Ion and electron spectroscopy of strontium in the vicinity of the two-photon-excited $5p^2$ ${}^1{S}_0$ state

Two-photon ionization of ground-state strontium is investigated experimentally in the 360–370-nm spectral range with dye laser pulses of long (∼ns) duration and low $\mathrm{(}\mathrm{\sim }10{}^{10}W\mathrm{\hspace{0.17em}cm}{}^{-2}$) intensity. The ${\mathrm{Sr}}^{+}$ spectra recorded with linear laser polarization are dominated by the presence of the highly correlated $5p^2$ ${}^1{S}_0$ state and by the even parity $[4d$$6d]$]${}_J$${}_{=0,2}$ autoionizing states. The partial $J=0$ and $J=2$ two-photon ionization cross sections are recovered from these data along with the spectra obtained with circular polarization. For linear polarization, the observed wavelength dependence of ${\mathrm{Sr}}^{+}$ production is compared with earlier theoretical work based on the $R$-matrix–multichannel-quantum-defect-theory approach and the agreement is generally found to be quite satisfactory. There are, however, a few, albeit noticeable, discrepancies. The latter motivated us to proceed to a more comprehensive experimental characterization of the examined energy range, by also measuring the kinetic energy and angular distribution of the ejected photoelectrons under linear laser polarization. The shapes of the angular distributions vary rapidly in the neighborhood of each resonance, while these distributions are found to be almost spherically symmetric on the maxima of the sharp $[4d$$6d]$]${}_J$${}_{=0}$ lines. On these, and only these, maxima, electron energy spectra reveal the absorption of a third photon, resulting in production of ${\mathrm{Sr}}^{+}$ into its excited $4d_j$ and $5p_j$ states. The non-negligible $5p_j$ branching ratio reflects the mixing between the $[4d$$6d]$]${}_J$${}_{=0}$ states and the $5p^2$ ${}^1{S}_0$ perturber, found to be rather underestimated by the aforementioned theoretical work. Thus, the presently acquired ion and electron spectra as well as the asymmetry parameters obtained by fitting the photoelectron angular distributions provide a stringent test of future theoretical efforts, addressing structure as well as excitation and ionization issues in an improved manner.

Figure 1

Partial energy level diagram of Sr along with the multiphoton-excitation scheme. The two-photon-excited autoionizing states and the decay pathways are discussed in the text.

Figure 2

Schematic drawing of the experimental setup. (a) Optical arrangement. DL: dye laser system; BBO: BBO type-III frequency doubling crystal; F: filter for the suppression of the fundamental wavelength laser beam; P: right-angle prism; VA: variable attenuator; LP: linear polarizer; DFR: double Fresnel rhomb; SFR: single Fresnel rhomb (removed for PAD measurements); L: fused silica lens. (b) Interaction chamber and ion and electron detection. i-TOF: positive ion time-of-flight mass spectrometer; V${}_{\mathrm{TOF}}$: positive HV pulse. EL: Electrostatic lens; SEA: spherical sector electron energy analyzer; MCP: microchannel plates.

Figure 3

Experimental ${\mathrm{Sr}}^{+}$ spectra recorded as a function of UV laser wavelength with (a) linear laser polarization ($J=0$ and 2 final states) and (b) circular polarization ($J=2$ final states only). Apart from the different polarizations the two spectra were recorded under identical conditions and laser power density $I$≈2 × $10{}^{10}$ W ${\mathrm{cm}}^{-2}$. (c) ${\sigma }_{J=0,\mathrm{Lin}}^{\left(2\right)}$ and (d) ${\sigma }_{J=2,\mathrm{Lin}}^{\left(2\right)}$ partial two-photon cross sections for linear polarization (both in arbitrary units), estimated as explained in the text and using spectra (a) and (b). The $y$ scales of all plots (a)–(d) can be compared to each other. Details on level assignments are given in the text.

Figure 4

Electron energy spectra acquired at different wavelengths and with linear laser polarization pointing towards the direction of detection (θ = 0°). The pass energy of the electrostatic analyzer was set at $E_{\mathrm{o}}=30$ eV. (a) Spectrum recorded at λ≈365.3 nm (on the blue side of $5p^2$ ${}^1{S}_0$ resonance) for laser power density $I$≈2 × $10{}^{10}$ W ${\mathrm{cm}}^{-2}$. Only the process described by Eq. (1) is observed. (b), (c) Spectra on the maxima of the $4d$$6d$ ${}^3{P}_0$ (λ≈363.5 nm) and $4d$$6d$ ${}^1$$S_0$ (λ≈360.7 nm) lines, respectively, for $I$≈4 × $10{}^{10}$ W ${\mathrm{cm}}^{-2}$. The processes described by Eqs. (2) and (3) are also observed. In plot (c) an additional electron peak is visible, whose energy (∼2.1 eV) corresponds to four-photon ionization and the ion left to its $6s_{1/2}$ state (see Fig. 1). This peak, however, is quite weak and not fully reproducible. The curves drawn in (a)–(c) were obtained after smoothing the recorded data. The signal error bars, given for a single point of each plot, correspond to the maximum (and typical) amplitude of the residual (nonsmoothed minus smoothed) curve. The electron energy scales were calibrated using known two-photon resonant, three-photon ionization processes of Xe atom [24], recorded under unsaturated and space-charge-free conditions.

Figure 5

Selected experimental and fitted PADs from two-photon ionization of ground-state Sr [process of Eq. (1)], for $I$≈2 × $10{}^{10}$ W ${\mathrm{cm}}^{-2}$. The quoted error bars are the standard deviation of the experimental data accumulated over a few thousand laser shots. Vertical as well as horizontal scales are the same for all graphs. Each row shows the PADs in the vicinity of a given $J=0$ final doubly excited state, i.e., the $4d$$6d$ ${}^1$$S_0$ (upper row), the $4d$$6d$ ${}^3{P}_0$ (middle row), and the $5p^2$ ${}^1{S}_0$ one (bottom row). The maximum of the latter broad resonance occurs at ≈367 nm. On the maxima of the two $[4d$$6d]$]${}_J$${}_{=0}$ resonances the PADs are almost spherically symmetric.

Figure 6

(a) Reproduction of the ${\mathrm{Sr}}^{+}$ spectrum given in Fig. 3 and recorded with linear laser polarization. It represents ${\sigma }_{\mathrm{tot},\mathrm{Lin}}^{\left(2\right)}$ [Eq. (7a)], which, in turn, is proportional to ${\beta }_0^{\left(2\right)}$ [Eq. (8b)]. (b) UV laser wavelength dependence of the asymmetry parameter ratio ${\beta }_2^{\left(2\right)}/{\beta }_0^{\left(2\right)}$, determined by fitting the PADs from two-photon ionization of ground-state Sr to Eq. (8a). (c) The same as in (b) for the ratio ${\beta }_4^{\left(2\right)}/{\beta }_0^{\left(2\right)}$. In (b) and (c) the symbols are connected by straight lines. (d) Partial cross-section ratio ${\sigma }_{J=0,\mathrm{Lin}}^{\left(2\right)}/{\sigma }_{J=2,\mathrm{Lin}}^{\left(2\right)}$, as estimated via the ratios ${\beta }_{2k}^{\left(2\right)}/{\beta }_0^{\left(2\right)}$ and Eqs. (9a)–(9c) (white squares) and by the ratio of the ${\mathrm{Sr}}^{+}$ spectra of Figs. 3 and 3 (gray dashed line). The latter exhibit “spikes” on the locations of $J=2$ resonances due to the quasizero signal minima of their Fano profiles. (e) Phase difference Δδ = ${\delta }_2$–${\delta }_0$ between 5sεs ${}^1$$S_0$ and 5sεd ${}^1$$D_2$ continua. Δδ (assumed to be positive) is estimated through the ratios ${\beta }_{2k}^{\left(2\right)}/{\beta }_0^{\left(2\right)}$ and Eqs. (9a)–(9c).

Figure 7

Experimental (points) and fitted (lines) polar plots of PADs from two-photon (2ω) and three-photon (3ω) ionization at the maxima of (a) $4d$$6d$ ${}^1$$S_0$ and (b) $4d$$6d$ ${}^3{P}_0$ resonances. The vertical dashed double-arrowed line indicates the linear laser polarization direction. The plots do not have the same radial scale. The 2ω case ($I$≈2 × $10{}^{10}$ W ${\mathrm{cm}}^{-2}$) refers to the ionization pathway of Eq. (1), while in the 3ω case ($I$≈4 × $10{}^{10}$ W ${\mathrm{cm}}^{-2}$) there are two pathways leaving the ion either to its $4d_j$ state [Eq. (2)] or its $5p_j$ state [Eq. (3)].