The angular distribution of scattered Lyman-$\ensuremath{\alpha}$ photons from atomic hydrogen is calculated as a function of an applied magnetic field. The intensity of the scattered radiation is a function of the energy difference of the excited-
2P levels and shows an extremum at the point where two levels cross. Neglecting hyperfine structure, there are two level crossings of interest: one at 3484 G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\frac{1}{2}}$), and the other 5223G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\ensuremath{-}\frac{1}{2}}$), respectively. The coher$\stackrel{\mathrm{\ifmmode \breve{}\else \u{}\fi{}}}{\mathrm{e}}$nt and incoherent resonance scattering is determined near these crossing points by using a Hamiltonian that includes hyperfine structure and higher-order radiative effects. In the low-field region (3484 G), the hyperfine crossings that contribute to the coherent signal are at 3476.06 and 3491.93 G, respectively. The radiative width of the levels is considerably larger than the hyperfine splittings, and the total scattering intensity has a single peak at 3483.97 G. In the high-field region (5223 G), two hyperfine levels with ${m}_{F}=\ensuremath{-}1$ repel each other (anticross) with a minimum energy separation of 15.3 Mc/sec at 5200.1 G. Resonances occur at 5220.6 and 5223.9 G, and the maximum of the total signal is at 5222.6 G.
The narrow electromagnetically-induced transparency (EIT) resonance peaks are observed with two low-power counter-propagating diode lasers in cesium (Cs) 6S1/2 - 6P1/2 - 8S1/2 ladder-type atomic system. To precisely determine the centers of resonance peaks, multiple background-free EIT signals are achieved using a novel scanning scheme in which the coupling laser driving Cs 6P1/2 - 8S1/2 transition is scanned and the probe laser driving Cs 6S1/2 – 6P1/2 is frequency locked. A temperature-stabilized fiber-pigtailed waveguide-type phase electro-optical modulator (EOM) and a stable confocal Fabry-Perot cavity are used as a precise frequency marker to measure the hyperfine splitting of Cs 8S1/2 state. The impact of the external magnetic field on the measurement is also investigated. Furthermore, the hyperfine structure constant (here it is the hyperfine magnetic dipole constant, A) of Cs 8S1/2 state is determined to be A = 219.06 MHz ± 0.12 MHz based on the measured hyperfine splitting (Δhfs = 876.24 MHz ± 0.50 MHz).