Density functional studies on the hollow resonances in Li-isoelectronic sequence (Z=4--10

TL;DR

This study employs density functional theory to investigate hollow resonances in Li-isoelectronic ions (Z=4-10), providing new calculations for high-n resonances and demonstrating the method's accuracy and potential for broader applications.

Contribution

The paper introduces a DFT-based approach to accurately calculate hollow resonances in Li-like ions, including high-n states previously unexamined, showing excellent agreement with existing data.

Findings

Resonance positions for n=16-25 calculated for the first time.

Excellent agreement with literature for lower states, deviations below 0.5%.

Radial densities presented for selected states.

Abstract

In this sequel to our work on triply excited hollow resonances in three-electron atomic systems, a density functional theory (DFT)-based formalism is employed to investigate similar resonances in Li-isoelectronic series (Z=4--10). A combination of the work-function-based local nonvariational exchange potential and the popular gradient plus Laplacian included Lee-Yang-Parr correlation energy functional is used. First, all the 8 n=2 intrashell states of B$^{2+}$, N$^{4+}$ and F$^{6+}$ are presented, which are relatively less studied in the literature compared to the remaining 4 members. Then calculations are performed for the 8 $2l2l'$n$l"$ (3$\leq$n$\leq$6) hollow resonance series; {\em viz.,} 2s$^2$ns $^2$S$^e$, 2s$^2$np $^2$P$^o$, 2s$^2$nd $^2$D$^e$, 2s2pns $^4$P$^o$, 2s2pnp $^4$D$^e$, 2p$^2$ns $^4$P$^e$, 2p$^2$np $^4$D$^o$ and 2p$^2$ns $^2$D$^e$, of all the 7 positive ions. Next, as an illustration, higher resonance positions of the 2s$^2$ns $^2$S$^e$ series are calculated for all the ions with a maximum of n=25. The excitation energies calculated from this single-determinantal approach are in excellent agreement with the available literature data (for the n=2 intrashell states the deviation is within 0.125% and excepting only one case, the same for the resonance series is well below 0.50%). With an increase in Z, the deviations tend to decrease. Radial densities are also presented for some of the selected states. The only result available in the literature for the lower resonances (corresponding to a maximum of n=17) have been reported very recently. The n$>$16 ($>17$ for F$^{6+}$) resonances are examined here for the first time. This gives a promising viable and general DFT scheme for the accurate calculation of these and other hollow resonances in many-electron atoms.