The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part II. Some Results and Discussion

Author:

Hartree D. R.

Abstract

The methods of solution of the wave equation for a central field given in the previous paper are applied to various atoms. For the core electrons, the details of the interaction of the electrons in a single nk group are neglected, but an approximate correction is made for the fact that the distributed charge of an electron does not contribute to the field acting on itself (§2).For a given atom the object of the work is to find a field such that the solutions of the wave equation for the core electrons in this field (corrected as just mentioned for each core electron) give a distribution of charge which reproduces the field. This is called the self-consistent field, and the process of finding it is one of successive approximation (§ 3).Approximations to the self-consistent field have been found for He (§ 4), Rb+ (§ 5), Na+, Cl (§ 9). For He the energy parameter for the solution of the wave equation for one electron in the self-consistent field of the nucleus and the other corresponds to an ionisation potential of 24·85 volts (observed 24·6 volts); this agreement suggests that for other atoms the values of the energy parameter in the self-consistent field (corrected for each core electron) will probably give good approximations to the X-ray terms (§4).The most extensive work has been carried out for Rb+. The distribution of charge given by the wave functions in the self-consistent field is compared with the distribution calculated by other methods (§ 6). The values of X-ray and optical terms calculated from the self-consistent field show satisfactory agreement with those observed (§ 7).The wave mechanical analogue of the case in which on the orbital model an internal and an external orbit of the same energy are possible is discussed (§ 8).

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference24 articles.

1. Integer values of k were used in these calculations. The writer has tried some work with half integral values of k, but without any very marked improvement in the general agreement between observed and calculated values.

2. With the half integer values of k there are no circular orbits. The curve for the orbital model is really much more broken than as shown in Fig. 3 (see second footnote on page 119).

3. The theoretical prediction of the physical properties of many electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space

4. loc cit.

5. The charge density is calculated from the wave functions from which the final field is built up, not by numerical differentiation of Z.

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