The Theory of Line Intensities in the Spectrum of Scattered Light. I. The Quantum Model (Condon Approximation)

Mateusz Borkowski, R. Ciuryło, Paul S. Julienne +5 more

We study theoretically the properties of photoassociation spectra near the 1S0‐3P1 inter‐combination line of bosonic ytterbium. We construct a mass scaled model of the excited state interaction potential that well describes bound state energies obtained in a previous photoassociation experiment. We then use it to calculate theoretical photoassociation spectra in a range of ultracold temperatures using semianalytical theory developed by Bohn and Julienne.Photoassociation spectra not only give us the energies of excited bound states, but also provide information about the behavior of the ground state wavefunction. In fact, it can be shown that within the so‐called reflection approximation the line intensity is proportional to the ground state wavefunction at the transition’s Condon point. We show that in the case of ytterbium, the rotational structure of the photoassociation spectra depends heavily on the behavior of the ground‐state wavefunction. The change of the scattering length from one isotope to another and the resulting occurence of shape resonances in higher partial waves determines the appearance and disapperance of rotational components, especially in the deeper lying states, whose respective Condon points lie near the ground state centrifugal barrier. Thus, photoassociation spectra differ qualitatively between isotopes.

Milan Pospíchal

T. Fujimoto, A. V. Phelps

Experimental line profiles and integrated intensities for backscattered and forward-scattered resonance radiation using white-light excitation are compared with theory for Na densities between ${10}^{19}$ and ${10}^{22}$ atoms/${\mathrm{m}}^{3}$. Absorption measurements are used to verify linewidth and line-wing asymmetry parameters and Na-vapor densities. The scattered spectral intensities are normalized to the incident flux using calibrated diffusers. Measurements of scattered intensities were also made as ${\mathrm{N}}_{2}$ was added to the Na. The line profiles and integrated intensities were calculated using a model which assumes complete redistribution of the radiation scattered by an atom and takes into account both radiative and nonradiative transport of the resonance excitation. The theory includes the effects of quenching by ${\mathrm{Na}}_{2}$ and by admixed ${\mathrm{N}}_{2}$. With the white-light excitation used in these experiments the radiative transport is found to dominate the nonradiative transport except at wavelengths very near line center. The agreement between experimental and theoretical line profiles is good at high sodium densities (\ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/${\mathrm{m}}^{3}$) where instrumental resolution is not a serious limitation. The agreement between experimental and theoretical integrated intensities is within experimental error for Na densities of (1-10) \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ and (2-5) \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/${\mathrm{m}}^{3}$. At the intermediate densities the approximately 20% discrepancy may be caused by the incomplete redistribution of radiation in the scattering process.

Daniel F. V. James, E. Wolf

The effect of the statistical properties of fluctuating light sources on the spectrum of the emitted radiation has been the subject of intense research over the last few years. It was first shown that due to spatial correlations, the spectrum of light was not, in general, invariant on propagation, even in free space.1 It was also shown that these effects can lead to shifts of spectral lines, a result which is of interest particularly for astrophysics.2 In view of the intimate connection between radiation from localized sources and scattering from media of finite extent, similar spectral changes may also be produced by scattering. In this paper a model scatterer is introduced, whose dielectric response function is a random function of space and time and whose space-time correlation function is a Gaussian function in all its variables. Using the first-order Born approximation, such scattering media are shown to generate frequency shifts of spectral lines that imitate the Doppler effect in its main features. The shifts may be arbitrarily large. Some numerical simulations of such shifts are presented and compared with Doppler shifts.

Milan Pospíchal