Abstract

The free–free continuum for oxygen was earlier computed by us using wavefunctions for the free electron whose computation ignores polarization and exchange. Here these effects are included and their influence on the free–free continuum in the presence of neutral oxygen is studied. The inclusion of polarization leads to results which available experimental data tell us are a notable improvement over the earlier calculation. The inclusion of exchange is not of nearly as much consequence.

© 1963 Optical Society of America

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References

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  1. R. G. Breene and M. C. Nardone, Phys. Rev. 115, 93 (1959).
    [Crossref]
  2. R. G. Breene, Phys. Rev. 123, 1718 (1961).
    [Crossref]
  3. R. G. Breene and M. C. Nardone, J. Opt. Soc. Am. 50, 1111 (1960).
    [Crossref]
  4. R. G. Breene and M. C. Nardone, J. Opt. Soc. Am. 51, 692 (1961).
    [Crossref]
  5. T. Ohmura and H. Ohmura, Astrophys. J. 131, 8 (1960).
    [Crossref]
  6. N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, London, 1949).
  7. N. M. Klein and K. A. Brueckner, Phys. Rev. 111, 1115 (1958).
    [Crossref]
  8. R. L. Taylor, Avco Research Report 88, June, 1960.
  9. R. G. Breene and M. C. Nardone, J. Quant. Spectry. Radiative Transfer 2, 272 (1962); GE R61SD020, May1961.

1962 (1)

R. G. Breene and M. C. Nardone, J. Quant. Spectry. Radiative Transfer 2, 272 (1962); GE R61SD020, May1961.

1961 (2)

1960 (2)

1959 (1)

R. G. Breene and M. C. Nardone, Phys. Rev. 115, 93 (1959).
[Crossref]

1958 (1)

N. M. Klein and K. A. Brueckner, Phys. Rev. 111, 1115 (1958).
[Crossref]

Breene, R. G.

R. G. Breene and M. C. Nardone, J. Quant. Spectry. Radiative Transfer 2, 272 (1962); GE R61SD020, May1961.

R. G. Breene, Phys. Rev. 123, 1718 (1961).
[Crossref]

R. G. Breene and M. C. Nardone, J. Opt. Soc. Am. 51, 692 (1961).
[Crossref]

R. G. Breene and M. C. Nardone, J. Opt. Soc. Am. 50, 1111 (1960).
[Crossref]

R. G. Breene and M. C. Nardone, Phys. Rev. 115, 93 (1959).
[Crossref]

Brueckner, K. A.

N. M. Klein and K. A. Brueckner, Phys. Rev. 111, 1115 (1958).
[Crossref]

Klein, N. M.

N. M. Klein and K. A. Brueckner, Phys. Rev. 111, 1115 (1958).
[Crossref]

Massey, H. S. W.

N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, London, 1949).

Mott, N. F.

N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, London, 1949).

Nardone, M. C.

R. G. Breene and M. C. Nardone, J. Quant. Spectry. Radiative Transfer 2, 272 (1962); GE R61SD020, May1961.

R. G. Breene and M. C. Nardone, J. Opt. Soc. Am. 51, 692 (1961).
[Crossref]

R. G. Breene and M. C. Nardone, J. Opt. Soc. Am. 50, 1111 (1960).
[Crossref]

R. G. Breene and M. C. Nardone, Phys. Rev. 115, 93 (1959).
[Crossref]

Ohmura, H.

T. Ohmura and H. Ohmura, Astrophys. J. 131, 8 (1960).
[Crossref]

Ohmura, T.

T. Ohmura and H. Ohmura, Astrophys. J. 131, 8 (1960).
[Crossref]

Taylor, R. L.

R. L. Taylor, Avco Research Report 88, June, 1960.

Astrophys. J. (1)

T. Ohmura and H. Ohmura, Astrophys. J. 131, 8 (1960).
[Crossref]

J. Opt. Soc. Am. (2)

J. Quant. Spectry. Radiative Transfer (1)

R. G. Breene and M. C. Nardone, J. Quant. Spectry. Radiative Transfer 2, 272 (1962); GE R61SD020, May1961.

Phys. Rev. (3)

R. G. Breene and M. C. Nardone, Phys. Rev. 115, 93 (1959).
[Crossref]

R. G. Breene, Phys. Rev. 123, 1718 (1961).
[Crossref]

N. M. Klein and K. A. Brueckner, Phys. Rev. 111, 1115 (1958).
[Crossref]

Other (2)

R. L. Taylor, Avco Research Report 88, June, 1960.

N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, London, 1949).

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Figures (4)

Fig. 1
Fig. 1

The free–free continuum for oxygen as computed including the effects of polarization and compared to the Taylor shock-tube data. The temperature is 8000°K and the density is 0.9 that of oxygen in normal air.

Fig. 2
Fig. 2

A comparison of the free-electron radial wavefunction for polarization only, polarization spin-up and polarization spin-down. The linear momentum in all cases is 0.2 a.u.

Fig. 3
Fig. 3

A comparison of the potential derivatives for the polarization case and the polarization plus exchange case.

Fig. 4
Fig. 4

A comparison of the free–free matrix element integrand for the polarization case and the polarization plus exchange case.

Equations (21)

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( d 2 χ l / d r 2 ) + { k [ l ( l + 1 ) / r 2 ] + 2 V } χ l = 0 ,
V = Z r + | Ψ ( P ) | 2 r i e d τ .
H = i = 1 Z 1 r e i ,
V = Z r + 2 V 1 s ( 0 ) + 2 V 2 s ( 0 ) + B 1 [ 4 Δ 4 2 Δ 5 2 V 2 p ( 0 ) + 3 Δ 5 2 H 34 2 V 2 p ( 4 ) + 3 Δ 4 2 H 35 2 V 3 p ( 5 ) + Δ 5 2 H 34 2 V 3 p ( 4 ) + Δ 4 2 H 35 2 V 3 p ( 5 ) + 2 Δ 4 Δ 5 ( H 34 2 + H 35 2 ) ] .
B = Δ 4 2 Δ 5 2 + Δ 5 2 H 34 2 + Δ 4 2 H 35 2 .
χ l ( r ) = ( 1 / k r ) sin [ k r ( l π / 2 ) + δ l ] .
σ = 4 π k 2 l = 0 ( 2 l + 1 ) sin 2 δ l .
σ = 29.75 × 10 39 .
M ( 0 , k 0 2 , k 1 2 ) = ( k 1 2 / 2 ) sin δ 0 + additional terms .
σ = 34.48 × 10 39 .
σ = 50.22 × 10 39 .
σ = 2.54 × 10 39 ( no smear ) , σ = 5.82 × 10 39 ( smeared ) .
I λ d λ = σ λ N 0 N e B λ d λ ( thin approx . ) .
V + = 0 R 1 s χ 0 r > d r + 0 R 2 s χ 0 r > d r + ( 3 2 ) 1 2 0 r < R 2 p χ 0 r > 2 d r ,
V = 0 R 1 s χ 0 r > d r + 0 R 2 s χ 0 r > d r + ( 2 3 ) 1 2 0 r < R 2 p χ 0 r > 2 d r .
d 2 χ 0 d r 2 + ( k 2 a r + n r 2 ) χ 0 = 0.
0 R 2 s χ 0 r > d r + ( 3 2 ) 1 2 0 r < R 2 p χ 0 r > 2 d r = 1 r 0 r R 2 s χ 0 d r + r R 2 s χ 0 r d r + = 1 r 2 ( 3 2 ) 1 2 0 r R 2 p r χ 0 d r + r r R 2 p χ 1 r 2 d r 1 r 0 r R 2 s χ 0 d r + 1 r 2 ( 3 2 ) 1 2 0 r R 2 p r χ 0 d r ,
a = 0 r R 2 s χ 0 d r , n = ( 3 2 ) 1 2 0 r R 2 p r χ 0 d r .
Φ 0 = j = 0 A j ρ j ; A 0 = 1 ; A j = η A j 1 A j 2 [ ( j + 1 2 ) ( j 1 2 ) + n ] ,
χ 0 = | e i κ / 2 Γ ( 1 2 + i l κ ) Γ ( 2 i l + 1 ) | ( ρ 2 ) 1 2 Φ 0 ( ρ ) ,
ρ = k r η = 2 a / k .