Stabilization method with the relativistic configuration-interaction calculation applied to two-electron resonances

We applied a relativistic configuration-interaction (CI) framework to the stabilization method as an approach for obtaining the autoionization resonance structure of heliumlike ions. In this method, the ion is confined within an impenetrable spherical cavity, the size of which determines the radial space available for electron wave functions and electron-electron interactions. By varying the size of the cavity, one can obtain the autoinization resonance position and width. The applicability of this method is tested on the resonances of He atom while comparing with benchmark data available in the literature. The present method is further applied on the determination of the resonance structure of heliumlike uranium ion, where a relativistic framework is mandatory. In the strong-confinement region, the present method can be useful to simulate the properties of an atom or ion under extreme pressure. An exemplary application of the present method to determine the structure of ions embedded in dense plasma environment is briefly discussed.

Figure 1

Stabilization diagram constructed with the energy eigenvalues obtained after solving Eq. (4) with $\mathrm{\Pi }=0$ and $J=0$ in the function of the cavity radius and for helium atom ($Z=2$). Configurations of state functions up to $l=2$ are included in the calculation. Each line (with specific color and style) represents an eigenvalue sorted by energy, e.g., the solid black line represents the first eigenroot, the dashed red line represents the second eigenroot, the solid green line represents the third eigenroot, and so on. Note that the lower panel uses the same color code for the energy eigenroots as that of the upper panel.

Figure 2

Combined plot of numerically estimated DOS [Eq. (24)] vs energy (in a.u.) for eigenvalue No. 8 from the stabilization diagram of Fig. 1.

Figure 3

The DOS peaks of eigenvalue Nos. 5–10 in the energy range –0.85 a.u. to –0.50 a.u.

Figure 4

Numerically estimated DOS vs energy (in a.u.) (black hollow circles) and the fitted Lorentzian (solid red line) for eigenvalue No. 8 showing the first resonance ($\sim -0.77$ a.u.) of He below the ${\mathrm{He}}^{+}\left(2s\right)$ threshold.

Figure 5

Stabilization diagram constructed with the energy eigenvalues obtained after solving Eq. (4) with $\mathrm{\Pi }=0$ and $J=0$ in the function of the cavity radius and for the heliumlike uranium atom ($Z=92$). Configurations of state functions up to $l=2$ are included in the calculation. Each line represents an eigenvalue sorted by energy. Each line (with specific color and style) represents an eigenvalue sorted by energy, e.g., solid black line represents the first eigenroot, dashed red line represents the second eigenroot, solid green line represents the third eigenroot, and so on. Note that the lower panel uses the same color code for the energy eigenroots as that of the upper panel.

Figure 6

Enlarged view of the stabilization diagram given in Fig. 5. For both upper and lower panels, the line colors and styles carry similar meaning as Fig. 5.

Figure 7

Numerically estimated DOS vs. Energy (in a.u.) (black hollow circles) and the fitted Lorentzian (solid red line) for eigenvalue no. 11 showing 1st resonance ($\sim$–2497 a.u.) of heliumlike uranium below ${\mathrm{U}}^{91+}\left(2s\right)$ threshold.

Figure 8

Numerically estimated DOS vs energy (in a.u.) (black hollow circles) and the fitted Lorentzian (solid red line) for eigenvalue No. 11 showing second resonance ($\sim -2490$ a.u.) of heliumlike uranium below ${\mathrm{U}}^{91+}\left(2s\right)$ threshold.

Figure 9

Numerically estimated DOS vs energy (in a.u.) (black hollow circles) and the fitted Lorentzian (solid red line) for eigenvalue No. 12 showing third resonance ($\sim -2159$ a.u.) of heliumlike uranium below ${\mathrm{U}}^{91+}\left(2s\right)$ threshold.