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  1. Jour. Math. and Phys. Mass. Inst. of Tech., May, 1924.See also Proc. Amer. Phys. Soc. 23, p. 552 (A8); 1924.
  2. “Critical Potentials.” K. T. Compton and F. L. Mohler.
  3. D. R. Hartree, Proc. Camb. Phil. Soc.,  22, p. 409; 1924.
    [CrossRef]
  4. See A. Sommerfeld, Atombau und Spektrallimien, 3d Ed. p. 456 ff., particularly tables 41 and 42.
  5. See N. Bohr, Annalen der Physik,  71, p. 242 ff; 1923; particularly the diagrams at the end of the article.
  6. A. Sommerfeld, loc. cit., p. 462.
  7. E. Fues, Ann. der Physik,  63, p. 1; 1920.
    [CrossRef]
  8. L. A. Turner, Phil. Mag.Sept., 1924 andPhil. Mag.Nov., 1924;F. S. Brackett and R. T. Birge, Jour. Opt. Soc. 8, p. 213; 1924.
    [CrossRef]
  9. D. R. Hartree, Proc. Camb. Phil. Soc. loc. cit.

1924 (3)

Jour. Math. and Phys. Mass. Inst. of Tech., May, 1924.See also Proc. Amer. Phys. Soc. 23, p. 552 (A8); 1924.

D. R. Hartree, Proc. Camb. Phil. Soc.,  22, p. 409; 1924.
[CrossRef]

L. A. Turner, Phil. Mag.Sept., 1924 andPhil. Mag.Nov., 1924;F. S. Brackett and R. T. Birge, Jour. Opt. Soc. 8, p. 213; 1924.
[CrossRef]

1923 (1)

See N. Bohr, Annalen der Physik,  71, p. 242 ff; 1923; particularly the diagrams at the end of the article.

1920 (1)

E. Fues, Ann. der Physik,  63, p. 1; 1920.
[CrossRef]

Bohr, N.

See N. Bohr, Annalen der Physik,  71, p. 242 ff; 1923; particularly the diagrams at the end of the article.

Compton, K. T.

“Critical Potentials.” K. T. Compton and F. L. Mohler.

Fues, E.

E. Fues, Ann. der Physik,  63, p. 1; 1920.
[CrossRef]

Hartree, D. R.

D. R. Hartree, Proc. Camb. Phil. Soc.,  22, p. 409; 1924.
[CrossRef]

D. R. Hartree, Proc. Camb. Phil. Soc. loc. cit.

Mohler, F. L.

“Critical Potentials.” K. T. Compton and F. L. Mohler.

Sommerfeld, A.

See A. Sommerfeld, Atombau und Spektrallimien, 3d Ed. p. 456 ff., particularly tables 41 and 42.

A. Sommerfeld, loc. cit., p. 462.

Turner, L. A.

L. A. Turner, Phil. Mag.Sept., 1924 andPhil. Mag.Nov., 1924;F. S. Brackett and R. T. Birge, Jour. Opt. Soc. 8, p. 213; 1924.
[CrossRef]

Ann. der Physik (1)

E. Fues, Ann. der Physik,  63, p. 1; 1920.
[CrossRef]

Annalen der Physik (1)

See N. Bohr, Annalen der Physik,  71, p. 242 ff; 1923; particularly the diagrams at the end of the article.

Jour. Math. and Phys. Mass. Inst. of Tech. (1)

Jour. Math. and Phys. Mass. Inst. of Tech., May, 1924.See also Proc. Amer. Phys. Soc. 23, p. 552 (A8); 1924.

Phil. Mag. (1)

L. A. Turner, Phil. Mag.Sept., 1924 andPhil. Mag.Nov., 1924;F. S. Brackett and R. T. Birge, Jour. Opt. Soc. 8, p. 213; 1924.
[CrossRef]

Proc. Camb. Phil. Soc. (1)

D. R. Hartree, Proc. Camb. Phil. Soc.,  22, p. 409; 1924.
[CrossRef]

Proc. Camb. Phil. Soc. loc. cit. (1)

D. R. Hartree, Proc. Camb. Phil. Soc. loc. cit.

Other (3)

A. Sommerfeld, loc. cit., p. 462.

See A. Sommerfeld, Atombau und Spektrallimien, 3d Ed. p. 456 ff., particularly tables 41 and 42.

“Critical Potentials.” K. T. Compton and F. L. Mohler.

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Figures (1)

Tables (11)

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Table I Potential Energy V as a function of r

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Table 2 Effective quantum numbers

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Table 3 Aphelial distances in terms of a0

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Table 4 Values of quantum integrals

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Table 5 Ratio of quantum defects

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Table 6 Ratio of quantum defects

Equations (31)

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T = 1 2 m ( p r 2 + p φ 2 / r 2 )
E = V + 1 2 m ( p r 2 + p φ 2 / r 2 )
p r 2 = 2 m E 2 m V p φ 2 / r 2
p φ = k h 2 π
p r d r = 2 m E 2 m V k 2 h 2 4 π 2 r 2 d r = ( n k ) h
V = ( N q ) e 2 r e 2 a r 2 a 2
σ = e 4 π a 2 ( q a ( r + a ) ( r a ) 2 ) = 0
V = ( N q ) e 2 r e 2 ( d 2 1 ) 2 a f ( r ) , a < r < r 1
V = N e 2 r + q e 2 a e 2 ( d 2 1 ) 2 a f ( r ) , r min < r < a
f ( r ) = 1 b d c [ b + ( d + 1 ) 2 d + 1 b + ( d 1 ) 2 d 1 ] ,
V = ( N q ) e 2 r + S ( r ) e 2 ( d 2 1 ) 2 a f 1 ( r )
n * 2 = N * 2 e 2 2 E a 0
q / q = 1 + f i
1 h i p r d r + 1 h o p r d r = n k
n * k = 1 h e p r d r
q = n n * = 1 h [ i p r d r + o p r d r e p r d r ]
e p r d r o p r d r = e i p r d r
q = I i I e i
q / q = I i I e i I i I e i
I i = I i
q / q = 1 + I e i I e i I i I e i
I e i = 1 2 π h r min b Z 2 n 2 + 2 Z r k 2 r 2 d r
I e i = 1 π { 2 Z b Z 2 b 2 / n 2 k 2 + n arc sin ( Z b / n 2 1 ) k arc sin ( Z b k 2 Z b ) + ( n k ) π 2 }
q = ( I i I e i ) + ( I o I e o )
I e i = 1 2 π h r min Z / 2 b Z / 2 x 2 + 4 x 1 x d x
I e i = 2 Z 2 π ( b r min )
I = 2 2 π [ ( N 10 ) b 1 / ( 1 + ) ]
I i I e i = 8.06 .15 N N 5.17
I o I e o = 1.38 .020 N N 6.70
q = 5.87 + .002 N N 6.70
q / q = 1 + 1 N 6.70