Avoided level crossings in very highly charged ions

We report a systematic measurement of the ${\left(2p_{1/2}^{-1}3d_{3/2}\right)}_{J=1}$ and ${\left(2s_{1/2}^{-1}3p_{1/2}\right)}_{J=1}$ levels in 14 neonlike ions between ${\mathrm{Ba}}^{46+}$ and ${\mathrm{Pb}}^{72+}$ and document the effects of their avoided crossing near $Z=68$. Strong mixing affects the oscillator strengths over a surprisingly wide range of atomic numbers and leads to the vanishing of one transition two atomic numbers below the crossing. The crossing voids the otherwise correct expectation that the ${\left(2p_{1/2}^{-1}3d_{3/2}\right)}_{J=1}$ level energy is only weakly affected by quantum electrodynamics (QED). For about 10 atomic numbers surrounding the crossing, its QED contributions are anomalously large, attaining almost equality to those affecting the ${\left(2s_{1/2}^{-1}3p_{1/2}\right)}_{J=1}$ level. As a result, the accuracy of energy level calculations appears compromised near the crossing.

Figure 1

(a) Predicted energies of levels ${\left(2p_{1/2}^{-1}3d_{3/2}\right)}_{J=1}$ and ${\left(2s_{1/2}^{-1}3p_{3/2}\right)}_{J=1}$, denoted $3C$ and $3B$, respectively. Dashed lines represent single-configuration calculations and the reversal in the energy ordering can be seen near $Z=68$. Solid lines represent multiconfiguration calculations. (b) The corresponding mixing coefficients for the lower level. The dominant components reverse near $Z=68$.

Figure 2

$L$-shell spectra from ${\mathrm{Er}}^{58+}$ and ${\mathrm{Yb}}^{60+}$. The two lines are labeled by their dominant components in accordance with Table 1.

Figure 3

$Z$-dependent intensity of line $3B$ relative to $3C$. Error bars are statistical. Note that the intensity of $3B$ exceeds that of $3C$ at the crossing and virtually vanishes for $Z=66$.

Figure 4

Self-energies of levels $3B$ and $3C$ calculated with approach A1 (open circles) and approach A2 (solid circles) discussed in the text. The differences in the non-QED energies of the two levels calculated with the two procedures are shown for comparison.

Figure 5

$Z$-dependent differences between measured and calculated energies for lines $3B$ and $3C$, and their sum. Open blue (solid green) circles represent calculations using approach A1 (A2). RMBPT calculations are represented with solid yellow diamonds. Error limits represent the quadrature sum of the individual experimental uncertainties listed in Table 1.