such as magnetometers with nanometric local spatial resolution and tunable atomic frequency references.
We suggest to use for $XY_2$ molecules some results previously established in a series of articles for vibrational modes and electronic states with an $E$ symmetry type. We first summarize the formalism for the standard $u(2)supset su(2)supset so(2)$
chain which, for its most part, can be kept for the study of both stretching and bending modes of $XY_2$ molecules. Next the also standard chain $u(3)supset u(2) supset su(2) supset so(2)$ which is necessary, within the considered approach, is introduced for the stretching modes. All operators acting within the irreducible representation (textit{irrep}) $[N00]equiv [Ndot{0}]$ of $u(3)$ are built and their matrix elements computed within the standard basis. All stretch-bend interaction operators taking into account the polyad structure associated with a resonance $omega_1approx omega_3 approx 2 omega_2$ are obtained. As an illustration, an application to the $D_2S$ molecular system is considered, especially the symmetrization in $C_{2v}$. It is shown that our unitary formalism allows to reproduce in an extremely satisfactory way all the experimental data up to the dissociation limit.
