In the book, The theory of atomic structure and spectra, Robert D. Cowan says that the allowed terms of $p^2$ are $^1S$, $^1D$, $^3P$ and so the possible terms of $p^2 + p\quad$ (obtained by using the vector model) are:

$$^2P^\circ,\quad ^2P^\circ D^\circ F^\circ,\quad ^{2,4}S^\circ P^\circ D^\circ \tag1$$

I am having trouble in understand the notation in $(1)$. For example the term $^2P^\circ$ means that $s=1/2,l=1$ and $^\circ$ means odd parity, but for the term $^{2,4}S^\circ P^\circ D^\circ$, I do not know what it means. Can anyone explain me it please?

  • $\begingroup$ My guess is that $\quad ^{2,4}S^\circ P^\circ D^\circ $ means $^2S^\circ, ^2P^\circ,^2D^\circ,^4S^\circ, ^4P^\circ,^4D^\circ$ $\endgroup$ Apr 28 '20 at 21:25

Copied table below from "Quantum chemistry", Donald A. McQuarrie, University Science Books, 2008, page 472

This illustrates the notion that $p^2$ and $p^4$ are equivalent.

enter image description here

I think the 2,4 superscript in Cowan's book for $^{2,4}S^\circ P^\circ D^\circ$ is a peculiar notation of his. Most other books seem to presume the reader knows the equivalency.


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