Effective Range Approach for High Harmonic Generation by Negative Ions

We extend a recently-developed model-independent quantum approach for describing laser detachment of an electron with a non-zero angular momentum [1] to the case of high harmonic generation (HGG) by a negative ion. Our results are mainly focused on the dependence of high harmonic yield on the spatial symmetry of the bound state of a weakly-bound electron. Our numerical results for H$^-$ and F$^-$ ions (with $s$ and $p$ outer electrons, respectively) and linear laser polarization show that the HHG spectrum for $s$ and $p$-states are significantly different, whereas the plateau cutoff position is insensitive to the bound state symmetry. For F$^-$, harmonic generation rates for the different magnetic sublevels of the active $p$-electron differ by about 3-5 orders of magnitude. We also discuss the accuracy of Keldysh-like approximations for the HHG amplitude. [1] M.V. Frolov et al., Phys. Rev. Lett. {\bf 91}, 053003 (2003).