DOI: 10.1017/s0305004100018594. The dispersion electrons of lithium

10.1017/s0305004100018594

Crossref journal-article

Cambridge University Press (CUP)

Mathematical Proceedings of the Cambridge Philosophical Society (56)

Abstract

An attempt has been made in the work described in the present paper to use the method initiated by Hartree, for the numerical solution of the Schrödinger wave equation for an atom with a non-Coulomb field of force, to estimate the number of dispersion electrons (hereinafter denoted by “ƒ” for brevity), corresponding to the lines of the principal series of the optical spectrum of lithium, and also to the continuous spectrum at the head of the series. Various attempts have been made to do this for hydrogen and other atoms by an application of the Correspondence Principle, but the first successful attempt at a complete description was made by Sugiura†, who has calculated ƒ for the Lyman, Balmer, and Paschen series and the corresponding continuous spectra, by using the known analytical solutions of the wave equation for an electron in a Coulomb field. The same author has also calculated ƒ for the first two lines of the principal series of sodium, by the utilisation of an empirical field of force in the atom calculated from the observed term-values by a method based on the old quantum theory. He has estimated the contribution to Σƒ (summed for the whole series) due to the continuous spectrum by the theorem that Σƒ = 1 in the one-electron problem§. This property provides a useful check on the work when ƒ for the continuous spectrum is also calculated. In the present paper ƒ for the continuous spectrum is actually calculated and it is found that Σƒ = 1 to a good approximation.

Bibliography

Hargreaves, J. (1929). The dispersion electrons of lithium. Mathematical Proceedings of the Cambridge Philosophical Society, 25(1), 75â96.

Authors 1

J. Hargreaves (first)

References 27 Referenced 52

10.1007/BF01451659
Hartree , loc. cit. p. 436.
Whittaker and Watson , loc. cit. p. 343.
10.1002/andp.19263861905
Zeit. f. Phys. L, 228 (1928).
10.1007/BF01351301
10.1007/BF01328494
10.1007/BF01558908
10.1007/BF01328322
10.1098/rspa.1927.0039
{'key': 'S0305004100018594_ref025', 'first-page': '448', 'author': 'Sommerfeld', 'year': '1923', 'journal-title': 'Atomic Structure and Spectral Lines'} / Atomic Structure and Spectral Lines by Sommerfeld (1923)
Hartree , loc. cit. p. 428, equation (3·1) et seq.
10.1007/BF01331244
{'key': 'S0305004100018594_ref013', 'first-page': '121', 'volume': 'XVIII', 'year': '1917', 'journal-title': 'Phys. Zeit.'} / Phys. Zeit. (1917)
See Whittaker and Watson , Modern Analysis, p. 188.
{'key': 'S0305004100018594_ref012', 'first-page': '318', 'volume': 'XVIII', 'author': 'Einstein', 'year': '1916', 'journal-title': 'Verh. Deuts. Physikal. Gesells. Jahrg.'} / Verh. Deuts. Physikal. Gesells. Jahrg. by Einstein (1916)
Lorentz , Problems of Modern Physics, p. 169 et seq.
10.1002/andp.19263861802
10.1007/BF01322017
10.1007/BF01554355
See, e.g., Richardson , Electron Theory of Matter, ch. VIII,
Lorentz , loc. cit., esp. equations 215, 216.
10.1017/S0305004100011919
{'key': 'S0305004100018594_ref002', 'first-page': '113', 'volume': 'VIII', 'author': 'Sugiura', 'year': '1927', 'journal-title': 'Journ. de Phys.'} / Journ. de Phys. by Sugiura (1927)
10.1080/14786440908564355
10.1080/14786442408634360
{'key': 'S0305004100018594_ref004', 'first-page': '322', 'volume': 'XXXIX', 'year': '1926', 'journal-title': 'Zeit. für Phys.'} / Zeit. für Phys. (1926)

Dates

Type	When
Created	16 years, 9 months ago (Nov. 7, 2008, 11:05 a.m.)
Deposited	6 years, 2 months ago (June 9, 2019, 3:45 p.m.)
Indexed	1 year, 6 months ago (Feb. 10, 2024, 4:41 a.m.)
Issued	96 years, 7 months ago (Jan. 1, 1929)
Published	96 years, 7 months ago (Jan. 1, 1929)
Published Online	16 years, 10 months ago (Oct. 24, 2008)
Published Print	96 years, 7 months ago (Jan. 1, 1929)

Funders 0

None

BibTeX

@article{Hargreaves_1929, title={The dispersion electrons of lithium}, volume={25}, ISSN={1469-8064}, url={http://dx.doi.org/10.1017/s0305004100018594}, DOI={10.1017/s0305004100018594}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Hargreaves, J.}, year={1929}, month=jan, pages={75–96} }

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