Isolated-core quadrupole excitation of highly excited autoionizing Rydberg states

The structure and photoexcitation dynamics of high-lying doubly excited states of the strontium atom with high angular momenta are studied in the vicinity of the ${\mathrm{Sr}}^{+}(N=5)$ threshold. The spectra recorded using resonant multiphoton isolated-core excitation are analyzed with calculations based on configuration interaction with exterior complex scaling, which treats the correlated motion of the two valence electrons of Sr from first principles. The results are rationalized with a model based on multichannel quantum-defect theory and transition dipole moments calculated with a perturbative treatment of electron correlations. Together, both approaches reveal that most of the lines observed in the spectra arise from the interaction of a single optically active state, coupled to the initial state by an electric-dipole transition, with entire doubly excited Rydberg series. The long-range electron correlations responsible for this interaction unexpectedly vanish for identical values of the initial and final principal quantum numbers, a fact related to the quasihydrogenic nature of the high-$l$ Rydberg electron. This special situation, and, in particular, the vanishing interaction, leads to the surprising observation of an electric-quadrupole isolated-core excitation with a similar intensity to that of the neighboring electric-dipole transitions.

Figure 1

Left: Multiphoton ICE scheme. Right: Photoionization spectra recorded in the region of the ${\mathrm{Sr}}^{+}\left(5f\right)$ and ${\mathrm{Sr}}^{+}\left(5g\right)$ ionization thresholds for $5d{n}_i{l}_i$ initial states with $l_i\sim 12$ and $n_i=16$, 18, 19, and 21. The assignment bars on the top axis and lower half of the right panel show the principal quantum numbers $n^{\prime }$ and $n$ relative to the ${\mathrm{Sr}}^{+}\left(5g\right)$ and ${\mathrm{Sr}}^{+}\left(5f\right)$ thresholds, respectively. The horizontal solid black lines in the $n_i=19$ spectrum show the widths of the $5g{n}^{\prime }{l}^{\prime }$ resonances (see text).

Figure 2

Energies relative to ${\mathrm{Sr}}^{2+}$ and widths of autoionizing states with predominant $5fn(l=12)$, $5gn(l=11)$, and $5gn(l=13)$ character (solid green, blue, and orange circles, respectively) calculated with CI-ECS for all possible $L$ values. The dashed curve shows the $n^{-3}$ scaling of the autoionization rates above the ${\mathrm{Sr}}^{+}\left(5f\right)$ threshold. The upper horizontal axis shows the principal quantum numbers $n^{\prime }$ relative to the $5g$ ionization threshold and the positions of the $5f$ and $5g$ thresholds. The lower assignment bar shows the principal quantum numbers $n$ relative to the $5f$ threshold. The solid gray circles are continuum states (see text).

Figure 3

(a) Comparison between the experimental spectrum (red curve) and the spectrum calculated with CI-ECS (green curve) for $n_i=19$ and $l_i=12$. The theoretical spectrum is plotted on a negative scale for clarity. (b) Absolute values of the energy-dependent transition dipole moments $D$ in atomic units (dashed curves) from an initial state with $n_i=19$, $l_i=12$ to final states with $n^{\prime }=17\text{–}23$ and with $l^{\prime }=11$ (brown) and $l^{\prime }=13$ (orange), respectively. Brown and orange circles show the values of $\left|D\right|$ at the position of the $5g{n}^{\prime }{l}^{\prime }$ Rydberg states [assignment bar at the top of (a)], and gray circles show the ICE transition dipole moments to $5fnl$ states with $n=30\text{–}45$ and $l=12$ for comparison. (c), (d), (e), and (f) Comparison of the experimental spectra (red curves) for $n_i=16$, 18, 19, and 21, respectively, and the results of the four-channel MQDT analysis (blue curves). The positions of quadrupole transitions, neglected in the calculations shown in this figure, are marked by asterisks.

Figure 4

(a) Experimental and (b) and (c) theoretical CI-ECS spectrum for $n_i=19$ and $l_i=12$. (b) shows the contribution of electric-quadrupole transitions to the theoretical spectrum, and (c) shows the total spectrum in which E1 and E2 transitions are summed.

Figure 5

Spectra of doubly excited states excited from the (a) $5d16n_i(l_i=12)$ and (b) $5d19n_i(l_i=12)$ states. Theoretical curves obtained from a five-channel analysis using the MQDT parameters given in Sec. 4a2: excitation of the $5f$ channel via ICE (shake-up and shake-off excitation) following the model described in Sec. 4a3 and in the Appendix (orange); excitation through the admixture of the $5fn(l=12)$ into the two $5g$ channels following the model described in Sec. 4a2 (green). Experiment: black curves (same as in Fig. 3).