Theoretical photoionization spectra for the Mg-like S${}^{4+}$ ion: Partial and total cross sections for the ground $3s^2{}^{1}S$ and excited $3s3p{}^{3}P$ and $3s3p{}^{1}P$ states

The partial and total photoionization cross sections of the Mg-like S${}^{4+}$ ion for the ground $3s^2$ ${}^1{S}^e$ and the excited $3s3p$ ${}^3{P}^o$ and $3s3p$ ${}^1{P}^o$ initial states, leaving the residual S${}^{5+}$ 3$l$ states, have been calculated in both the dipole length and velocity forms using a noniterative eigenchannel $R$-matrix method combined with multichannel quantum-defect theory at the $R$-matrix surface. Noticeable features in the cross sections are found for the autoionizing Rydberg series converging to the S${}^{5+}$ 3$l$ thresholds, owing to the effect of interlopers which converge to the other threshold limits. The resonance parameters for low members of these autoionizing levels are identified and characterized. Our calculational results are compared with the available previous results, and the ionization thresholds are in better agreement with NIST data than Opacity Project (OP) results. The present photoionization cross sections are in overall agreement with the OP results, but some discrepancies are found.

Figure 1

Partial photoionization cross sections for the processes ${}^1{S}^e\to {}^{1}P$ of the Mg-like S${}^{4+}$ ion in the energy range up to the S${}^{5+}$ $4s$ threshold limit as a function of the photon energy: (a) cross sections ${\sigma }_{3s\epsilon p}{}^{1}P$, (b) cross sections ${\sigma }_{3p\epsilon s}{}^{1}P$, (c) cross sections ${\sigma }_{3p\epsilon d}{}^{1}P$, (d) cross sections ${\sigma }_{3d\epsilon p}{}^{1}P$, (e) cross sections ${\sigma }_{3d\epsilon f}{}^{1}P$. The black solid and red dotted lines represent the present length and velocity results, respectively.

Figure 2

Photoionization cross sections from the ground-state of the Mg-like S${}^{4+}$ ion in the energy range up to the S${}^{5+}$ $4s$ threshold limit as a function of the photon energy: (a) Present length (black solid line) velocity results (red dotted), (b) OP results [21]. The vertical dotted lines represent the S${}^{5+}$ $3p$ and $3d$ thresholds, respectively.

Figure 3

Partial photoionization cross sections for the processes ${}^{3,1}{P}^o\to {}^{3,1}S$ of the Mg-like S${}^{4+}$ ion in the energy range up to the S${}^{5+}$ $4s$ threshold limit as a function of the photon energy: (a) cross sections ${\sigma }_{3s\epsilon s}$ ${}^{3}S$, (b) cross sections ${\sigma }_{3p\epsilon p}$ ${}^{3}S$, (c) cross sections ${\sigma }_{3d\epsilon d}$ ${}^{3}S$, (d) cross sections ${\sigma }_{3s\epsilon s}$ ${}^{1}S$, (e) cross sections ${\sigma }_{3p\epsilon p}$ ${}^{1}S$, (f) cross sections ${\sigma }_{3d\epsilon d}$ ${}^{1}S$. The black solid and red dotted lines represent the present length and velocity results, respectively.

Figure 4

Partial photoionization cross sections for the processes ${}^{3,1}{P}^o\to {}^{3,1}P$ of the Mg-like S${}^{4+}$ ion in the energy range up to the S${}^{5+}$ $4s$ threshold limit as a function of the photon energy: (a) cross sections ${\sigma }_{3p\epsilon p}$ ${}^{3}P$, (b) cross sections ${\sigma }_{3d\epsilon d}$ ${}^{3}P$, (c) cross sections ${\sigma }_{3p\epsilon p}$ ${}^{1}P$, (d) cross sections ${\sigma }_{3d\epsilon d}$ ${}^{1}P$. The black solid and red dotted lines represent the present length and velocity results, respectively.

Figure 5

Partial photoionization cross sections for the processes ${}^{3,1}{P}^o\to {}^{3,1}D$ of the Mg-like S${}^{4+}$ ion in the energy range up to the S${}^{5+}$ $4s$ threshold limit as a function of the photon energy: (a) cross sections ${\sigma }_{3s\epsilon d}$ ${}^{3}D$, (b) cross sections ${\sigma }_{3p\epsilon p}$ ${}^{3}D$, (c) cross sections ${\sigma }_{3p\epsilon f}$ ${}^{3}D$, (d) cross sections ${\sigma }_{3d\epsilon s}$ ${}^{3}D$, (e) cross sections ${\sigma }_{3d\epsilon d}$ ${}^{3}D$, (f) cross sections ${\sigma }_{3s\epsilon d}$ ${}^{1}D$, (g) cross sections ${\sigma }_{3p\epsilon p}$ ${}^{1}D$, (h) cross sections ${\sigma }_{3p\epsilon f}$ ${}^{1}D$, (i) cross sections ${\sigma }_{3d\epsilon s}$ ${}^{1}D$, (j) cross sections ${\sigma }_{3d\epsilon d}$ ${}^{3}D$. The black solid and red dotted lines represent the present length and velocity results, respectively.

Figure 6

Photoionization cross sections for the processes ${}^{3,1}{P}^o\to {}^{3,1}S$, ${}^{3,1}P$, ${}^{3,1}D$ of the Mg-like S${}^{4+}$ ion in the energy range up to the S${}^{5+}$ $4s$ threshold limit as a function of the photon energy: (a) cross sections for the ${}^3{P}^o\to {}^{3}S$ process, (b) cross sections for the ${}^3{P}^o\to {}^{3}P$ process, (c) cross sections for the ${}^3{P}^o\to {}^{3}D$ process, (d) cross sections for the ${}^1{P}^o\to {}^{1}S$ process, (e) cross sections for the ${}^1{P}^o\to {}^{1}P$ process, (f) cross sections for the ${}^1{P}^o\to {}^{1}D$ process. The black solid and red dotted lines represent the present length and velocity results, respectively.

Figure 7

Total photoionization cross sections for the excited $3s3p{}^{3,1}P$ states of the Mg-like S${}^{4+}$ ion as a function of photon energy. (a) Present results for ${}^{3}P$: black solid curve, present length; red dashed, present velocity. (b) OP results for ${}^{3}P$. (c) Present results for ${}^{1}P$: black solid curve, present length; red dashed, present velocity. (d) OP result for ${}^{1}P$.

Figure 8

The convoluted photoionization cross sections in the energy range 56–93 eV as a function of the photon energy: (a) Convoluted cross sections for the ground state, (b) convoluted cross sections for the excited $3s3p{}^{3}P$ state, and (c) convoluted cross sections for the excited $3s3p{}^{1}P$ state. The present results have convoluted with a Gaussian profile assuming a broadening of 250 meV (FWHM). The vertical dotted lines represent the thresholds for the ground $3s^2$ ${}^{1}S$ and $3s3p$ ${}^{3,1}P$ states, respectively.