Energy Levels in Ca XV

A discussion of the structure of term spectra in isoelectronic sequences. shows that spectral terms fall naturally into certain groups, which we call “ complexes ”. A complex is completely specified by the set of principal quantum numbers ( n ) and the parity p , and contains one or more entire configurations. The interval between terms that belong to the same complex varies asymptotically as the nuclear charge Z for large values of Z , while the interval between terms that belong to complexes with different sets of principal quantum numbers ( n ) varies asymptotically as Z² . The electrostatic coupling between configurations whose terms belong to different complexes tends to vanish with increasing Z ; but the coupling between configurations whose terms belong to the same complex approaches constancy. This circumstance greatly simplifies the discussion of configuration mixing in highly ionized atoms. In Ca XV the configurations $$({1s}^{2})\,({2s}^{2})\,({2p}^{2})\,\text{and}\,({1s}^{2})\,({2p}^{4})$$ are strongly coupled, but the complex $$({1}^{2}{2}^{4})$$ is weakly coupled with higher complexes. On the approximation of zero coupling between $$({1}^{2}{2}^{4})$$ and higher complexes, the energy levels of $$({1}^{2}{2}^{4})$$ are the eigenvalues of a tenth-order matrix, which reduces to two fourth-order matrices and a second-order matrix. We have evaluated the matrix elements partly by extrapolation along the isoelectronic sequence and partly by theoretical considerations. The predicted wavelengths for the transitions $${2p}^{2}\,^{3}{P}_{2\rightarrow 1},\,^3{P}_{1\rightarrow 0}$$ are 5456 A and 5650 A respectively. These agree with the observed wave-lengths of the coronal lines λλ 5445, 5694 to within the uncertainty of the calculation, thus confirming the identifications of Edlén and Waldmeier.