Some Relations between the Optical Spectra of Different Atoms of the same Electronic Structure. II. Aluminium-like and Copper-like Atoms

Abstract

The relevant results from the writer's previous paper on the relation between spectra of atoms of different atomic structure are summarised.For non-penetrating orbits no new theoretical results are obtained, and there are few known spectra (other than those of lithium-like or sodium-like atoms already treated in the first paper) on which to test the relations previously obtained. Values of the polarisability for the A1+ and Si++ ions are calculated from terms of Al I and Si II respectively corresponding to non-penetrating orbits, and are shown to be very much greater than the values of the polarisability of the neon-like ions Al+++ and Si++++.The main new results are those for penetrating orbits. Assuming a central field of force, it is shown that the quantum defect q for such an orbit can be expressed as the sum of contributions from the electrons in groups of core orbits of different principal quantum number n, and further that if for a given atom in different states of ionisation corresponding orbits of the series electron are compared, the contribution to q from a set of core orbits of given n is very nearly independent of the degree of ionisation so long as the number of electrons in core orbits in the group remains the same. It follows that, if q is the quantum defect for a term of the spectrum of an atom core charge C, the core of which contains SM orbits of principal quantum number M and none of higher quantum number, and q″ is the quantum defect for the corresponding term in the spectrum of the atom of the same element with core charge C + sM, which differs from the atom of core charge C only in lacking the core orbits of principal quantum number M, then q −; q″ is approximately the contribution from the core orbits of principal quantum number M to the quantum defect for the term of the atom core charge C.Further, it is shown that if corresponding terms of different atoms of the same electronic structure are compared, then for large values of C the contribution to q from any group of core orbits should tend asymptotically to be proportional to the average time mean radius of these orbits, and its reciprocal should tend asymptotically to be linear in C.Somewhat similar relations are obtained for the quantity Q = dq/d (ν/R) which measures the variation of quantum defect within a sequence.These theoretical results, and in particular the result that l/(q − q″) should tend asymptotically to be proportional to C, are compared with the values of q deduced from the terms of such observed spectra of aluminium-like and copper-like atoms as are available, and it is found that though the theoretical relations are only established as asymptotically true for large C, there is a considerable measure of agreement with spectra for small values of C, which are the only ones which can be observed.