SCALED-ENERGY FLOQUET SPECTROSCOPY IN A STRONG ELECTRIC-FIELD - A SEMIQUANTAL CALCULATION OF THE RECURRENCE SPECTRUM

We consider a hydrogen atom in a strong static electric field with a w eak parallel radio-frequency (rf) field. We compute the photoabsorptio n spectrum by calculating the spectrum of Floquet states, including th eir quasienergies and their oscillator strengths. Our calculation is b ased upon ''semiquantal'' formulas: we calculate the discrete spectrum of quasienergy states by using a quantum adiabatic approximation comb ined with semiclassical (Bohr-Sommerfeld) quantization rules. We expre ss this spectrum in a manner consistent with the method of scaled-vari able spectroscopy, and then calculate the Fourier transform. These cal culated absorption spectra and recurrence spectra are in good agreemen t with experiments on Li atoms. Additional approximations show that th e recurrence spectrum is approximately equal to the product of the rec urrence spectrum in a static field times an envelope function. That en velope function is the Fourier transform of a cluster of sidebands sur rounding a progenitor level in the rf field. The resulting formula agr ees with the low-frequency limit of a formula obtained from a semiclas sical treatment.