Power-dependent line shapes of transitions to autoionizing Rydberg states

The line shapes of the $6sns$, ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-6\mathrm{}{P}_{\frac{1}{2}}\mathrm{ns}$ transitions in Ba as a function of the laser intensity are modeled with the use of two-channel multichannel quantum-defect theory and the isolated-core-excitation model. An analytical expression for the line shape is derived and used to obtain a value of $\left|〈g\right|r\left|e〉\right|=4.1\mathrm{}$ a.u. for the dipole transition moment of the ${\mathrm{Ba}}^{+}$ ionic $6s-6P_{\frac{1}{2}}$ transition, in agreement with a recent theoretical calculation.