Experimental Link of Photoionization of $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ to Photorecombination of $\mathrm{S}{\mathrm{c}}^{\mathrm{3}\mathrm{+}}$: An Application of Detailed Balance in a Unique Atomic System

The principle of microscopic time reversal of physical processes, detailed balance, is widely used and depended upon in the theoretical community as a connection between photorecombination (PR) and photoionization (PI). This paper reports on a novel use of detailed balance and the comparison of experimental results obtained by two very distinct techniques to determine both the metastable fraction of an ion beam and partial $\mathrm{S}{\mathrm{c}}^{\mathrm{3}\mathrm{+}}$ PR cross sections and partial $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ PI cross sections for the ground state and for two metastable states. The $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ to $\mathrm{S}{\mathrm{c}}^{\mathrm{3}\mathrm{+}}$ system presents a unique opportunity to obtain comprehensive state-selective information by combining results from PR and PI experiments.

Figure 1

Experimental (shaded curve) and theoretical (full line) [13] $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ PI cross section in the energy range 32.5–43.5 eV. Resonances have been identified with the aid of atomic structure calculations [14]. In the designation of the resonances [Ar]$3d$ or [Ar]$4s$ have been omitted in the case of the $2D_{3/2}$, $2D_{5/2}$, and $2S_{1/2}$ initial states and [Mg]$3p^5$ in the case of the doubly excited intermediate states. The experimental energy spread is $\sim 25\mathrm{m}\mathrm{e}\mathrm{V}$.

Figure 2

Energy level diagram for the dielectronic (resonant) recombination of $\mathrm{S}{\mathrm{c}}^{\mathrm{3}\mathrm{+}}$ ions. Initially the ion in the $3p^6{}^{1}S$ ground state ($f$) collides with a free electron with energy $E_{\mathrm{c}\mathrm{m}}$ above the first $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ ionization threshold. If $E_{\mathrm{c}\mathrm{m}}\approx E_{\mathrm{r}\mathrm{e}\mathrm{s}}$ a $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$($3p^{5}3d{n}^{\prime }{l}^{\prime }$) doubly excited state ($d$) may be formed by dielectronic capture (inverse autoionization) with nonzero probability (horizontal full arrow). The recombination event is completed by a subsequent radiative transition to a bound state below the $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ ionization threshold (vertical arrows). For $3p^{5}3d^2$ and $3p^{5}3d4s$ doubly excited intermediate states the radiative decay paths to the PI initial states $3p^{6}3d$ ($i$, thick full vertical arrow) and $3p^{6}4s$ ($i^{\prime }$, thick dash-dotted vertical arrow) respectively ($3d\to 3p$ transitions) are unique; i.e., for the decay of $3p^{5}3d^2$ and $3p^{5}3d4s$ states the multitude of other energetically allowed transitions (vertical thin full arrows) can be neglected (see text). On the scale of the figure fine-structure level splittings are not resolved.

Figure 3

Fit of the weighted sum of partial PR cross sections derived from the present PI measurements to the experimental PR cross section (open symbols) measured at the Heidelberg heavy-ion storage-ring TSR [11]. The resonance line shapes were convoluted with a normalized Gaussian representing the resolution of the $\mathrm{S}{\mathrm{c}}^{\mathrm{3}\mathrm{+}}$ PR experiment. The partial cross sections [cf. Eq. (2)] adding up to the total fit result [full line in (b)] are shown separately in (a).

Figure 4

State selective $\mathrm{S}{\mathrm{c}}^{\mathrm{2}\mathrm{+}}$ PI cross section. The systematic uncertainty of the cross section scale is $\pm 20\%$. The energy spread is $25\mathrm{m}\mathrm{e}\mathrm{V}$, i.e., approximately the same as in Fig. 1.