Generalized local-frame-transformation theory for excited species in external fields

A rigorous theoretical framework is developed for a generalized local-frame-transformation theory (GLFT). The GLFT is applicable to the following systems: Rydberg atoms or molecules in an electric field and negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local-frame-transformation theory developed initially by U. Fano [Phys. Rev. A 24, 619 (1981)] and D. A. Harmin [Phys. Rev. A 26, 2656 (1982)]. This revised GLFT theory yields nontrivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semianalytical GLFT Stark spectra with ab initio numerical simulations yield errors in the range of a few tens of MHz, an improvement over the original Fano-Harmin theory, whose errors are 10–100 times larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.

Figure 1

The quantity $J_{\ell {\ell }^{\prime }}$ as a function of the total number of ${\beta }^F$ fractional charges. The field strength is $F=1000$ V/cm, the energy is set to $\epsilon =-0.0021$ a.u., and the polarization of the photon is $m=0$. The three different curves correspond to different $\ell$ angular momentum combinations, i.e., $J_{0,0}$ (red solid line and pluses), $J_{0,1}$ (green dashed line and crosses), and $J_{1,1}$ (blue dotted line and stars). The vertical black line indicates the total number of ${\beta }^F$ where the corresponding fractional charges ${\beta }^F$ are less than 1.

Figure 2

An illustration of the GLFT quantities $|{\overline{h}}_{\ell {\ell }^{\prime }}^F|$ (scattered points) and the LFT quantities $|h_{\ell {\ell }^{\prime }}^F|$ (solid lines) as a function of the electric field strength $F$ ($\mathrm{V}/\mathrm{cm}$) at an energy $\epsilon =-0.0021\mathrm{a}.\mathrm{u}.$ for $\ell \ne {\ell }^{\prime }$. Note that $m=0$.

Figure 3

The top panel illustrates the single-pulse photoionization cross section for Na atoms versus energy $\epsilon$ for $F=4$ kV/cm, where the photon's polarization is parallel to the electric field. The shaded areas from left to right refer to resonances depicted in the bottom panel, where three different methods are compared. The orange solid line (TDSE) denotes the full numerical calculations, whereas the gray dots refer to the Fano-Harmin theory (LFT) results, and the black dots indicate the GLFT. Note that the arrow brackets denote the absolute difference in resonance energies between the LFT and GLFT. In addition, in the bottom panel all the calculations are scaled by the same factor such that the far right resonance peaks are the same in the LFT, GLFT, and TDSE approaches.