Linear quantum capacitance scaling for lanthanide and actinide atoms: Analysis of two differing sets of electron-affinity predictions

Scaling of quantum capacitances is explored for lanthanide and actinide atoms. For lighter atoms, quantum capacitances have been seen to scale linearly with mean radii of the atoms’ outermost occupied orbitals. This scaling law is used to analyze two recent, differing sets of theoretical calculations for lanthanide electron affinities $A$. Consistent with the scaling law, $A$ values predicted by O’Malley and Beck for lanthanides [Phys. Rev. A 78, 012510 (2008)], using a relativistic configuration interaction (RCI) method, produce capacitances that scale with the atoms’ mean radii along a single line to a high degree of confidence. Similar linear scaling behavior also results for the actinides from O’Malley and Beck's RCI calculations of their $A$ values. However, lanthanide $A$ values predicted by Felfli et al. [Phys. Rev. A 81, 042707 (2010)], using a Regge-pole approach, unexpectedly produce capacitance scaling along two different lines for atoms with similar neutral electron configurations. Both types of linear capacitance scaling are internally consistent, though, and do not serve to determine definitively which set of electron affinity predictions for the lanthanides is likely to be more accurate. Still, evidence from this and prior capacitance scaling investigations tends to favor the O'Malley and Beck results. In addition, linear capacitance scaling for the actinides is applied to estimate the previously unknown $A$ values for Fm and Md as 0.007 eV and $-0.006$ eV, respectively.

Figure 1

O'Malley and Beck's $A$ values for lanthanide atoms [1, 2] are used to calculate their quantum capacitances in fundamental positive charges per volt ($+e$/V), plotted here vs the atoms' mean radii. Coordinates of the points are given in columns 4 and 8 of Table . A regression line is fit to just the points plotted as dark filled circles, and parameters for the line are displayed in its regression equation and correlation coefficient. Filled and unfilled circles indicate different types of neutral electron configurations for the atoms the points represent. See text.

Figure 2

Felfli et al.'s $A$ values for lanthanide atoms [4] are used to calculate their quantum capacitances in fundamental positive charges per volt ($+e$/V), plotted here vs the atoms' mean radii. Coordinates of the points are given in columns 4 and 9 of Table . Dotted and dashed regression lines each are fit to a different subset of the nine filled points but intersect near the Tm point. Black-filled points correspond to neutral lanthanides with the electron configuration [Xe]$4f^{n}6s^2$, $n\ne 7,14$, while unfilled points correspond to other types of neutral electron configurations. For each line, the regression equation and correlation coefficient are displayed. Values of $A$ for points along the dotted line are found here to correspond to anionic Regge resonances of Felfli et al. with Re$L=4$ for the real part of their complex total angular momentum; points along the dashed line correspond to Re$L=3$. See Table and text.

Figure 3

O'Malley and Beck's $A$ values for actinide atoms [5] are used to calculate their quantum capacitances in fundamental positive charges per volt ($+e$/V), plotted here vs the atoms' mean radii. Coordinates of the points are given in columns 4 and 7 of Table . A regression line is fit to just the dark filled diamonds and parameters for the line are displayed in its regression equation. Filled and unfilled diamonds indicate different types of electron configurations for the atoms the points represent. See text.