Valence-shell single photoionization of chlorine-like ${\mathrm{K}}^{2+}$ ions: Experiment and theory

The absolute single-photoionization cross section was measured for Cl-like ${\mathrm{K}}^{2+}$ over the photon energy range from 44.2 to 69.7 eV at a constant energy resolution of 0.045 eV. The experiments were performed by merging an ion beam with a beam of synchrotron radiation from an undulator. The ground-state ionization threshold was measured at 0.004-eV energy resolution to be $45.717\pm 0.030$ eV. The measurements are rich in resonance structure due to multiple Rydberg series of transitions to autoionizing states. These series are assigned spectroscopically using the quantum defect method, guided by pseudorelativistic Hartree-Fock calculations for the energies and oscillator strengths of transitions to autoionizing states. The experimental results, which include significant contributions from ${\mathrm{K}}^{2+}$ ions initially in metastable states, are in satisfactory agreement with a linear superposition of semirelativistic R-matrix calculations of photoionization cross sections from these initial states.

Figure 1

Overview of photoionization cross-section measurements over the energy range 20–70 eV. The data from 20 to 44 eV (open circles) have an energy resolution of 0.1 eV and a total uncertainty of $\pm 50$%, while those from 44 to 70 eV (filled black circles) have a resolution of 0.045 eV and an uncertainty of $\pm 22$%. Vertical lines indicate the ionization threshold energies listed in Table 1. The highest in energy is for the ground state and the remainder are for metastable states.

Figure 2

Photoionization cross-section measurements at 0.004-eV resolution near the ${}^2{P}_{3/2}^o$ ground-state ionization threshold of ${\mathrm{K}}^{2+}$ at 45.717 eV.

Figure 3

Absolute cross-section measurements for photoionization of ${\mathrm{K}}^{2+}$ at a photon energy resolution of 0.045 eV. Vertical dashed and dotted lines indicate the ${}^2{P}_{3/2}^o$ ground-state and ${}^2{P}_{1/2}^o$ metastable-state ionization threshold energies. Eight Rydberg series of resonances from the ${}^2{P}_{1/2}^o$ metastable state and ${}^2{P}_{3/2}^o$ ground state of ${\mathrm{K}}^{2+}$ converging to the $3s^{2}3p^4{(}^1{D}_2)$ and $3s^{2}3p^4{(}^1{S}_0)$ limits of ${\mathrm{K}}^{3+}$ are identified. The measured cross section below the ${}^2{P}_{1/2}^o$ threshold is attributed to the population of higher lying quartet metastable states in the ${\mathrm{K}}^{2+}$ ion beam.

Figure 4

Overview of photoionization cross-section measurements over the energy range 20–44 eV at a photon energy resolution of 0.1 eV and an energy step size of 0.1 eV.

Figure 5

Absolute photoionization cross-section measurements for ${\mathrm{K}}^{2+}$ at a photon energy resolution of 0.045 eV in the photon energy range 26–30 eV. The solid line represents a Lorentzian fit to the broad resonance feature attributed to photoionization from the $3d{}^4{P}_{5/2,3/2,1/2}$, $4s{}^4{P}_{5/2,3/2,1/2}$, and $3d{}^4{G}_{9/2,7/2}$ metastable states.

Figure 6

Absolute photoionization cross-section measurements for ${\mathrm{K}}^{2+}$ at 0.045-eV resolution in the energy range from 51.4 to 69.7 eV. Open squares with error bars represent absolute measurements to which the energy scan is normalized. Eight Rydberg series of resonances due to inner-shell excitation $3s\to np$ converging to the ${}^3{P}_2^o$, ${}^3{P}_1^o$, ${}^3{P}_0^o$, and ${}^1{P}_1^o$ excited states of ${\mathrm{K}}^{3+}$ are identified.

Figure 7

Breit-Pauli R-matrix photoionization cross-section calculations for the metastable (a) (1/4) $3s^{2}3p^5{}^2{P}_{1/2}^{\circ }$ and (b) (1/4) $3s^{2}3p^5{}^2{P}_{3/2}^{\circ }$ ground states of ${\mathrm{K}}^{2+}$; (c) comparison between theory and experiment. Theoretical results have been convoluted with a Gaussian distribution having a profile of 45-meV FWHM to simulate the photon energy resolution of the experiment and a nonstatistical admixture of the ground state and metastable states in the primary ${\mathrm{K}}^{2+}$ ion beam (see text for details).

Figure 8

Rydberg fits for the $3s^{2}3p^4{(}^1{D}_2)nd$ series originating from both the ${}^2{P}_{3/2}^o$ ground state and the ${}^2{P}_{1/2}^o$ metastable state.

Figure 9

Fits of the Rydberg formula for the $3s^{2}3p^4{(}^1{S}_0)nd$ resonance energies for series originating from the ${}^2{P}_{3/2}^o$ ground state and the ${}^2{P}_{1/2}^o$ metastable state.

Figure 10

Fits of Rydberg formula for the $3s3p^5{(}^3{P}_{2,1,0}^o)np$ and $3s3p^5{(}^1{P}_1^o)np$ series originating from the ${}^2{P}_{3/2}^o$ ground state and the ${}^2{P}_{1/2}^o$ metastable state.

Figure 11

Breit-Pauli R-matrix photoionization cross-section calculations for the metastable (a) $3s^{2}3p^5{}^2{P}_{1/2}^{\circ }$ and (b) $3s^{2}3p^5{}^2{P}_{3/2}^{\circ }$ ground state of ${\mathrm{K}}^{2+}$. Theoretical results have been convoluted with a Gaussian of 45-meV FWHM to simulate the photon energy resolution of the experiment.

Figure 12

Breit-Pauli R-matrix photoionization cross-section calculations for the (a) $3d{}^4{P}_{1/2}$, (b) $4s{}^4{P}_{1/2}$, (c) $3d{}^4{F}_{9/2}$, and (d) $3d{}^2{G}_{9/2}$ metastable states of ${\mathrm{K}}^{2+}$ as listed in Table 1. Theoretical results have been convoluted with a Gaussian of 45-meV FWHM to simulate the photon energy resolution of the experiment.

Figure 13

Breit-Pauli R-matrix photoionization cross-section calculations for the (a) $3d{}^4{D}_{3/2}$, (b) $3d{}^4{P}_{3/2}$ (c) $4s{}^4{P}_{3/2}$, and (d) $4s{}^4{P}_{5/2}$ metastable states of ${\mathrm{K}}^{2+}$ as listed in Table 1. Theoretical results have been convoluted with a Gaussian of 45-meV FWHM to simulate the photon energy resolution of the experiment.

Figure 14

Breit-Pauli R-matrix photoionization cross-section calculations for the (a) $3d{}^4{D}_{5/2}$, (b) $3d{}^4{F}_{5/2}$, (c) $3d{}^4{P}_{5/2}$, and (d) $3d{}^2{F}_{5/2}$ metastable states of ${\mathrm{K}}^{2+}$ as listed in Table 1. Theoretical results have been convoluted with a Gaussian of 45-meV FWHM to simulate the photon energy resolution of the experiment.

Figure 15

Breit-Pauli R-matrix photoionization cross section calculations for the (a) $3d{}^4{D}_{7/2}$, (b) $3d{}^4{F}_{7/2}$, (c) $3d{}^2{F}_{7/2}$, and (d) $3d{}^2{G}_{7/2}$ metastable states of ${\mathrm{K}}^{2+}$ as listed in Table 1. Theoretical results have been convoluted with a Gaussian of 45-meV FWHM to simulate the photon energy resolution of the experiment.