Abstract
The present article is less comprehensive than the title would suggest. Firstly, the treatment is confined to spectra arising through the excitation of the outermost electrons in free atoms or ions, thus excluding, for instance, X-ray spectra, which are the subject of other articles in this Encyclopedia1. Also the influence on atomic spectra of external magnetic and electric fields—that is, the Zeeman and the Stark effects, is treated elsewhere2 and therefore not included here. The same applies to hyperfine structure and isotope shifts3. Finally, since the theory of atomic spectra is covered in the articles4 by Hund and by Bethe and Salpeter, no attempt has been made to give a consistent picture of the theory, although the results of theoretical derivations are frequently quoted and used. In brief, the present article is concerned with the undisturbed gross structure of the energy-level systems of free atoms and ions, the main content being a description—in terms of the theory and with quantitative examples from observed spectra—of regularities in various types of atomic systems and of relationships between different, especially isoelectronic, systems. The article is intended to give a survey of empirical data in a form useful to the theorist and at the same time to provide the experimentalist with a collection of theoretical results for direct application and with efficient methods for the analysis and description of his observations. A considerable part of the material, in particular of the chapter on isoelectronic sequences, has not been previously published.
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References
Articles by A. E. SandstrÖM and by D. H. Tomboulian: This Encyclopedia, Vol. Xxx.
The Zeeman effect by J. C. Van Den Bosch: This Encyclopedia, Vol. Xxviii.
See, especially, the articles by F. M. Kelly and L. Wilets in this Encyclopedia, Vol. Xxxviii /1, pp. 59–118. See also H. Kopfermann: Nuclear moments. New York: Academic Press 1958.
F. Hund: Quantenmechanik der Atome, Vol. Xxxvi, pp. 1–108. — H. A. Bethe and E. E. Salpeter: Quantum Mechanics of One-and Two-Electron Systems, Vol. Xxxv pp. 88 — 436. See also P. GoMbas: Statistische Behandlung des Atoms, Vol. Xxxvi, pp. 109–229.
B. Edlen: Physica, Haag 13, 545 (1947).
For a discussion of transition probabilities see D. R. Bates and A. Damgaard: Phil. Trans. Roy. Soc. Lond. A 242, 101 (1949) References to recent papers may be found in Trans. Internat. Astronom. Union 9, 214–218 (1957); 10, 220–225 (1960). Cambridge: Cambridge University Press.
R. G. Fowler: This Encyclopedia, Vol. Xxii, pp. 211–215; R. G. Breene: ibid. Vol. Xxvii.
K. Bockasten: Ark. Fysik 9, 457 (1955). — For a comprehensive review of spectroscopic light-sources see a forthcoming monograph by D. A. Jackson.
Standard air is defined in spectroscopic context as dry air, containing 0.03% by volume of CO2, at normal pressure and a temperature of 15° C.
B. Edlen: J. Opt. Soc. Amer. 43, 339 (1953).
Joint Comission for Spectroscopy: J. Opt. Soc. Amer. 43, 411 (1953); 47, 1035 (1957).
The main references are: H. Kayser and R. RitscHL: Tabelle der Hauptlinien der Linienspektren aller Elemente. Berlin: Springer 1939. G. R. H.Rrison: M.I.T. Wavelength Tables. New York 1939. CH. E. MooRE: A Multiplet Table of Astrophysical Interest. Contrib. Princeton Univ. Observatory No 20, Parts I and II. Princeton 1945. CH. E. Moore: An Ultraviolet Multiplet Table. Circ. Nat. Bur. Stand. 488, Sects. I and II. Washington D.C. 1950. J. C. Boyce and H. A. Robinson: Wave-length identification lists for the extreme ultraviolet. J. Opt. Soc. Amer. 26, 133 (1936).
The primary standard, adopted in 1907, and the system of standard wavelengths, developed during the past half-century, have been created through the work of a special commission of the International Astronomical Union and its forerunner, The International Union for Co-operation in Solar Research. The present situation is summarized in the Trans. Internat. Astronom. Union 9, 201–226 (1957); 10, 211–232 ( 1960 ). Cambridge: Cambridge University Press.
Procès-verbaux du Comité Intern. des Poids et Mesures, Vol. 24 (1954); Vol. 26B (1958). Definition adopted by the General Conference on Weights and Measures in 1960.
G. D. Liveing and J. Dewar: Proc. Roy. Soc. Lond. 29, 398 (1879).
W. N. Hartley: J. Chem. Soc. Lond. 43, 390 (1883).
J. J. Balmer: Ann. Physik u. Chemie 25, 80 (1885).
J. R. Rydberg: Recherches sur la constitution des spectres d’émission des éléments chimiques. Kgl. svenska Vetensk.-Akad. Handl., Stockh. 23, No. 11 (1890). See also OsTwald’S Klassiker der exakten Naturwissenschaften, Nr. 196, Leipzig 1922.
W. Ritz: Phys. Z. 9, 521 (1908).
F. Paschen: Ann. Physik 50, 901 (1916).
F. Paschen: Ann. Physik 60, 405 (1919); 63, 201 (1920).
F. Paschen and R. GÖTze: Seriengesetze der Linienspektren. Berlin: Springer 1922.
A. Fowler: Report on Series in Line Spectra. London: Fleetway Press 1922. 8 M. A. Catalan: Phil. Trans. Roy. Soc. Lond. A 223, 127 (1922).
A. Fowler: Phil. Trans. Roy. Soc. Lond. A 225, 1 (1925).
H.N. Russell and F.A. Saunders: Astrophys. Journ. 61, 38 (1925). — The nomenclature now in use was outlined in a paper by H.N. Russell, A. G. Shenstone, and L. A. Turner: Phys. Rev. 33, 900 (1929).
The main references are: H. Kayser and R. RitscHL: Tabelle der Hauptlinien der Linienspektren aller Elemente. Berlin: Springer 1939. G. R. H.Rrison: M.I.T. Wavelength Tables. New York 1939. CH. E. MooRE: A Multiplet Table of Astrophysical Interest. Contrib. Princeton Univ. Observatory No 20, Parts I and II. Princeton 1945. CH. E. Moore: An Ultraviolet Multiplet Table. Circ. Nat. Bur. Stand. 488, Sects. I and II. Washington D.C. 1950. J. C. Boyce and H. A. Robinson: Wave-length identification lists for the extreme ultraviolet. J. Opt. Soc. Amer. 26, 133 (1936).
E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge University Press 1935; reprinted with corrections in 1951 and 1953.
R. F. Bacher and S. Goudsmit: Atomic Energy States as Derived from the Analyses of Optical Spectra. New York: McGraw-Hill 1932.
CH. E. MooRE: Atomic Energy Levels as Derived from Optical Spectra. Circ. Nat. Bur. Stand. 467, Washington; Vol. 1 (1949), elements 1–23; Vol. 2 (1952), elements 24–41; Vol. 3 (1958), elements 42–57 and 72–89.
G. Herzberg: Atomic Spectra and Atomic Structure. New York: Prentice-Hall 1937; second ed. New York: Dover Publications 1944.
H. E. White: Introduction to Atomic Spectra. New York: McGraw-Hill 1934.
A. Sommerfeld: Atombau und Spektrallinien. Braunschweig: F. Vieweg Sohn 1919; 7th ed. 1951.
F. Hund: Linienspektren und periodisches System der Elemente. Berlin: Springer 1927.
L. Pauling and S. Goudsmit: The Structure of Line Spectra. New York: McGraw-Hill 1930.
W. Grotrian: Graphische Darstellung der Spektren von Atomen und Ionen mit ein, zwei und drei Valenzelektronen. Berlin: Springer 1928.
A. C. Candler: Atomic Spectra. Cambridge: Cambridge University Press 1937.
H. Kayser (later volumes with H. Konen): Handbuch der Spectroscopie, Vol. I— Viii. Leipzig: S. Hirzel 1900–1934.
References 4 and 5 on p. 83.
Also named the total and sometimes the radial quantum number, though the latter name is usually reserved for n — k (cf. Sect. 5).
For numerical values of the atomic constants see E.R. Cohen and J.W.M. DuMoND: This Encyclopedia, Vol. Xxxv, pp. 1–89. See also Table 50.
The number of electrons occupying the same kind of orbit is limited by the Pauli exclusion principle (see Sect. 8), which explains why the s series of LiI starts with 2s and not with 1s.
In the early work the terms were written R/(m + d)2, where the running numbers m were chosen in such a way as to make I dl 0.5. At the same time one tried to get the same m for homologous terms in different spectra. This gave rise to various systems of numbering, in one of which the term series always start with 1s, 2p, 3d, 41,etc. It has certain merits and continued to be used long after the introduction of the principal quantum number n.
Unfortunately there is no short name or well established symbol for this important number, which also appears as the Roman numeral in the spectrum symbol. It has often been denoted by Z.0 or z,but we prefer the symbol 4 to avoid any confusion with the nuclear charge Z.
W. Pauli: Z. Physik 31, 765 (1925).
See, for instance, the instructive diagram in Hund’s article, this Encyclopedia, Vol. Xxxvi, p. 35.
Pair coupling was first discussed by G. H. Shortley and B. Fried: Phys. Rev. 54, 739 (1938): the quantum number K was introduced by G. Racah: Phys. Rev. 61, 537 (1942).
H. N. Russell and F. A. Saunders: Astrophys. Journ. 61, 38 (1925).
The rare-gas configurations are in this context equivalent with two-electron configurations; cf. the concept of holes, Sect. 10.
Cf. F. Hund: This Encyclopedia, Vol. Xxxvi, pp. 70 and 92–93.
O. Laporte: Z. Physik 23, 135 (1924). The parity may be indicated by a superscript ° to the symbol for odd terms. This is necessary in the case of experimentally determined terms for which the parity is known from the combining properties but the configuration is not known or not given.
Theoretical intensity ratios have been calculated for a wide range of multiplets in LS and jj coupling by H. E. White and A. Y. Eliason: Phys. Rev. 44, 753 (1933).
For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
The quantities labelled Fk and Gk,which were introduced to get simpler coefficients in the energy expressions, differ from the original Slater integrals Fk and Gk by constant factors, which depend on 1,1’,and k. Some of these factors are defined differently by different authors, which causes some ambiguity concerning the values of Fk and Gk. In this article we shall adhere to the usage in Tas.
Term, level, and state are here defined in accordance with Tas. The word state,however, will often be used in a less specific meaning.
From Tas, pp. 197–207 and 298–299.
G. R4Cah: Phys. Rev. 62, 438 (1942).
Of the double signs the upper one refers to the singlet and the lower to the triplet. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
Tas, p. 205. All parameter values are in cm-1. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
J. H. Van Vleck: Phys. Rev. 45, 405 (1934); the information on p4 given in Tas, p. 199 is not quite correct. — The energy expressions for the complete set of dk configurations will be found in Sect. 40.
Various attempts have been made to explain the bad agreement with theory in the first period. An investigation by D. LayzeÌ, Ann. of Phys. 8, 271 (1959), indicates that configuration mixing is a natural explanation (see Sect. 31). See also G. Racah, Proc. Rydberg Cent. Conf. (Kgl. fysiogr. Sällsk. Handl. 65, Nr. 21) Lund 1955, pp. 36–38.
Cf. also Sect. 40. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
Fo represents here a linear expression in Fo (ll), F2(11),and Fo (1l’),common to the whole configuration. LS formulae like (13.8) for almost-closed shells are of little practical interest because actual cases depart considerably from LS coupling and therefore call for a different type of approximation (see Sects. 17 and 18).
Cf. Tas, p. 216. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
The difference 1P —3P departs from the expected value because of an accidental perturbation of 3 s 3P by 2s 2p’ 3P. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
cL denotes the centre of gravity of the two terms with equal L. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
T. Yamanoucxi: Proc. Phys.-Math. Soc. Japan 20, 547 (1938). — See also T. Yamanouchi and A. Amemiya: J. Phys. Soc. Japan 1, 18 (1946), and R.F. Kingsbury: Phys. Rev. 99, 1846 (1955).
Cf. application to 0I 2p3 np, B. Edlen: Kgl. svenskaVetensk.-Akad. Handl., Stockh. 20, No. 10 (1943). For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
Tas, pp. 120–124. — We assume here that l$ 0.
A. Lande: Z. Physik 25, 46 (1924).
See Sect. 5 for the definition of n and The use of in two different meanings need not cause ambiguity as the spin-orbit integral “nl is always indexed by nl or 1. In Hunds article (this Encyclopedia, Vol. Xxxvi) the spin-orbit integrals are denoted s~nl•
R. G. Barnes and W.V. Smith: Phys. Rev. 93, 95 (1954), suggest for np orbits the approximate relation Zi =Z — n.
Note that the same symbol L is used both for a term with arbitrary L and for the quantum number itself.
The Lande interval rule will give a straight line if the levels are plotted against For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
It should be noticed, however, that an s electron, though not contributing to the splittings of the terms, may cause a shift in their centres of gravity.
S. GounsNirT and C. J. Humphreys: Phys. Rev. 31, 960 (1928); Tas, p. 219.
The diagrams shown in Figs. 11–13 are a modification of those given by Condon and SxoRtley in Tas (pp. 272–276, 301, 304). The form adopted here is more symmetrical and more convenient for practical use.
An exception is Pb I, where 3Po, 313 and 3132 were fitted exactly since the position of 7s 113 is strongly perturbed by interaction with 8s 3131. The latter level is included in the diagram and seen to give a better fit than the level labeled 7s 1P in the literature.
Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The configurations 2p2 and 21,4 of the first short period have not been included since they fall very close to the LS end of the diagram. As mentioned in Sect. 13 they depart grossly from the theory (see also Sect. 31).
H. A. Robinson and G. H. Shortley: Phys. Rev. 52, 713 (1937). Cf. also B. Edlen: Z. Astrophys. 22, 30 (1942) and Monthly Notices Roy. Astronom. Soc. London 114, 700 (1954).
Tas, p. 307. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
These interactions, which are a characteristic feature of the rare-gas spectra, will be discussed in Sect. 24. For a systematic and comprehensive account of the theory see E. U. Condon and G. H. Shortley: The Theory of Atomic Spectra. Cambridge: Cambridge Univ. Press 1935 (1953). It will be referred to as “Tas” in the following. See also the articles by G. Racah: Theory of Complex Spectra, Phys. Rev. 61,.186; 62, 438 (1942); 63, 367 (1943); 76, 1352 (1949), in which the theory is further developed with a somewhat different technique. We also recommend, especially for an introduction, J.C. Slater: Quantum Theory of Atomic Structure, Vol. I and II. New York: McGraw-Hill 1960.
G. H. Shortley and B. Fried: Phys. Rev. 54, 749 (1938).
G. Recex: Phys. Rev. 61, 537 (1942). — Note that the parameters F2 are larger than F2,as defined in Tas, by the following factors: F2 (p f) = 75 F2 (p f), F2 (d f) = 105 F2 (d f), F2 (p g) = 385 F2 (p g), F2 (dg) = 539 F2 (dg). Consequently, the coefficients of F2 are larger than /5 by the same factors. — The same f2 with reversed sign applies to the corresponding two-electron configurations pi, dl,etc.
A. G. Shenstone: Phil. Trans. Roy. Soc. Lond. A 235, 195 (1936).
K. B. S. ErikssoN: Phys. Rev. 102, 102 (1956); Ark. Fysik 13, 303 (1958).
A. Fowler: Report on Series in Line Spectra. London: Fleetway Press 1922.
W. Ritz: Phys. Z. 4, 406 (1903). In another formula due to Ritz, n* = in +a -- ßm the serial number m, it should be noted, is not identical with the principal quantum number n but rather close to n*. The same remark applies to Hicics’ formula, n* = m +cc + The latter formula is of historical interest as it was consistently used in Fowler’S Report.
P. Risberg: Ark. Fysik 9, 483 (1955). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
D. R. Hartree: Proc. Cambridge Phil. Soc. 24, 426 (1928). See also F. Hund: This Encyclopedia, Vol. Xxxvi, p. 18.
When determining the parameters it is convenient to have the following expressions at hand [B. Edlen and P. Rtsberg: Ark. Fysik 10, 553 (1956)]. By using the abbreviations
M. Born and W. Heisenberg: Z. Physik 23, 338 (1924). - I. Waller: Z. Physik 38, 635 (1926). j
TH = R 2 4 I, a being the Sommerfeld fine-structure constant. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
J. H. Van Vr.Eck: Proc. Roy. Soc. Lond., Ser. A 143, 679 (1934). See also K. BocKasten: Ark. Fysik 10, 567 (1956), The application to two-electron spectra has been discussed by J. H. Van Vleck and N. G. Whitelaw: Phys. Rev. 44, 551 (1933).
See papers by P. Risberg, K. Bockasten, I. Johansson and Y. Toresson on Li I, Civ, Na I, Mg II, SiIV, KI, and CaII, in Ark. Fysik 1955–1960.
F. Paschen: Ann. Physik 71, 148 (1923). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
A. Lande: Z. Physik 25, 46 (1924). Handbuch der Physik, Bd. Xxvii. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The series is subject to some configuration interaction. The slightly anomalous position of 7s 3P,might be due to such effects or to a misinterpretation of the observations.
Tas, p. 268. The formula was first derived by S. GounsMlr: Phys. Rev. 35, 1325 (1930). For applications see, e.g., B. Edlan: Z. Physik 104, 407 (1937), and K. LidÉN: Ark. Mat. Astronom. Fys., Ser. A 35, No. 24 (1948).
K. LInÉN: Ark. Fysik 1, 229 (1949). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The small difference showing up at n = 6 is due to a perturbation of 6s 2P,1, caused by an accidental coincidence with 5d 4.M12.
Cf. B. EdlÉN: Z. Physik 104, 407 (1937). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The same would be expected of the level with K = o; the deviation at n = 5 is quantitatively explained by the interaction with 6s 2p11 previously mentioned (footnote 1, p. 133).
G. Racah: Phys. Rev. 61, 537 (1942). — The complete energy matrices for p4l have been derived by N.H. MÖLler [Ark. Fysik 18, 135 (1960)]. They have been applied by L. Minnhagen [Ark. Fysik 18, 97 (1960)] to the configurations 3p4 n f and 3p4 ng of ArII, which give excellent illustration to the pair-coupling case of series convergence.
A.G. Shenstone and H.N. Russell: Phys. Rev. 39, 415 (1932). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
N. G. Whitelaw: Phys. Rev. 44, 544 (1933). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
R. F. Bacher: Phys. Rev. 43, 264 (1933); 56, 385 (1939). — L. Pincherle: Atti Accad. Lincei 16, 35 (1932); see also J. H. Van Vleck and N. G. Whitelaw: Phys. Rev. 44, 551 (1933). 2 See, for instance, E. Rasmussen: Z. Physik 73, 779 (1932); 75, 695 (1932).
B. Edlen: Unpublished results. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. Rohrlicx: Astrophys. Journ. 123, 521 (1956).
The levels are given in the pair-coupling notation (cf. Table 13). For a correlation with the Paschen notation see CH. E. MooRE: Atomic Energy Levels, Vol. 1, neon table.
There is, however, a trend in the curves of nd(2)1,o which indicates the presence of the lowest levels of ns’(2)1 u near the series limit. Cf. B. Edlen: Ark. Mat. Astronom. Fys., Ser. A 29, No. 21 (1943).
K. L. Andrew and K. W. Meissner: J. Opt. Soc. Amer. 49, 146 (1959). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
C. W. Allen: Phys. Rev. 39, 42, 55 (1932). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
A. G. Shenstone: Phil. Trans. Roy. Soc. Lond. A 241, 297 (1948), Cu I. — Phys. Rev. 57, 894 (1940), AgI.
W. R. S. Garton and A. Rajaratnam: Proc. Phys. Soc. Lond. A 68, 1107 (1955). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
If d a is the line width in cm-1, x the life-time of the level and P=7–1- the de-excitation probability in sec-I-, it follows from the uncertainty relation, z Lie h/2n, that P 27cc d a.
B. Edlen: Kg1. svenska Vetenskapsakad. Handl. 20, No. 10 (1943). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
H. Beutler et al.: Z. Physik 86, 495, 710; 87, 19, 176, 188 (1933); 88, 25; 91, 131 (1934); 93, 177 (1935).
See B. Edlbn: Spectra of highly ionized atoms. Physica, Haag 13, 545 (1947), with further references.
We may interpret c as a rough approximation for p in (26.1). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Data for Co Viii taken from unpublished observations. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
G. Hertz: Z. Physik 3, 19 (1920). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The constant c represents, roughly, (p p2)/2 in (28.2). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
B. EdlÉN: Physica, Haag 13, 545 (1947). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The measurements (not previously published) are not very accurate as the available spectrograms contain too few reference lines.
B. Edlen: Z. Physik 100, 621 (1936). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The component 2P,i, - 2S,i,is chosen in order to minimize the influence of relativity effects, which for this combination are largely compensated because the factors a (n, j) in the relativity correction a (n, j) (Z - s)4 are nearly equal for 3p 2133„ and 4s 2S,1, (see Table 51).
P. G. Kruger and L.W. Phillips: Phys. Rev. 51, 1087 (1937), Fig. 1, and B. Edlen: Z. Physik 104, 407 (1937), Fig. 2.
The screening defined by (30.1) will be denoted by s to distinguish it from the value s obtained from the complete; S o m m e r f e l d formula, which includes powers higher than
A. E. SandstrÖM: This Encyclopedia, Vol. Xxx, p. 204. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
B. Edlen: Z. Astrophys. 22, 30 (1942). - Monthly Notices Roy. Astronom. Soc. London 114, 700 (1954).
It should be remembered that Sommerfeld found it necessary to include some of these higher terms in his study of X-ray doublets.
See, e.g., H. E. White: Introduction to Atomic Spectra, p. 147. New York: McGraw-Hill 1934.
Cf. footnote 1 on p. 115. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
According to singlet-triplet combinations in Si Iii recently found by Y. Toresson (1. c., p. 178, footnote 1) the triplet terms as given in Ael should be changed by - 95 cm-1. The singlet-triplet connection accepted for Piv depends on the tentative identification of a single intercombination line.
Cf. Eq. (31. 2). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
For the calculation of hydrogenic values of Gk and Fk see Tas pp. 117, 177, and W. Bingel: Z. Naturforsch. 9a, 675 (1954).
Identified intercombination lines (Edlen, unpublished) require that the relative term values as given in Ael be shifted by the following amounts (in cm-1): NaIV singlets - 288, NaV doublets + 767, NaVI singlets + 120, NaVii quartets - 500, MgV singlets - 458, MgVI doublets +1095, Mg Vii singlets -538, A1VI singlets -460, Al Vii doublets +1380, Si Vii singlets - 450. Also, published results of Bockasten and Eriksson call for the following shifts: Ciii triplets + 52, Nii quintets - 384.
F. Rohrlich: Phys. Rev. 101, 69 (1956). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
D. Layzer: Ann. of Phys. 8, 271 (1959). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
In Fig. 57, as well as in Tables 37, 40, and 41, terms with a fine structure are represented by their centres of gravity in order to eliminate as far as possible the influence of spin effects.
It is of interest to mention that the ratios in 2s2 2p 3p are very similar to those in 2s2 2p2. The Slater formulae (13.2) for np n’p give actually two ratios, one formed from the mean values mL, viz. R (F2) _ (mS - mD)/(mD - mP), and another involving the multiplicity splittings, AL -11L - 3L I, which we write as R (G1) _ (d S - AD)/(AD - d P), both ratios being predicted to be z. Observed values for CI, N II, and 0Iii are, respectively, R (F2) 1.137, 1.136, 1.146 and R (G2) = 0.92, 1.135, 1.209. The observations are incomplete for higher members of the sequence. The constancy of R (F2) is remarkable, especially as the relative position of 2s2 2p 3p and 2p4 is rapidly changing with and in 0Iii the two configurations overlap completely.
In Tables 39 to 41 the symbol L designates the centre of gravity of terms with equal L but different multiplicity, the weights being proportional to the multiplicity.
Data for SiIii from a recent analysis by Y. ToResson: Ark. Fysik 18, 389 (1960). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
See also Sect. 37, where the values of 2p have been improved by taking account of the spin-spin and spin-other-orbit interactions, and the values of Ln p for n s2 n p3 have been derived from the splitting of 2D rather than 2P.
Waller: Z. Physik 38, 635 (1926); L. Pauling: Proc. Roy. Soc. Lond., Ser. A 114, 181 (1927). — As in Sect. 20, the values of ad will here be expressed in units of ag = 0.14816 x 10–24 cm3. For conversion to the unit As they should be multiplied by 0. 14816.
Cf. H. A. Robinson: Ark. Fysik 2, 61 (1950). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
This holds for strictly non-penetrating orbits. A similar behaviour of the 6-curves for 2p in the LiI sequence or 3d in the K I sequence, for example, must rather be ascribed to the fact that these orbits are on the verge of becoming penetrating and as the radius of the orbit decreases faster than that of the core, penetration suddenly sets in for a small increase in As a consequence, 6 will rise steeply in the beginning of the sequence, then turn over and finally decrease as expected for a penetrating orbit.
References p. 185, footnote 1. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
C. and M. Cuthbertson: Proc. Roy. Soc. Lond., Ser. A 135, 40 (1932). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The choice is based on the experience with the screening parameters discussed in Sects. 31 and 32. Other possible forms are s = a + b (Z - a)-1 or s = a + bZ-1. The latter gives s = 0.3326 + 0.141Z-1 and a (H-) = 117, in better agreement with theoretical calculations (cf. Table 49).
J.E. Mayer and M. Goeppert Mayer: Phys. Rev. 43, 605 (1933). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Calculated values from the formula (33.10) with A and k as given in Table 45. Observed values for LiI from I. Johansson [Ark. Fysik 15, 169 (1959)]; for Civ from Bockasten [Ark. Fysik 10, 567 (1956)], increased by 1.4 cm-1; other values from Ael, partly revised. A figure in parentheses is the calculated value, adopted as a basis for the absolute term values of a particular spectrum.
It is easy to devise extrapolation formulae with fewer adjustable constants, for instance, dp = 9 P(n, l) ~4 (Z - 0.367)-4 (1 -I- 0.816q (n, l) ~2/Z) serves quite well, but preference is given to the more flexible formula, which provides a clear separation of ad and can be applied in the same form to other isoelectronic sequences.
For sources of experimental data see the footnote to Table 48. From the Zip’s of a given spectrum one obtains A, and hence ad, most efficiently by the graphic method illustrated in Fig. 17.
C. and M. Cuthbertson, I. C. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Calculated values according to formula (33.10) with A and k from Table 47. Observe data: NaI and MgII from P. Risberg [Ark. Fysik 9, 483 (1955); 10, 583 (1956)3, NaI 4 from I. Johansson (unpublished); SiIV from Y. Toresson [Ark. Fysik 17, 179 (1960) Aiiii, PV, and Svi from Ael, adjusted by adopting the calculated value of dp(5g) as a basis for the absolute term values.
R.M. Sternheimer: Phys. Rev. 107, 1565 (1957). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
E.C. Wikner and T.P. Das: Phys. Rev. 107, 497 (1957). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
C. Schwartz: Ann. of Physics 2, 170 (1959). The expression given by Schwartz, may be written ma- 9/(Z -5)4 with s = if= 0.3594, which is identical with the result of A. Dalgarno and A.L. Stewart: Proc. Roy. Soc. Lond., Ser. A 247, 245 (1958).
R.M. Sternheimer: Phys. Rev. 115, 1198 (1959). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
A. Dalgarno and D. Parkinson: Proc. Roy. Soc. Lond., Ser. A 250, 422 (1959). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Cf. footnote 1 on p. 187. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Cf. also the recent calculations for He by A. Dalgarno, Proc. Roy. Soc. Lond., Ser. A 251, 282 (1959), and S. Kaneko: Phys. Soc. Japan 14, 1600 (1959), which represent a still higher approximation and give 1.404 and 1.323, respectively, for ad(He). The value 1.404 was obtained already by T.D. Baber and H.R. HassÉ: Proc. Cambridge Phil. Soc. 33, 253 (1937).
The tacit assumption of a hydrogenic spin-orbit splitting is confirmed by the observations as far as they go.
An error of 0.0021 in the measurement of 2p 2P - 3d 2D corresponds to a wave-number error of about 0.1
Cf. Sect. 28. The extrapolation can be made with the formula a = 15 393’ + 6053–19Z 752 (C 2 2)-1 + Ar (’S111) - A, (2/3111), where d
A form equivalent with (34.2) was used already by E. Fues: Ann. Physik 76, 299 (1925). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
C.L. Pekeris: Phys. Rev. 112, 1649 (1958). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Note that T(c) — d, and T(d) — d, may be written (R/2’) [2+ 2a — (2b — a2) + 2b (c — a) (C + c)-1 + b2 (~ + c)’2] and (R/23) [2-k 2a — (2b — a’) + b2 (C + a)-2], respectively. When T(c) or T(d) gives a negative effective charge for C=0, the term value is interpreted to be negative.
See, e.g., the comprehensive survey by E. Lisrrzix: Comm. Phys.-Math. Soc. Sci. Fenn. Helsingfors 10, 121 (1938).
In connection with this work the Ael values of series limits were revised in a number of cases. Note, also, that for all spectra of the sequences N = 6 and 7, except Fiii, the figures given in Ael refer to the highest fine-structure component of the limit, 24, or 3132, and not to 213,,’ or 3130 as stated. — Present knowledge of the spectra NeII, NeIIl, NaII, and Na Iii is too limited to permit a reliable determination of their series limits. The formula for N = 9 is based on FI, Mg IV, and A1V, the limits in MgIV and A1V being derived by assuming the series 3, 4, 5d 2.F,s, with the limit 3130, to be exactly Ritzian
See Sect. 32. If 2p in 2s2 2p is considered as a one-electron configuration, one would expect d, = a (2, 2 p) (Z — s)4 = ë y2 p, but the trend of the fairly accurate data for this sequence requires that the factor be slightly increased. — The value of 2p used in Table 57 for 2.32 2p2 is the mean from the intervals 3132 — 3130 and 3132 — 313, which explains why it differs from the value in Table 42.
Small systematic differences between the values in Table 58 and those reported in the literature for Z=. 11 to 15 in the sequences N = 3 and N = 4 need not indicate an error in the formula; the literature values are also based on extrapolations and may easily be affected by systematic errors of this magnitude.
W. Finkelnburg and W. Humbach: Naturwiss. 42, 35 (1955). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
D. Layzer: Ann. of Physics 8, 271 (1959). See also Sect. 31. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
For references see the review article on negative ions by L. M. BranscoMB in “Advances in Electronics and Electron Physics”, Vol. IX, pp. 43–92. New York: Academic Press 1957. See also H.R. Johnson and F. Rohrltch: J. Chem. Phys. 30, 1608 (1959).
B. Edlen: J. Chem. Phys. 33, 98 (1960). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
M. A. Catalan and F.R. Rico: An. Real Soc. espaíï. Fis. y Quim. A 54, 5 and 289 (1958).
Observed electron affinities are taken from the following sources: F- and Cl-from D. Cubicciotti: J. Chem. Phys. 31, 1646 (1959). O- and C- from L.M. Branscomb et al.: Phys. Rev. 111, 504 (1958). S- from L.M. Branscome and S. J. Smith: J. Chem. Phys. 25, 598 (1956).
It may be remarked that the formula T(c) in Table 55 gives + 67 cm-1= 4–0.01 eV for He-in agreement with the expectation that the electron affinity of helium should be close to zero.
See G. Boldt: Z. Physik 154, 330 (1959). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
In order to connect doublets and quartets in Ne IV an estimated value of 41.18 kK was used for the difference 2D51, —4.331„
Johnson and Rohrlich (1. C. p. 199, footnote 2) have proposed a formula which is equivalent to (34.3) with an additional term in a)-2. As they allow the coefficient of C2 to be adjustable, their formula contains five empirical constants. To determine so many parameters they had to rely on the asymptotic trend of the ionization potentials for large ~. The physical meaning of this procedure appears somewhat doubtful when we recall that most part of the values for large originates from previous empirical extrapolations.
Cf. footnote 1 on p. 205. Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
The value for Br Iii in Table 61, which is based on the latest analysis [Y. Bhupala Rao: Indian J. Phys. 30, 371 (1956)], would come too high in the diagram, suggesting an error in the experimental data.
According to the energy expressions for p3 given by L.H. Aller, C. W. Ufford and J.H. Van Vleck [Astrophys. J. 109, 42 (1949)], we have showing that by including the spin-spin parameter we can only increase the value of 4. For a calculation of the 2D and 2P splittings in the first period we may put DS = 9 F.z and DS/PD = 1.92 (cf. Table 40), which gives PD = 4.691; and PS= 13.69F2. The above formulae are thereby reduced to Here we may insert values of 2p and r/ obtained by a linear interpolation between those of 2s2 2p2 and 2s2 2p4 of the same element.
H. H. Marvin: Phys. Rev. 71, 102 (1947) — R. H. Garstang: Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951).
In this connection we may recall that spin-spin effects are most important in the very light elements, where they completely distort the 3P intervals of the 1snp configurations in the HeI sequence [see, for instance, B. EdlÉN: Ark. Fysik 4, 441 (1952)]. They are appreciable also in 1 s2 2 sn p of the BeI sequence. The case of 1 s2 2s 2p 3P has been treated by A.M. Naqvi: Thesis, Harvard University, 1951, and Proc. Nat. Inst. Sci. India A 21, 238 (1955).
R.F. Backer and S. GounsMit: Phys. Rev. 46, 948 (1934). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
S. Meshkov and C.W. Ufford: Phys. Rev. 94, 75 (1954). — R.E. Trees: J. Res. Nat. Bur. Stand. 53, 35 (1954); J. Opt. Soc. Amer. 48, 293 (1958).
K.L. Andrew and K.W. Meissner: J. Opt. Soc. Amer. 47, 850 (1957). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
4 Analogous diagrams may be constructed for other terms of the same configurations. We have chosen the lowest term, because it is likely to be the least perturbed and, except in the case of spa 5S, the first to be found experimentally. In a similar study M.A. Catalan and M.T. Antunes [An. Real Soc. espan. Fis. Quim. A 51, 5 (1955)] chose one or the other of the two terms of 2s 2ph+1 arising from the lowest term of 2 pk+l, taking always the difference between terms of equal multiplicity (d S = o). The data were plotted separately for each value of to show the variation with k for constant ~.
The only case where an observed point departs significantly from the expected position occurs for BiIii. It is probably to be explained by an interaction of individual levels of spe 4P with levels of 6s 6d 2D and 6s2 7s 2S, which is conceivable because the LS character of 4P is here practically lost.
H.N. Russell [J. Opt. Soc. Amer. 40, 618 (1950)], M.A. Catalan and R. Velasco [An. Real Soc. espar. Fis. Quim. A 48, 247 (1952)], and M.A. Catalan and F.R. Rico [An. Real Soc. espar. Fis. Quim. A 48, 328 (1952); 53, 85 (1957); 54, 5, 289, 301 (1958)].
To simplify the discussion we have assumed the parameter values to be the same for two consecutive ions.
Catalan and Rico (1. c. footnote 1 above) based a similar study of ionization potentials on empirical relations between the absolute term values (or n*) of the configurations nsr n pk-1 n’s, with n’ = n 1 and n + 2, as functions of N. The present method is simpler and avoids the difficulty with the accidental configuration interactions that may afflict the relatively high ns’ terms. — In order to check and complete the analyses Catalan and Rico plotted against k the values of the ns2 npk—in’s terms referred to the ground level of ns2 npk. The curves obtained are similar to those in Fig. 69, as one would expect, considering that the n’s terms should follow the trend of their series limits, i.e. the ionization potentials.
The configurations that are responsible for the majority of terms observed in these spectra are contained in the following three groups: where n’=n+1 and n“=n+2.
From Tas, pp. 202, 206, 233; 0. Laporte: Phys. Rev. 61, 302 (1942); 0. Laporte and J.R. Platt: Phys. Rev. 61, 305 (1942). See also M.A. Catalan and M. T. Antunes: Z. Physik 102, 432 (1936).
The parameters A, B, and C were introduced by G. Racah: Phys. Rev. 62, 438 (1942). For the transformation from Fk to Fk we have F° (d d) = F° (d d), F2 (d d) = F2 (d d)/49, F4 (d d) F4 (d d)/441.
D. Layzer: Thesis, Harvard University, 1951. R. E. Trees: Phys. Rev. 83, 756; 84, 1089 (1951).
G. Racah: Phys. Rev. 85, 381 (1952). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
For references see G. Racah and Y. Shadmi: Bulletin of the Research Council of Israel 8F, 15 (1959). See also J.C. Slater: Quantum Theory of Atomic Structure, p. 376. New York: McGraw-Hill 1960.
G. Racah and Y. Shadmi, 1. c. The deepest term of each configuration, being identically zero, is not counted in this figure. — In this treatment we neglect spin-orbit interactions and define a term by the centre of gravity of its fine-structure components. Individual levels may be obtained by adding the spin-orbit energy, calculated by means of the splitting factors given in Sect. 15 with suitable values of Cid
The deepest term of each configuration, being identically zero, is not counted in this figure. — In this treatment we neglect spin-orbit interactions and define a term by the centre of gravity of its fine-structure components. Individual levels may be obtained by adding the spin-orbit energy, calculated by means of the splitting factors given in Sect. 15 with suitable values of Cid
The values of these five constants have been chosen so as to get a reasonable average fit to all the term systems here considered. As an alternative procedure one might adopt, as far as practicable, hydrogenic values for the parameters, thereby obtaining expressions that would probably give a better asymptotic representation of the term systems for large values of C. With hydrogenic wave functions we have.1 (3 d 3 d) = 299RZ/161 280 = 203.4Z and F4/F2 =5/69 = 0.0725, that is, according to (40.1), B = 130Z cm-1 and C/B = 3.98. In the expression for B we should then replace C by (ç p) with p (C) approaching a constant value for large C.
Some questionable term designations, as given in the Ael, were found in this connection. For instance, in Crl the term value of d2 (b’F) 4s 3F is much too low, and the configuration assignments for b 31) and c 3D should be interchanged. In Cr Iii the terms a1F, b 3P,and b ‘G of d4 are too high; all singlets seem to need checking. The term d3 2P is much too low in both V Iii and Cr IV. See also the revisions in the second spectra of the iron group suggested by Racah and Shadmi (1. c.).
According to a formula by J.H. Van Vleck [Phys. Rev. 45, 405 (1934)] the energy of lks may be written
where M = 2 S + 1 and M, = 2 So + 1, S and So being the total spin for the term of lks and lk, respectively.
H.N. Russell: Astroph. J. 66, 283 (1927). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
M.A. Catalan, F. Rohrlich and A.G. Shenstone: Proc. Roy. Soc. Lond., Ser. A 221, 421 (1954). Because of the approximate nature of the theoretical formulae here discussed nothing would be gained by trying to derive the parameters by a least-squares solution from all the observed levels. A more elaborate theoretical treatment of p2 and p4 by R. H. Garstang [Monthly Notices Roy. Astronom. Soc. London 111, 115 (1951)] includes the magnetic interactions of different electrons and to some extent configuration interactions. As the number of parameters introduced is equal to the number of levels no check is possible, and, of course, the results cannot be displayed in a two-dimensional diagram. Configuration interaction was explicitly included by D. Layzer: Monthly Notices Roy. Astronom. Soc. London 114, 692 (1955). See also F. RoHrlicx: Astrophys. Journ. 123, 521 (1956).
Phys. Rev. 74, 1372, 1381 (1948); T. Ishidzu and S. Obi: J. Phys. Soc. Japan 5, 124 (1950); N. Rosenzweig: Phys. Rev. 88, 580 (1952); S. Meshkov: Phys. Rev. 91, 871 (1953); R.E. Trees: Phys. Rev. 97, 686 (1955); N. Sack: Phys. Rev. 102, 1302 (1956); G. Racah and N. Spector: Bull. Res. Council of Israel 9F, 75 (1960).
Transactions of the Joint Commission for Spectroscopy: J. Opt. Soc. Amer. 50, 405–411, 1960. The list of references has been further amended by CH. E. Moore in a report to the Ottawa meeting (September 1960) of the Triple Commission on Spectroscopy.
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Edlén, B. (1964). Atomic Spectra. In: Flügge, S. (eds) Spectroscopy I / Spektroskopie I. Encyclopedia of Physics / Handbuch der Physik, vol 5 / 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-35391-2_2
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