Fano Line Shapes Reconsidered: Symmetric Photoionization Peaks from Pure Continuum Excitation

In a photoionization spectrum in which there is no excitation of the discrete states, but only the underlying continuum, we have observed resonances which appear as symmetric peaks, not the commonly expected window resonances. Furthermore, since the excitation to the unperturbed continuum vanishes, the cross section expected from Fano’s configuration interaction theory is identically zero. This shortcoming is removed by the explicit introduction of the phase shifted continuum, which demonstrates that the shape of a resonance, by itself, provides no information about the relative excitation amplitudes to the discrete state and the continuum.

Figure 1

Excitation scheme of the experiment. The excitation of the Sr $5d17l$ state is done with four fixed frequency lasers and Stark switching. The frequency of the final fifth laser is swept through the energy from the ${\mathrm{S}\mathrm{r}}^{+}$ $5f$ to $5g$ limits. As shown, there is no excitation amplitude to the $5gn{l}^{\prime }$ states, only to the $5fϵl$ continuum.

Figure 2

Photoionization spectrum observed by scanning the fifth laser (a) from slightly below the $5f$ limit, shown by the arrow, to the vicinity of the $5g$ limit at about 544 nm. The resonances corresponding to $5g19l^{\prime }$ and $5g24l^{\prime }$ states have the numbers 19 and 24, respectively, above them. (b) Expanded view of the $5g19l^{\prime }–5g24l^{\prime }$ resonances.

Figure 3

Relative cross sections for pure continuum excitation assuming the same value of $⟨{\psi }_E|\mu |i{⟩}_{\max }$, or equivalently, the maximum cross section, in all cases. Four values of the initial state continuum phase are shown: ${\varphi }_i=0$, $\pi /4$, $\pi /3$, and $\pi /2$ corresponding to $q=0$, $-1$, $-1.732$, and $-\infty$. For $\varphi <0$ the profiles are reflected through $ϵ=0$.