Abstract

The polarization of radiation scattered by an electronic system in a magnetic field is worked out on the classical theory. It is shown that it is improbable that the experimental facts can be accounted for on a classical analogy. Instead, a quantum hypothesis is made which appears to account for the phenomena more satisfactorily.

© 1926 Optical Society of America

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References

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  1. J. A. Eldridge, Physical Rev.,  24, p. 234; 1924.
    [Crossref]
  2. G. Breit, J.O.S.A. & R.S.I. 10, p. 439; 1925;also Phil. Mag.,  47, p. 832; 1924.
    [Crossref]
  3. Phys. Rev., pp. 330-365; Oct.1924.
  4. J. Wash. Acad. Sci.,  15, p. 269; 1925.
  5. A. Ellett, J.O.S.A., & R.S.I.,  10, p. 427, especially p. 433;G. Breit, J.O.S.A., & R.S.I.,  10, p. 439, especially p. 446.

1925 (2)

G. Breit, J.O.S.A. & R.S.I. 10, p. 439; 1925;also Phil. Mag.,  47, p. 832; 1924.
[Crossref]

J. Wash. Acad. Sci.,  15, p. 269; 1925.

1924 (2)

J. A. Eldridge, Physical Rev.,  24, p. 234; 1924.
[Crossref]

Phys. Rev., pp. 330-365; Oct.1924.

Breit, G.

G. Breit, J.O.S.A. & R.S.I. 10, p. 439; 1925;also Phil. Mag.,  47, p. 832; 1924.
[Crossref]

Eldridge, J. A.

J. A. Eldridge, Physical Rev.,  24, p. 234; 1924.
[Crossref]

Ellett, A.

A. Ellett, J.O.S.A., & R.S.I.,  10, p. 427, especially p. 433;G. Breit, J.O.S.A., & R.S.I.,  10, p. 439, especially p. 446.

J. Wash. Acad. Sci. (1)

J. Wash. Acad. Sci.,  15, p. 269; 1925.

J.O.S.A. & R.S.I. (1)

G. Breit, J.O.S.A. & R.S.I. 10, p. 439; 1925;also Phil. Mag.,  47, p. 832; 1924.
[Crossref]

J.O.S.A., & R.S.I. (1)

A. Ellett, J.O.S.A., & R.S.I.,  10, p. 427, especially p. 433;G. Breit, J.O.S.A., & R.S.I.,  10, p. 439, especially p. 446.

Phys. Rev. (1)

Phys. Rev., pp. 330-365; Oct.1924.

Physical Rev. (1)

J. A. Eldridge, Physical Rev.,  24, p. 234; 1924.
[Crossref]

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Equations (39)

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H = H + e i ( x i E x + y i E y + z i E z ) cos 2 π ( ν t + 0 )
( E x , E y , E z ) cos 2 π ( ν 0 t + 0 )
( x i , y i , z i )
x = e i x i e i , y = e i y i e i , z = e i z i e i , e = e i
E x = E 0 cos 2 π ( ν t + 0 ) cos 2 π ν 0 t E y = E 0 cos 2 π ( ν t + 0 ) sin 2 π ν 0 t
E x = E 0 2 [ cos 2 π ( ( ν + ν 0 ) t + 0 ) + cos 2 π ( ( ν ν 0 ) t + 0 ) ] E y = E 0 2 [ cos 2 π ( ( ν + ν 0 ) t + 0 1 4 ) cos 2 π ( ( ν ν 0 ) t + 0 1 4 ) ]
x = A τ exp 2 π i w τ , y = B τ exp 2 π i w τ , z = C τ exp 2 π i w τ
A τ = A τ 1 , τ 2 τ n w τ = τ 1 w 1 + τ 2 w 2 + τ n w n
( E x , E y , E z , ) cos 2 π ( ν t + 0 )
Δ x ¯ = e 2 exp 2 π i ( w τ + τ ± ν t ± 0 ) [ τ l J l ( E x A τ + E y B τ + E z C τ ) A τ C ( ω τ ± ν ) ( E x A τ + E y B τ + E z C τ ) C ( ω τ ± ν ) ( τ l + τ l ) A τ J l ]
w τ + τ = ( τ 1 + τ 1 ) w 1 + ( τ 2 + τ 2 ) w 2 +
C ( ω τ ± ν ) = 2 π i T 0 1 + 2 π i T 0 ( ω τ ± ν )
τ l + τ l = 0 Δ x = e E 0 4 exp 2 π i ( ± ( ν + ν 0 ) t ± 0 ) τ l J l { A τ A τ C ( ω τ ± ( ν + ν 0 ) ) } + e E 0 4 exp 2 π i ( ± ( ν ν 0 ) t ± 0 ) τ l J l { A τ A τ C ( ω τ ± ( ν ν 0 ) ) } + e E 0 4 exp 2 π i ( ± ( ν ν 0 ) t ± ( 0 1 4 ) ) τ l J l { B τ A τ C ( ω τ ± ( ν + ν 0 ) ) } e E 0 4 exp 2 π i ( ± ( ν ν 0 ) t ± ( 0 1 4 ) ) τ l J l { B τ A τ C ( ω τ ± ( ν ν 0 ) ) }
Δ y = e E 0 4 exp 2 π i ( ± ( ν + ν 0 ) t ± 0 ) τ l J l { A τ B τ C ( ω τ ± ( ν + ν 0 ) ) } + e E 0 4 exp 2 π i ( ± ( ν ν 0 ) t ± 0 ) τ l J l { A τ B τ C ( ω τ ± ( ν ν 0 ) ) } + e E 0 4 exp 2 π i ( ± ( ν ν 0 ) t ± ( 0 1 4 ) ) τ l J l { B τ B τ C ( ω τ ± ( ν ν 0 ) ) } e E 0 4 exp 2 π i ( ± ( ν ν 0 ) t ± ( 0 1 4 ) ) τ l J l { B τ B τ C ( ω τ ± ( ν ν 0 ) ) }
Δ x + i Δ y = e 2 π i t ν 0 ( Δ x + i Δ y )
Δ x + i Δ y e E 0 4 exp 2 π i ( ν t + 0 ) τ l J l { | D τ ( 1 ) | 2 C ( ω τ + ν + ν 0 ) } e E 0 4 exp 2 π i ( ν t 0 ) τ l J l { | D τ ( 2 ) | 2 C ( ω τ ν + ν 0 ) } + e E 0 4 exp 2 π i ( ( ν 2 ν 0 ) t + 0 ) τ l J l { D τ ( 1 ) D τ ( 1 ) C ( ω τ + ν ν 0 ) } e E 0 4 exp 2 π i ( ( ν + 2 ν 0 ) t 0 ) τ l J l { D τ ( 1 ) D τ ( 1 ) C ( ω τ ν ν 0 ) }
D τ ( 1 ) = A τ + i B τ D τ ( 2 ) = A τ i B τ
( Δ x + i Δ y ) 2 ¯ = Δ x 2 ¯ Δ y 2 ¯ + 2 i Δ x Δ y ¯
( Δ x + i Δ y ) ( Δ x i Δ y ) ¯ = Δ x 2 ¯ + Δ y 2 ¯
P = 0 ( Δ x 2 ¯ Δ y 2 ¯ ) d ν 0 ( Δ x 2 + Δ y 2 ) d ν
( Δ x + i Δ y ) 2 ¯ = e 2 E 0 2 8 [ τ l J l { | D τ ( 1 ) | 2 C ( ω τ + ν + ν 0 ) } ] × [ τ l J l { | D τ ( 2 ) | 2 C ( ω τ + ν ν 0 ) } ]
e 2 E 0 2 8 ( l τ l J l { | D 1 ( 1 ) | 2 C ( ω τ + ν + ν 0 ) } ) ( l τ l J l { | D 1 ( 2 ) | 2 C ( ω τ ν ν 0 ) } )
Δ x 2 ¯ Δ y 2 ¯ + 2 i Δ × Δ y ¯ = π 2 e 2 E 0 2 T 0 2 2 { ( τ l | D τ ( 1 ) | 2 J l ) ( τ l | D τ ( 2 ) | 2 J l ) [ 1 + 2 π i T 0 ( ν ω 1 ) ] [ 1 2 π i T 0 ( ν ω 2 ) ] + 4 π 2 T 0 2 ( τ l ω τ J l ) 2 | D τ ( 1 ) | 2 | D τ ( 2 ) | 2 [ 1 + 2 π i T 0 ( ν ω 1 ) ] 2 [ 1 2 π i T 0 ( ν ω 2 ) ] 2 + 2 π i T 0 ( τ l ω τ J l ) [ 1 + 2 π i T 0 ( ν ω 1 ) ] [ 1 2 π i T 0 ( ν ω 2 ) ] × [ | D τ ( 1 ) | 2 τ l | D τ ( 2 ) | 2 J l 1 + 2 π i T 0 ( ν ω 1 ) | D τ ( 2 ) | 2 τ l | D τ ( 1 ) | 2 J l 1 2 π i T 0 ( ν ω 2 ) ] }
ω 1 = ω τ ν 0 , ω 2 = ω τ + ν 0
+ d ν [ 1 + 2 π i T 0 ( ν ω 1 ) ] [ 1 2 π i T 0 ( ν ω 2 ) ] = 1 2 T 0 ( 1 + 2 π i T 0 ν 0 ) + d ν [ 1 + 2 π i T 0 ( ν ω 1 ) ] 2 [ 1 2 π i T 0 ( ν ω 2 ) ] = + d ν [ 1 + 2 π i T 0 ( ν ω 1 ) ] [ 1 2 π i T 0 ( ν ω 2 ) ] 2 = 1 4 T 0 ( 1 + 2 π i T 0 ν 0 ) 2 + d ν [ 1 + 2 π i T 0 ( ν ω 1 ) ] 2 [ 1 2 π i T 0 ( ν ω 2 ) ] 2 = 1 4 T 0 ( 1 + 2 π i T 0 ν 0 ) 3
+ ( Δ x 2 ¯ Δ y 2 ¯ ) d ν = π 2 T 0 e 2 E 0 2 4 { ( τ l | D τ ( 1 ) | 2 J l ) ( τ l | D τ ( 2 ) | 2 J l ) 1 + 4 π 2 T 0 2 ν 0 2 + ( 1 12 π 2 T 0 2 ν 0 2 ) 4 π 2 T 0 2 | D τ ( 1 ) | 2 | D τ ( 1 ) | 2 2 ( 1 + 4 π 2 T 0 2 ν 0 2 ) 3 ( τ l ω τ J l ) 2 + 4 π 2 T 0 2 ( τ l ω τ J l ) ν 0 ( | D τ ( 1 ) | 2 τ l | D τ ( 2 ) | 2 J l | D τ ( 2 ) | 2 τ l | D τ ( 1 ) | 2 J l ) ( 1 + 4 π 2 T 0 2 ν 0 2 ) 2 }
2 + Δ x Δ y ¯ d ν = π 2 T 0 e 2 E 0 2 4 { 2 π T 0 ν 0 1 + 4 π 2 T 0 2 ν 0 2 ( τ l | D τ ( 1 ) | J l ) ( τ l | D τ ( 2 ) | 2 J l ) + 4 π 3 T 0 3 ν 0 3 3 π T 0 ν 0 ( 1 + 4 π 2 T 0 2 ν 0 2 ) 3 4 π 2 T 0 2 | D τ ( 1 ) | 2 | D τ ( 2 ) | 2 ( τ l ω τ J l ) 2 + π T 0 ( τ l ω τ J l ) 1 4 π 2 T 0 2 ν 0 2 ( 1 + 4 π 2 T 0 2 ν 0 2 ) 2 ( | D τ ( 1 ) | 2 τ l | D τ ( 2 ) | 2 J l | D τ ( 2 ) | 2 τ l | D τ ( 1 ) | 2 J l ) }
+ ( Δ x + i Δ y ) ( Δ x i Δ y ) ¯ d ν = π 2 e 2 E 0 2 T 0 8 { [ ( τ l | D τ ( 1 ) | 2 J l ) 2 + ( τ l | D τ ( 2 ) | 2 J l ) 2 + 2 ( τ l ( D τ ( 1 ) D τ ( 1 ) ) J l ) ( τ l ( D τ ( 2 ) D τ ( 2 ) ) J l ) ] + 2 π 2 T 0 2 ( τ l ω τ J l ) 2 × [ | D τ ( 1 ) | 4 + | D τ ( 2 ) | 4 + 2 D τ ( 1 ) D τ ( 1 ) D τ ( 2 ) D τ ( 2 ) ] }
2 π T 0 ν 0 = x
P = A 1 1 + x 2 + A 2 1 3 x 2 ( 1 + x 2 ) 3 + A 3 x ( 1 + x 2 ) 2
D τ ( 1 ) | 2 τ l | D τ ( 2 ) | 2 J l | D τ ( 2 ) | 2 τ l | D τ ( 1 ) | 2 J l
tan 2 α = 2 Δ x Δ y ¯ Δ x 2 ¯ Δ y 2 ¯
tan 2 α = A 1 x 1 + x 2 + 1 2 A 2 1 + x 2 ( 1 + x 2 ) 2 + A 3 3 x x 3 ( 1 + x 2 ) 3 A 1 1 + x 2 + A 2 x ( 1 + x 2 ) 2 + A 3 1 3 x 2 ( 1 + x 2 ) 3
α d t
a d t
X = 1 2 ( 1 + P 0 ) a a + α + 1 2 a a + α Y = 1 2 ( 1 P 0 ) a a + α + 1 2 a a + α
P = P 0 / ( 1 + α / a )
P = P 0 / ( 1 + k H / a )
P = P 0 ( 1 + a H ) ( 1 + b H 2 )