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Doublet and Triplet Separations in Optical Spectra as Evidence whether Orbits penetrate into the Core

Published online by Cambridge University Press:  24 October 2008

D. R. Hartree
D. R. Hartree
Affiliation:
St John's College
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Abstract

Landé has indicated a connection between the “relativity” doublets of X-ray spectra, and the doublets and triplets of optical spectra, and so has obtained a formula for the separation of optical doublets and triplets. This formula can only be expected to hold if the orbit of the series electron penetrates into the core, so it may be possible to obtain evidence on the question whether an orbit penetrates from the doublet or triplet separation of the corresponding term.

From this evidence it is concluded that, except for lithium-like atoms, p terms of all known spectra correspond to penetrating orbits; this disagrees with Bohr's assignment of quantum numbers for those terms of the spectra of neutral atoms of the Cu and Zn sub-groups. For d terms the evidence is not so definite, but it seems possible that for Cs I and Tl I the d terms correspond to penetrating orbits, in disagreement with Bohr's assignment. It is shown that the Landé formula seems to hold approximately for separations in multiplet spectra when the terms belong to a sequence of the Rydberg type.

Ideas suggested by Heisenberg in a recent paper would involve some modifications of the interpretation of the magnitudes of doublet separations, but at least the conclusions as to the p orbits penetrating still stand.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 6 , November 1925 , pp. 904 - 918
Copyright
Copyright © Cambridge Philosophical Society 1925

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References

* Landé, A., Zeit. f. Phys. vol. xxv, p. 46 (1924).CrossRefGoogle Scholar

† Bohr, N., Ann. der Phys. vol. LXXI, p. 253 (1923), particularly § 6.Google Scholar

‡ Born, M., Vorlesungen über Atommechanik (Springer, 1924), ch. III, § 31.Google Scholar

* The part of Landé's paper relevant to the present paper is that dealing with the connection between the doublet separations of optical spectra and the “relativity” doublets of X-ray spectra. The formula for these “relativity” doublets may be taken as known from experimental data on X-ray spectra. The question of the mechanism of the X-ray “relativity” doublet is at present irrelevant.Google Scholar

* A formula equivalent to (4) is given by Landé, but no special emphasis is laid on it.Google Scholar

† The writer believes that this significance of the constancy of Δq within a sequence of terms of a single spectrum has already been pointed out by Bohr, but has been unable to find the reference.Google Scholar

* For example, in an atom whose core orbit consists of a complete group plus a pair of electrons n 1 orbits (atoms of Al sub-group types, e.g. Al, Si+, P++, Ga, In, Tl), the aphelion of the first p orbit, which has the same value of n as the two outermost orbits with k = 1 already present in the core, is probably not far outside the aphelia of these orbits, so that the field there differs considerably from that of a point charge C. This is shown in the corresponding spectra (at any rate for the less highly ionised atoms of these types), by the fact that the first p term is greater than C 2R/4, i.e. the effective quantum number n − q is less than the azimuthal quantum number k. This can only be the case if the field at aphelion of the orbit of the series electron is appreciably different from that of a point charge C.Google Scholar

† I am indebted to Mr J. A. Carroll for permission to use some yet unpublished data for the spectra Ga III, Ge IV, Hg II, and T1 III.Google Scholar

‡ The accuracy with which Δq can be determined from the observed spectra decreases rather rapidly from one term of a sequence to the next, so it is best to determine it from the earliest term available. The value plotted has been found from the second p term except for Ga I and In I for which no lines involving the second p term have been observed. The values of Δq have been calculated by evaluating q separately for the two members of the doublet and subtracting, and not from the first order formula (3).Google Scholar

* The series for the relativity doublet separation between the 21, and 22 terms had to be taken to 2 terms further than those given by Sommerfeld, in order to obtain 4 significant figures in γ for the heavy elements. The formula for γ is

In calculating γ, the value of Z i has been taken as N − 2.

† Certainly the values of Δq for the p terms of lithium-like atoms agree closely with the linear relation for the p terms of other atoms, and the orbits do not penetrate, but they form a special case, since for them the value of N − 8 (with the value of 8 deduced from penetrating orbits) is not far different from the core charge C.Google Scholar

‡ Loc. cit. It may perhaps be mentioned that the relation between the first p terms of Cu I, Zn II, Ga III and Ga IV appears to confirm that the corresponding orbits penetrate, and the same is true for the spectra Ag I, Cd II and In III.Google Scholar

* Cf. footnote*, p. 907. The first d term of Ba II is doubtful. Fowler and Paschen-Götze in their tables give different groups of lines for the doublet and satellite 3d − 2p.Google ScholarRussell, H. N. and Saunders, F. A. (Ap. J. vol. LXI, p. 60 (1925)) agree with Paschen-Götze, and the 3d pair of terms determined from these lines seems more probable than Fowler's, both from its q and Δq. The point plotted has been determined from it. The first d term of Ra II is not known.Google Scholar

* For the significance of the negative sign Δq for K I, see § 7. The separation of the first d term of Rb I has not been observed.Google Scholar

* Catalan, M. A., Phil. Trans. Roy. Soc. vol. ccxxiii, p. 127. Catalan's “wide triplet” series are part of the octet system, and the “narrow triplet” series and the multiplets part of the sextet system.Google Scholar

† The values of the terms for Mn II have been found from the first principal an first diffuse triplet (see Catalan, loc. cit. p. 162) assuming l8 = 119,000, which value has been estimated by the writer without reference to the magnitude of the separations of the terms.Google Scholar (Nature, vol. cxvi, p. 356 (1925).)Google Scholar

* Sommerfeld, A., Atombau und Spectrallinien, 4th Ed. p. 685.Google Scholar

Negative separations and deviations from Landé's “Interval Rule” have been discussed recently in a paper by Stoner (Phil. Mag. vol. XLIX, p. 1289 (1925), § 9) from the point of view of the magnetic theory of the origin of multiple terms.Google Scholar

† See Sommerfeld, A., loc. cil.Google Scholar

‡ Bohr, N., Ann. der Phys. loc. cit. pp. 268–9, footnote. On the recent theory of Heisenberg (see below), however, the interpretation of these terms is rather different, and the negative sign of the separation is explained.Google Scholar (See Hund, , Zeit. f. Phys. vol XXXIII, p. 345 (1925).)CrossRefGoogle Scholar

* Another interpretation of the d terms of Al II has been given recently by Schrödinger (Ann. der Phys. vol. LXXVII, p. 43). The principal quantum numbers of the later f terms are increased by l so that the quantum defect is small and negative; this is ascribed to a negative polarisation of the core due to an effect of the nature of anomalous dispersion.Google Scholar

† Heisenberg, W., Zeit. f. Phys. vol. XXXII, p. 841 (1925).CrossRefGoogle Scholar

‡ German:—Duplizität,Google Scholar