Abstract

On the basis of a semiclassical approach, the dynamic polarizability and the index of refraction of helium near 11S–21P resonance are calculated. The steady-state solution of the Schrödinger equation used is well behaved at resonance; hence the decay width, in the Weisskopf and Wigner theory, need not be introduced. The result agrees, in essence, with the results of the Weisskopf and Wigner theory if the irradiance is weak. For great irradiance, the results differ significantly over a broad range of frequencies.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. S. Rozhdestvenskii, Tr. Gos. Opt. Inst. 2,(13) (1922).
  2. V. K. Prokofev, Tr. Gos. Opt. Inst. 3,(25) 1 (1924).
  3. V. F. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930).
    [Crossref]
  4. S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).
    [Crossref]
  5. I. I. Rabi, Phys. Rev. 51, 652 (1937).
    [Crossref]
  6. N. F. Ramsey, Molecular Beams (Oxford U. P., London, 1956).
  7. C. Cohen-Tannoudji and S. Haroche, J. Phys. (Paris) 30, 125 (1969); J. Phys. (Paris) 30, 153 (1969).
    [Crossref]
  8. J. H. Shirley, Phys. Rev. 138, B979 (1965).
    [Crossref]
  9. D. T. Pegg, Phys. Rev. A 8, 2214 (1973).
    [Crossref]
  10. K. T. Chung, Phys. Rev. 166, 1 (1967).
    [Crossref]
  11. G. Lochak and M. Thiounn, C. R. Acad. Sci. B 264, 1533 (1967).
  12. S. Pancharatnam, Proc. R. Soc. Lond. A 330, 281 (1972).
    [Crossref]
  13. This steady-state result can be obtained by using the time-dependent phase-factor perturbation method [see K. T. Chung, Phys. Rev. 163, 1343 (1967)] and by summing the divergent term in the perturbation series to infinite orders. The validity of this solution can be proved by a direct substitution into the Schrödinger equation.
    [Crossref]
  14. A. Sommerfeld, Electrodynamics (Academic, New York, 1954), p. 75.
  15. B. Schiff and C. L. Pekeris, Phys. Rev. 134, A638 (1964).
    [Crossref]
  16. C. L. Pekeris, B. Schiff, and H. Lifson, Phys. Rev. 126, 1057 (1962).
    [Crossref]

1973 (1)

D. T. Pegg, Phys. Rev. A 8, 2214 (1973).
[Crossref]

1972 (1)

S. Pancharatnam, Proc. R. Soc. Lond. A 330, 281 (1972).
[Crossref]

1969 (1)

C. Cohen-Tannoudji and S. Haroche, J. Phys. (Paris) 30, 125 (1969); J. Phys. (Paris) 30, 153 (1969).
[Crossref]

1967 (3)

K. T. Chung, Phys. Rev. 166, 1 (1967).
[Crossref]

G. Lochak and M. Thiounn, C. R. Acad. Sci. B 264, 1533 (1967).

This steady-state result can be obtained by using the time-dependent phase-factor perturbation method [see K. T. Chung, Phys. Rev. 163, 1343 (1967)] and by summing the divergent term in the perturbation series to infinite orders. The validity of this solution can be proved by a direct substitution into the Schrödinger equation.
[Crossref]

1965 (1)

J. H. Shirley, Phys. Rev. 138, B979 (1965).
[Crossref]

1964 (1)

B. Schiff and C. L. Pekeris, Phys. Rev. 134, A638 (1964).
[Crossref]

1962 (1)

C. L. Pekeris, B. Schiff, and H. Lifson, Phys. Rev. 126, 1057 (1962).
[Crossref]

1937 (1)

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[Crossref]

1932 (1)

S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).
[Crossref]

1930 (1)

V. F. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930).
[Crossref]

1924 (1)

V. K. Prokofev, Tr. Gos. Opt. Inst. 3,(25) 1 (1924).

1922 (1)

D. S. Rozhdestvenskii, Tr. Gos. Opt. Inst. 2,(13) (1922).

Breit, G.

S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).
[Crossref]

Chung, K. T.

K. T. Chung, Phys. Rev. 166, 1 (1967).
[Crossref]

This steady-state result can be obtained by using the time-dependent phase-factor perturbation method [see K. T. Chung, Phys. Rev. 163, 1343 (1967)] and by summing the divergent term in the perturbation series to infinite orders. The validity of this solution can be proved by a direct substitution into the Schrödinger equation.
[Crossref]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji and S. Haroche, J. Phys. (Paris) 30, 125 (1969); J. Phys. (Paris) 30, 153 (1969).
[Crossref]

Haroche, S.

C. Cohen-Tannoudji and S. Haroche, J. Phys. (Paris) 30, 125 (1969); J. Phys. (Paris) 30, 153 (1969).
[Crossref]

Korff, S. A.

S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).
[Crossref]

Lifson, H.

C. L. Pekeris, B. Schiff, and H. Lifson, Phys. Rev. 126, 1057 (1962).
[Crossref]

Lochak, G.

G. Lochak and M. Thiounn, C. R. Acad. Sci. B 264, 1533 (1967).

Pancharatnam, S.

S. Pancharatnam, Proc. R. Soc. Lond. A 330, 281 (1972).
[Crossref]

Pegg, D. T.

D. T. Pegg, Phys. Rev. A 8, 2214 (1973).
[Crossref]

Pekeris, C. L.

B. Schiff and C. L. Pekeris, Phys. Rev. 134, A638 (1964).
[Crossref]

C. L. Pekeris, B. Schiff, and H. Lifson, Phys. Rev. 126, 1057 (1962).
[Crossref]

Prokofev, V. K.

V. K. Prokofev, Tr. Gos. Opt. Inst. 3,(25) 1 (1924).

Rabi, I. I.

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[Crossref]

Ramsey, N. F.

N. F. Ramsey, Molecular Beams (Oxford U. P., London, 1956).

Rozhdestvenskii, D. S.

D. S. Rozhdestvenskii, Tr. Gos. Opt. Inst. 2,(13) (1922).

Schiff, B.

B. Schiff and C. L. Pekeris, Phys. Rev. 134, A638 (1964).
[Crossref]

C. L. Pekeris, B. Schiff, and H. Lifson, Phys. Rev. 126, 1057 (1962).
[Crossref]

Shirley, J. H.

J. H. Shirley, Phys. Rev. 138, B979 (1965).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, Electrodynamics (Academic, New York, 1954), p. 75.

Thiounn, M.

G. Lochak and M. Thiounn, C. R. Acad. Sci. B 264, 1533 (1967).

Weisskopf, V. F.

V. F. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930).
[Crossref]

Wigner, E. P.

V. F. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930).
[Crossref]

C. R. Acad. Sci. B (1)

G. Lochak and M. Thiounn, C. R. Acad. Sci. B 264, 1533 (1967).

J. Phys. (Paris) (1)

C. Cohen-Tannoudji and S. Haroche, J. Phys. (Paris) 30, 125 (1969); J. Phys. (Paris) 30, 153 (1969).
[Crossref]

Phys. Rev. (6)

J. H. Shirley, Phys. Rev. 138, B979 (1965).
[Crossref]

K. T. Chung, Phys. Rev. 166, 1 (1967).
[Crossref]

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[Crossref]

This steady-state result can be obtained by using the time-dependent phase-factor perturbation method [see K. T. Chung, Phys. Rev. 163, 1343 (1967)] and by summing the divergent term in the perturbation series to infinite orders. The validity of this solution can be proved by a direct substitution into the Schrödinger equation.
[Crossref]

B. Schiff and C. L. Pekeris, Phys. Rev. 134, A638 (1964).
[Crossref]

C. L. Pekeris, B. Schiff, and H. Lifson, Phys. Rev. 126, 1057 (1962).
[Crossref]

Phys. Rev. A (1)

D. T. Pegg, Phys. Rev. A 8, 2214 (1973).
[Crossref]

Proc. R. Soc. Lond. A (1)

S. Pancharatnam, Proc. R. Soc. Lond. A 330, 281 (1972).
[Crossref]

Rev. Mod. Phys. (1)

S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).
[Crossref]

Tr. Gos. Opt. Inst. (2)

D. S. Rozhdestvenskii, Tr. Gos. Opt. Inst. 2,(13) (1922).

V. K. Prokofev, Tr. Gos. Opt. Inst. 3,(25) 1 (1924).

Z. Phys. (1)

V. F. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930).
[Crossref]

Other (2)

N. F. Ramsey, Molecular Beams (Oxford U. P., London, 1956).

A. Sommerfeld, Electrodynamics (Academic, New York, 1954), p. 75.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

FIG. 1
FIG. 1

Graphic method for solving n2 near helium 11S–21P resonance. The crossing points between the straight line with various curves give the solutions for n2. In this figure F0 = 5 × 103 V/cm. The density of helium is taken as under standard pressure and temperature.

FIG. 2
FIG. 2

Graphic method for solving n2 near helium 11S–21P resonance. The crossing points between the straight line and the various curves give the solutions for n2. In this figure F0 = 5 × 104 V/cm. The density of helium is taken as under standard pressure and temperature.

FIG. 3
FIG. 3

The index of refraction of helium near 11S–21P resonance. —·—·—· F0 = 5 × 105 V/cm; – – – F0 = 5 × 104 V/cm; — shows the results of F0 = 5 × 103 V/cm and F0 = 500 V/cm which agree with those of Eq. (21).

Tables (2)

Tables Icon

Table I Dynamic dipole polarizability of helium near 11S–21P resonance (in 10−21 cm3).

Tables Icon

Table II Refractive index of helium near 11S–21P resonance (under standard pressure and temperature).

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

V ( r , t ) = j e m c A j · p j ,
F ( t ) = 2 F cos ω t ,
A = - 2 c ω F sin ω t = A 0 e i ω t + A 0 * e - i ω t ,
A 0 = i c ω F .
= E k - E 0 - ω ,
= ψ k j i e m ω F · P j ψ 0 / ,
Δ = 2 ,
ϕ 0 ( r , t ) = e - i ( E 0 - δ ) t [ c 0 ψ 0 ( r ) + c k ψ k ( r ) e - i ω t ] ,
c 0 = ( 1 + ( 1 + 4 Δ ) 1 2 2 ( 1 + 4 Δ ) 1 2 ) 1 2 ,
c k = - 2 [ 1 + 4 Δ + ( 1 + 4 Δ ) 1 2 ] 1 2 ,
δ = [ ( 1 + 4 Δ ) 1 2 - 1 ] / 2.
α ( ω ) = - e ϕ 0 j r j ϕ 0 / 2 F cos ω t = - ( c 0 c k D 0 k + c 0 c k * D k 0 ) / 2 F .
D k 0 = e ψ k j z j ψ 0 .
P ( t ) = N α F ( t ) = N α ( F 0 ( t ) + 4 3 π P ( t ) ) ,
F ( t ) = 1 1 - 4 3 π N α F 0 ( t ) .
n 2 - 1 n 2 + 1 = 4 π N 3 α ( ω ) ,
F ( t ) = n 2 + 2 3 F 0 ( t ) .
ψ k P z ψ 0 = ( E 0 - E k ) i ψ k z ψ 0 ,
= F ( E 0 - E k ) m ω ψ k j z j ψ 0 = F g / .
c 0 c k = - ( 1 + 4 Δ ) 1 2 .
n 2 - 1 n 2 + 2 = 4 N 3 g D k 0 [ 1 + 4 ( F g / ) 2 ] 1 2 .
n 2 - 1 = 4 π N g ( n 2 + 2 ) D k 0 3 { 1 + [ 2 ( n 2 + 2 ) F 0 g / 3 ] 2 } 1 2 ,
F 0 ( t ) = 2 F 0 cos ω t
α = g D k 0 / ( 2 + Γ k 2 / 4 )
n 2 = ( 1 + 8 π N α / 3 ) / ( 1 - 4 π N α / 3 ) ,
n 2 - 1 = ± 2 π N D k 0 / F 0 .
n 2 - 1 = 2 π N D k 0 F 0 n 2 + 2 [ ( n 2 + 2 ) 2 + ( 3 / 2 g F 0 ) 2 ] 1 2 .
- 2 n 2 < 1.
n 2 = 0 + 1 + 2 π N D k 0 / F 0
n 2 = 0 - 1 - 2 π N D k 0 / F 0
n 2 = 0 - - 2.
y = n 2 - 1 ,
y = 4 π N g ( n 2 + 2 ) D n 0 3 { 1 + [ 2 ( n 2 + 2 ) F 0 g / 3 ] 2 } 1 2 .