Approach towards the critical charge of some excited states of the Be isoelectronic series

A definitive determination of the nature of the approach to the critical charge is illustrated for the ${\left(1s^{2}2s3s\right)}^{1,3}S$ and the ${\left(1s^{2}2s3p\right)}^{1,3}P$ states of the Be isoelectronic series. The features that conclusively indicate that the outermost orbital becomes an infinitely diffuse hydrogenlike orbital upon approaching the critical charge $Z_c=3$ are the asymptotic proportionality of the ionization energy to ${(Z-3)}^2$ and the approach of the corresponding quantum defect to an integer which is equal to the number of orbitals of the same symmetry in the atomic core.

Figure 1

Binding energy of the $1s^{2}2s3s{}^3{S}_1$ and $1s^{2}2s3s{}^1{S}_0$ levels as a function of ${(Z-3)}^2$.

Figure 2

Quantum defect of the $1s^{2}2s3s{}^3{S}_1$ and $1s^{2}2s3s{}^1{S}_0$ levels as a function of Z.

Figure 3

$1s^{2}2s3p{}^3{P}_0$ level binding energy as a function of Z.

Figure 4

Quantum defect of the outermost electron for the $1s^{2}2s3p{}^3{P}_0$ level.

Figure 5

Plot of the average radius of the $3p_{1/2}$ electron for the $1s^{2}2s3p{}^3{P}_0$ level multiplied by $(Z-3)$ as a function of Z.

Figure 6

$1s^{2}2s3p{}^1{P}_1$ level binding energy as a function of Z.

Figure 7

Quantum defect of the outermost electron for the $1s^{2}2s3p{}^1{P}_1$ level.