Abstract

The International Business Machines Card Programmed Calculator has been wired (by members of the NOTS Mathematics Division) to compute wave functions of several terms of the sharp and diffuse series of potassium (up to 11s and 9d). Transition probabilities and “oscillator” and “line strengths” estimated from these are reported. The computational procedure employed was that developed by Biermann and Lübeck. Perfect agreement with Biermann and Lübeck was obtained for a check calculation of the 4p wave function. The reliability of the results is discussed.

© 1952 Optical Society of America

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  1. See for example, D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 166A, 450 (1938).
    [Crossref]
  2. D. R. Bates, Proc. Roy. Soc. (London) 188A, 350 (1947); D. R. Bates and Agnete Damgaard, Trans. Roy. Soc. (London) 242A, 101 (1949).
    [Crossref]
  3. Louis C. Green and Nancy E. Weber, Astrophys. J. 111, 582 (1950); Astrophys. J. 111587–92 (1950).
    [Crossref]
  4. L. Biermann and K. Lübeck, Z. Astrophys 22, 157 (1943); Z. Astrophys 25, 325 (1948); Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl., Heft 2, 116 (1946).
  5. D. R. Hartree, Proc. Cambridge Phil. Soc. 24, 89, 111 (1928); Proc. Roy. Soc. (London) 141A, 282 (1933); Proc. Roy. Soc. (London) 143A, 506 (1934).
    [Crossref]
  6. E. U. Condon and George H. Shortley, Theory of Atomic Spectra (Cambridge University Press, London, 1935), Chapter 4, p. 98.
  7. D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 164A, 183 (1938).
  8. A. Unsöld, Physik der Sternatmosphären (Julius Springer, Berlin, 1938), Chapter IX, Sec. 48.
    [Crossref]
  9. Y. Sugiura, Phil. Mag. [4],  7, 495 (1927).
  10. J. F. Heard, Monthly Notices Roy. Astron. Soc. London 94, 458–66 (1934). L. S. Ornstein and J. Key, Physica 1, 945–52 (1934). E. F. M. Van der Held and J. H. Heierman, Physica 3, 31–41 (1936). A. Filippov, Physik. Z. Sowjetunion 5, 1–5 (1934). K. H. Schwarz, Physica 7, 361–8 (1940).
    [Crossref]

1950 (1)

Louis C. Green and Nancy E. Weber, Astrophys. J. 111, 582 (1950); Astrophys. J. 111587–92 (1950).
[Crossref]

1947 (1)

D. R. Bates, Proc. Roy. Soc. (London) 188A, 350 (1947); D. R. Bates and Agnete Damgaard, Trans. Roy. Soc. (London) 242A, 101 (1949).
[Crossref]

1943 (1)

L. Biermann and K. Lübeck, Z. Astrophys 22, 157 (1943); Z. Astrophys 25, 325 (1948); Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl., Heft 2, 116 (1946).

1938 (2)

See for example, D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 166A, 450 (1938).
[Crossref]

D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 164A, 183 (1938).

1934 (1)

J. F. Heard, Monthly Notices Roy. Astron. Soc. London 94, 458–66 (1934). L. S. Ornstein and J. Key, Physica 1, 945–52 (1934). E. F. M. Van der Held and J. H. Heierman, Physica 3, 31–41 (1936). A. Filippov, Physik. Z. Sowjetunion 5, 1–5 (1934). K. H. Schwarz, Physica 7, 361–8 (1940).
[Crossref]

1928 (1)

D. R. Hartree, Proc. Cambridge Phil. Soc. 24, 89, 111 (1928); Proc. Roy. Soc. (London) 141A, 282 (1933); Proc. Roy. Soc. (London) 143A, 506 (1934).
[Crossref]

1927 (1)

Y. Sugiura, Phil. Mag. [4],  7, 495 (1927).

Bates, D. R.

D. R. Bates, Proc. Roy. Soc. (London) 188A, 350 (1947); D. R. Bates and Agnete Damgaard, Trans. Roy. Soc. (London) 242A, 101 (1949).
[Crossref]

Biermann, L.

L. Biermann and K. Lübeck, Z. Astrophys 22, 157 (1943); Z. Astrophys 25, 325 (1948); Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl., Heft 2, 116 (1946).

Condon, E. U.

E. U. Condon and George H. Shortley, Theory of Atomic Spectra (Cambridge University Press, London, 1935), Chapter 4, p. 98.

Green, Louis C.

Louis C. Green and Nancy E. Weber, Astrophys. J. 111, 582 (1950); Astrophys. J. 111587–92 (1950).
[Crossref]

Hartree, D. R.

See for example, D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 166A, 450 (1938).
[Crossref]

D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 164A, 183 (1938).

D. R. Hartree, Proc. Cambridge Phil. Soc. 24, 89, 111 (1928); Proc. Roy. Soc. (London) 141A, 282 (1933); Proc. Roy. Soc. (London) 143A, 506 (1934).
[Crossref]

Hartree, W.

D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 164A, 183 (1938).

See for example, D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 166A, 450 (1938).
[Crossref]

Heard, J. F.

J. F. Heard, Monthly Notices Roy. Astron. Soc. London 94, 458–66 (1934). L. S. Ornstein and J. Key, Physica 1, 945–52 (1934). E. F. M. Van der Held and J. H. Heierman, Physica 3, 31–41 (1936). A. Filippov, Physik. Z. Sowjetunion 5, 1–5 (1934). K. H. Schwarz, Physica 7, 361–8 (1940).
[Crossref]

Lübeck, K.

L. Biermann and K. Lübeck, Z. Astrophys 22, 157 (1943); Z. Astrophys 25, 325 (1948); Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl., Heft 2, 116 (1946).

Shortley, George H.

E. U. Condon and George H. Shortley, Theory of Atomic Spectra (Cambridge University Press, London, 1935), Chapter 4, p. 98.

Sugiura, Y.

Y. Sugiura, Phil. Mag. [4],  7, 495 (1927).

Unsöld, A.

A. Unsöld, Physik der Sternatmosphären (Julius Springer, Berlin, 1938), Chapter IX, Sec. 48.
[Crossref]

Weber, Nancy E.

Louis C. Green and Nancy E. Weber, Astrophys. J. 111, 582 (1950); Astrophys. J. 111587–92 (1950).
[Crossref]

Astrophys. J. (1)

Louis C. Green and Nancy E. Weber, Astrophys. J. 111, 582 (1950); Astrophys. J. 111587–92 (1950).
[Crossref]

Monthly Notices Roy. Astron. Soc. London (1)

J. F. Heard, Monthly Notices Roy. Astron. Soc. London 94, 458–66 (1934). L. S. Ornstein and J. Key, Physica 1, 945–52 (1934). E. F. M. Van der Held and J. H. Heierman, Physica 3, 31–41 (1936). A. Filippov, Physik. Z. Sowjetunion 5, 1–5 (1934). K. H. Schwarz, Physica 7, 361–8 (1940).
[Crossref]

Phil. Mag. [4] (1)

Y. Sugiura, Phil. Mag. [4],  7, 495 (1927).

Proc. Cambridge Phil. Soc. (1)

D. R. Hartree, Proc. Cambridge Phil. Soc. 24, 89, 111 (1928); Proc. Roy. Soc. (London) 141A, 282 (1933); Proc. Roy. Soc. (London) 143A, 506 (1934).
[Crossref]

Proc. Roy. Soc. (London) (3)

D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 164A, 183 (1938).

See for example, D. R. Hartree and W. Hartree, Proc. Roy. Soc. (London) 166A, 450 (1938).
[Crossref]

D. R. Bates, Proc. Roy. Soc. (London) 188A, 350 (1947); D. R. Bates and Agnete Damgaard, Trans. Roy. Soc. (London) 242A, 101 (1949).
[Crossref]

Z. Astrophys (1)

L. Biermann and K. Lübeck, Z. Astrophys 22, 157 (1943); Z. Astrophys 25, 325 (1948); Nachr. Akad. Wiss. Göttingen, Math.-physik. Kl., Heft 2, 116 (1946).

Other (2)

A. Unsöld, Physik der Sternatmosphären (Julius Springer, Berlin, 1938), Chapter IX, Sec. 48.
[Crossref]

E. U. Condon and George H. Shortley, Theory of Atomic Spectra (Cambridge University Press, London, 1935), Chapter 4, p. 98.

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Figures (1)

Fig. 1
Fig. 1

Dependence of oscillator strength on principal quantum number.

Tables (7)

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Table I Parameters for energy levels of K(I).

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Table III (Sample part). Normalized wave functions for the s states of K(I). 6s; ∊=0.06888; β=0.17432.

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Table IV (Sample part). Normalized wave functions for the d states of K(I). 3d; ∊=0.12279; β=0.12614.

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Table V Transition probability expressions.

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Table VI Comparison of transition probability, A(A, 4p)×10−6, with experiment.

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Table VII Comparison of line strength, S(A, 4p), with values calculated by others.

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Table IX Sensitivity of line strength to 0.1 percent change in .

Equations (36)

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( d 2 P / d r 2 ) + [ 2 v - - l ( l + 1 ) / r 2 ] P = 0
2 v = 2 v Hartree ( 1 + β r exp [ - ( r / r 0 ) 8 ] ) + ( α / r 4 ) ( 1 - exp [ - ( r / r 0 ) 8 ] ) .
α = 5.8
R = P - ( h 2 / 12 ) P
= P [ 1 - ( h 2 / 12 ) ( T + ) ] .
R ( r + h ) = 2 R ( r ) - R ( r - h ) + R I I ( r )
R I I ( r ) = h 2 ( T + ) 1 - ( h 2 / 12 ) ( T + ) R ( r ) = h 2 ( T + ) P ( r ) .
P l = r l + 1 [ 1 - { Z p / ( l + 1 ) } r + + 2 Z p ( { Z p / ( l + 1 ) } - β ) 4 ( l + 1 ) + 2 r 2 + ] .
I ( a , b ) = N ( a ) h ν ( 64 π 4 ν ˜ 3 / 3 h ) S ( a , b )
S ( a , b ) = { ψ ( a ) e r ψ ( b ) d τ } 2 .
ψ = ( 1 / r ) P ( r ) Φ ( θ , φ ) .
N ( A ) = g ( A ) N ( a )
g ( A ) = 2 ( 2 l A + 1 )
S ( A , B ) = a b S ( a , b ) .
S ( n l , n l ) = 2 Max ( l , l ) { P ( n l ) e r P ( n l ) d r } 2
I ( A , B ) = N ( A ) h ν A ( A , B ) .
I ( A , B ) = a , b I ( a , b ) .
A ( A , B ) = ( 64 π 4 ν ˜ 3 / 3 h ) ( 1 / g ( A ) ) S ( A , B )
= ( 4 / 3 ) ( h 3 / m 2 e 2 ) ν ˜ 3 ( 1 / g ( A ) ) S au ( A , B ) = 2.67708 × 10 9 ( ν / R ) 3 S au ( A , B ) / g ( A )
a H = h 2 / 4 π 2 m e 2 .
f ( A , B ) = ± ( m c / 8 π 2 e 2 ν ˜ 2 ) A ( A , B )
= ± ( 8 π 2 m / 3 h e 2 ) ν ( 1 / g ( A ) ) S ( A , B )
= ± ( 1 / 3 ) ( ν / R ) ( 1 / g ( A ) ) S au ( A , B ) .
g ( A ) f ( A , B ) = - g ( B ) f ( B , A ) .
P = P 0 + Δ P = 0 + Δ β = β 0 + Δ β } .
Δ P n - ( T 0 + 0 n ) Δ P n = P 0 n ( Δ T + Δ n ) .
Δ P n = i A n i P 0 i .
Δ n = - P 0 n Δ T P 0 n d r = Δ β 2 v H r exp [ - ( r / r 0 ) 8 ] P 0 n 2 d r
( Δ β / Δ ) n = [ 2 v H r exp [ - ( r / r 0 ) 8 ] P 0 n 2 d r ] - 1 .
P n r P m d r = P 0 n r P 0 m d r + Δ P n r P 0 n d r + P 0 n r Δ P m d r .
A n m = ( 0 m - 0 n ) - 1 P 0 n Δ T P 0 m d r .
( d 2 P / d r 2 ) - P = 0 r .
P = k exp [ ± 1 2 r ] .
( d ln β / d ln ) 10 s = 40.1.
0.000 017 360 - 0.052 055 350 + 0.001 629 800 - 15.577 354 400 = 0.001 647 160 - 15.629 409 750 = 15.627 762 590.
15.627 762 590 / 15.629 409 750 = 0.99989.