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  1. Brackett and Birge, J. O. S. A.,  8; Feb.1924.
    [Crossref]
  2. ZS. f. Physik,  12, p. 342; 1923.
    [Crossref]
  3. ZS. f. Physik,  16, p. 46; 1923.
    [Crossref]
  4. See Fowler’s “Report,” p. 111.
  5. Since the presentation of this paper; the, author has received an article by D. R. Hartee (Proc, Camb. Phil. Soc. XXI, VI.) in which the problem of the force fields has been approached in a somewhat similar manner. In order, to obtain more information in regard to the points lying between these given by the circular orbits, data from the eccentric orbits have been used. This necessarily introduces further assumptions about which there is considerable uncertainty. The curves in his article show the resemblance to shifted equilateral hyperbolas (except for departures introduced by using the eccentric orbits) which is mentioned in this paper. He has however not plotted the reciprocals of Za and hence has not obtained the relations given in this paper.

1924 (1)

Brackett and Birge, J. O. S. A.,  8; Feb.1924.
[Crossref]

1923 (2)

ZS. f. Physik,  12, p. 342; 1923.
[Crossref]

ZS. f. Physik,  16, p. 46; 1923.
[Crossref]

Birge,

Brackett and Birge, J. O. S. A.,  8; Feb.1924.
[Crossref]

Brackett,

Brackett and Birge, J. O. S. A.,  8; Feb.1924.
[Crossref]

Hartee, D. R.

Since the presentation of this paper; the, author has received an article by D. R. Hartee (Proc, Camb. Phil. Soc. XXI, VI.) in which the problem of the force fields has been approached in a somewhat similar manner. In order, to obtain more information in regard to the points lying between these given by the circular orbits, data from the eccentric orbits have been used. This necessarily introduces further assumptions about which there is considerable uncertainty. The curves in his article show the resemblance to shifted equilateral hyperbolas (except for departures introduced by using the eccentric orbits) which is mentioned in this paper. He has however not plotted the reciprocals of Za and hence has not obtained the relations given in this paper.

J. O. S. A. (1)

Brackett and Birge, J. O. S. A.,  8; Feb.1924.
[Crossref]

ZS. f. Physik (2)

ZS. f. Physik,  12, p. 342; 1923.
[Crossref]

ZS. f. Physik,  16, p. 46; 1923.
[Crossref]

Other (2)

See Fowler’s “Report,” p. 111.

Since the presentation of this paper; the, author has received an article by D. R. Hartee (Proc, Camb. Phil. Soc. XXI, VI.) in which the problem of the force fields has been approached in a somewhat similar manner. In order, to obtain more information in regard to the points lying between these given by the circular orbits, data from the eccentric orbits have been used. This necessarily introduces further assumptions about which there is considerable uncertainty. The curves in his article show the resemblance to shifted equilateral hyperbolas (except for departures introduced by using the eccentric orbits) which is mentioned in this paper. He has however not plotted the reciprocals of Za and hence has not obtained the relations given in this paper.

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Figures (5)

Fig. 1
Fig. 1

General character of field.

Fig. 2
Fig. 2

Linear relations within the atom body.

Fig. 3
Fig. 3

Dependence of slope on atomic number.

Fig. 4
Fig. 4

Dependence of quantum defect on number of orbital groups.

Fig. 5
Fig. 5

Linear Relation of Slopes for the “Saturated Conditions.”

Tables (1)

Tables Icon

Table 1 Table of Residuals βϵ

Equations (28)

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W = - R h Z a 2 n 2
h ν = - W
ν = R Z a 2 n 2
Z a = n ν R
D = R ν
Z a = n D
a a = n 2 h 2 4 π 2 m e 2 Z a = a 0 n 2 Z a = n D a 0
Z a a a = n 2 ( where the scale a 0 = 1 is used )
c = .35 = .23 = .11 ½
1 Z a = m a a a 0 + 1 Z
1 m = c Z + k
Z - Z a = m Z Z a a a a 0 = γ
n 2 = Z a a a a 0
γ n 2 = m Z
γ n 2 = Z c Z + k
c = .35             up to Z = 18 = .23             Z = 18 to 55 = .115             55 to 87
c = τ ρ where ρ = .115 and τ = 1 , 2 , or 3
m = C 1 Z + K             C = 1.84             K = .03
Y n 2 = C + K Z = 1.84 + .03 Z
γ = α + β n 2 or γ n 2 = α n 2 + β
α n 2 = 1.84 + .03 Z - ϵ
Δ β g = .3 for Ar and Kr . Δ β g = .5 for X . Δ β g = .6 for Nt .
Δ ( Δ β g ) = .2 in the first range where τ = 2 Δ ( Δ β g ) = .1 in the first range where τ = 1
Δ β k = .9 in the first range . Δ β k = .4 in the second range .
Δ β k Δ Z = .025 in the first range where τ = 2 = .0125 in the second range where τ = 1.
α n 2 = 1.74 ± .04 + .03 Z
n 2 = Z e a / a 0
α Z e = ( 1.74 ± .04 + .03 Z ) a a 0 = .