Relative single- and double-photoionization cross sections of Mg around the $2p\to nl$ resonances

Using highly monochromatized synchrotron light and the ion time-of-flight method to detect singly and doubly charged magnesium ions, we have measured relative single- and double-photoionization cross sections of Mg from $55\text{to}58\mathrm{eV}$, which includes the region of the $2p\to nl$ inner-shell excitations. The resonances were analyzed using Fano profiles and the resonance positions are compared to previously published data. The quantum defect theory is applied to the resonance energies revealing that the published Mg $2p_{1∕2}$ and $2p_{3∕2}$ thresholds need to be revised. In addition, we have determined the double-to-single photoionization ratio in the $55\text{to}71\mathrm{eV}$ region.

Figure 1

(Color online) Total photoionization cross section of Mg in the $2p\to nl$ resonance region (solid black line). The upper panel also shows the total cross section curve of Ederer et al. [3] (dotted line). The same curve has been shifted and compressed (gray line) for a better agreement with our data. The lower panel shows the calculated cross section for the $3s^2\to 3skp\left({}^{1}P\right)$ transitions in the $2p\to nd$, $ns$ resonance region [10] (dotted line) along with our data. The peaks in the theoretical data are cut off as they appear in the original presentation. The resonances are labeled by letters for identification purposes. Note that in both panels all data are multiplied by 3 above $56\mathrm{eV}$.

Figure 2

(Color online) Our total photoionization cross section of Mg between the $2p_{3∕2}$ and $2p_{1∕2}$ thresholds (solid black line) along with the theoretical $3s$ (dashed line) and $2p_{3∕2}$ (dotted line) cross sections of Deshmukh and Manson [12]. Note that the tips of all calculated resonances are cut off. The theoretical curves are shifted by about $4.4\mathrm{eV}$ to lower energies. The resonances are labeled by letters inside circles for identification purposes.

Figure 3

(Color online) Relative single (black) and double (gray) photoionization cross sections of Mg. Note that the cross sections are displayed on a log scale. The resonances are labeled by letters and the $2p$ thresholds are indicated in the figure.

Figure 4

(Color online) Relative single (black) and double (gray) photoionization cross sections of Mg near the $2p$ thresholds. Besides the new, revised thresholds, the previously reported thresholds are indicated as dotted lines.

Figure 5

(Color online) Resonance positions $E_R$ as a function of the principal quantum number $n$ for the two highest Rydberg series converging to the $2p_{1∕2}$ threshold (circles, series “2,” $2p^5\left({}^{2}P_{1∕2}\right)ns[1∕2]$; diamonds, series “5,” $2p^5\left({}^{2}P_{1∕2}\right)nd[3∕2]$). The top panel shows the deviation of the data from the fit curve when applying Eq. (2) to our data. The fit was performed in the region of the solid line while the dotted line is an extrapolation of that fit.

Figure 6

(Color online) Resonance positions $E_R$ as a function of the principal quantum number $n$ for the three lower Rydberg series converging to the $2p_{3∕2}$ threshold (circles, series “1,” $2p^5\left({}^{2}P_{3∕2}\right)ns[3∕2]$; diamonds, series “3,” $2p^5\left({}^{2}P_{3∕2}\right)nd[3∕2]$; asterisks, series “4,” $2p^5\left({}^{2}P_{3∕2}\right)nd[1∕2]$). The top panel shows the deviation of the data from the fit curve when applying Eq. (2) to our data. The fit was performed in the region of the solid line while the dotted line is an extrapolation of that fit.

Figure 7

(Color online) Double-to-single photoionization ratio of Mg on a logarithmic scale. The data depicted by a gray line were calculated from the photon energy scans for ${\mathrm{Mg}}^{+}$ and ${\mathrm{Mg}}^{2+}$ across the resonances. The squares (connected by a dotted line) are the ratios calculated from individual ion TOF spectra. The black circles are previously presented [4] nonresonant ratios. The $2p$ thresholds are indicated in the figure.

Figure 8

(Color online) Double-to-single photoionization ratio of Mg in the $2p\to nl$ resonance region. The ratios above the $2p_{3∕2}$ threshold are divided by 100.

Figure 9

(Color online) Double-to-single photoionization ratio of Mg near the $2p$ thresholds. The data have been smoothed for clarity.