Abstract

Potential scattering of free-electron wave packets is considered in the framework of non-stationary quantum-mechanical theory. The general expression for the average angle of scattering is obtained. The traditional quantum-mechanical plane-wave approximation and classical results are shown to be incorporated in the results derived.

© 1998 Optical Society of America

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References

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  1. R. Newton, “Scattering theory of waves and particles” (McGraw-Hill, New York1968).
  2. P.H. Bucksbaum, D.W. Schumacher, and M. Bashkansky, “High Intensity Kapitza-Dirac Effect”, Phys. Rev. Lett. 61, 1182 (1988).
    [Crossref] [PubMed]
  3. L.D. Landau and E.M. Lifshitz, “Mechanics” (Permagon Press, Oxford-New York1976).
  4. L.D. Landau and E.M. Lifshitz, “Quantum Mechanics”, (Permagon Press, Oxford-New York1977).
  5. M.V. Fedorov, S.P. Goreslavsky, and V.S. Letokhov, “Ponderomotive forces and stimulated Compton scattering on free electrons in a laser field”, Phys. Rev. E,  55, 1015 (1997)
    [Crossref]
  6. M.V. Fedorov and J. Peatross, “Strong-field photoionization and emission of light in the wave-packet-spreading regime”, Phys. Rev. A 52, 504 (1995).
    [Crossref] [PubMed]
  7. I.S. Gradstein and I.M. Ryzhik, “Table of Integrals, Series and Products” (Academic, New York1980).

1997 (1)

M.V. Fedorov, S.P. Goreslavsky, and V.S. Letokhov, “Ponderomotive forces and stimulated Compton scattering on free electrons in a laser field”, Phys. Rev. E,  55, 1015 (1997)
[Crossref]

1995 (1)

M.V. Fedorov and J. Peatross, “Strong-field photoionization and emission of light in the wave-packet-spreading regime”, Phys. Rev. A 52, 504 (1995).
[Crossref] [PubMed]

1988 (1)

P.H. Bucksbaum, D.W. Schumacher, and M. Bashkansky, “High Intensity Kapitza-Dirac Effect”, Phys. Rev. Lett. 61, 1182 (1988).
[Crossref] [PubMed]

Bashkansky, M.

P.H. Bucksbaum, D.W. Schumacher, and M. Bashkansky, “High Intensity Kapitza-Dirac Effect”, Phys. Rev. Lett. 61, 1182 (1988).
[Crossref] [PubMed]

Bucksbaum, P.H.

P.H. Bucksbaum, D.W. Schumacher, and M. Bashkansky, “High Intensity Kapitza-Dirac Effect”, Phys. Rev. Lett. 61, 1182 (1988).
[Crossref] [PubMed]

Fedorov, M.V.

M.V. Fedorov, S.P. Goreslavsky, and V.S. Letokhov, “Ponderomotive forces and stimulated Compton scattering on free electrons in a laser field”, Phys. Rev. E,  55, 1015 (1997)
[Crossref]

M.V. Fedorov and J. Peatross, “Strong-field photoionization and emission of light in the wave-packet-spreading regime”, Phys. Rev. A 52, 504 (1995).
[Crossref] [PubMed]

Goreslavsky, S.P.

M.V. Fedorov, S.P. Goreslavsky, and V.S. Letokhov, “Ponderomotive forces and stimulated Compton scattering on free electrons in a laser field”, Phys. Rev. E,  55, 1015 (1997)
[Crossref]

Gradstein, I.S.

I.S. Gradstein and I.M. Ryzhik, “Table of Integrals, Series and Products” (Academic, New York1980).

Landau, L.D.

L.D. Landau and E.M. Lifshitz, “Quantum Mechanics”, (Permagon Press, Oxford-New York1977).

L.D. Landau and E.M. Lifshitz, “Mechanics” (Permagon Press, Oxford-New York1976).

Letokhov, V.S.

M.V. Fedorov, S.P. Goreslavsky, and V.S. Letokhov, “Ponderomotive forces and stimulated Compton scattering on free electrons in a laser field”, Phys. Rev. E,  55, 1015 (1997)
[Crossref]

Lifshitz, E.M.

L.D. Landau and E.M. Lifshitz, “Quantum Mechanics”, (Permagon Press, Oxford-New York1977).

L.D. Landau and E.M. Lifshitz, “Mechanics” (Permagon Press, Oxford-New York1976).

Newton, R.

R. Newton, “Scattering theory of waves and particles” (McGraw-Hill, New York1968).

Peatross, J.

M.V. Fedorov and J. Peatross, “Strong-field photoionization and emission of light in the wave-packet-spreading regime”, Phys. Rev. A 52, 504 (1995).
[Crossref] [PubMed]

Ryzhik, I.M.

I.S. Gradstein and I.M. Ryzhik, “Table of Integrals, Series and Products” (Academic, New York1980).

Schumacher, D.W.

P.H. Bucksbaum, D.W. Schumacher, and M. Bashkansky, “High Intensity Kapitza-Dirac Effect”, Phys. Rev. Lett. 61, 1182 (1988).
[Crossref] [PubMed]

Phys. Rev. A (1)

M.V. Fedorov and J. Peatross, “Strong-field photoionization and emission of light in the wave-packet-spreading regime”, Phys. Rev. A 52, 504 (1995).
[Crossref] [PubMed]

Phys. Rev. E (1)

M.V. Fedorov, S.P. Goreslavsky, and V.S. Letokhov, “Ponderomotive forces and stimulated Compton scattering on free electrons in a laser field”, Phys. Rev. E,  55, 1015 (1997)
[Crossref]

Phys. Rev. Lett. (1)

P.H. Bucksbaum, D.W. Schumacher, and M. Bashkansky, “High Intensity Kapitza-Dirac Effect”, Phys. Rev. Lett. 61, 1182 (1988).
[Crossref] [PubMed]

Other (4)

L.D. Landau and E.M. Lifshitz, “Mechanics” (Permagon Press, Oxford-New York1976).

L.D. Landau and E.M. Lifshitz, “Quantum Mechanics”, (Permagon Press, Oxford-New York1977).

R. Newton, “Scattering theory of waves and particles” (McGraw-Hill, New York1968).

I.S. Gradstein and I.M. Ryzhik, “Table of Integrals, Series and Products” (Academic, New York1980).

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Figures (1)

Fig 1.
Fig 1.

The first-order angle of scattering θ¯(1)r 0) of the Gaussian wave packet scattered by a pure Coulomb potential.

Equations (26)

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Ψ ( r , t ) t = ( ħ 2 2 m 2 + U ( r ) ) Ψ ( r , t )
Ψ ( r , t ) = 1 ( 2 πħ ) 3 / 2 d p C p ( t ) exp [ i ħ ( r E p t ) ]
C ˙ p ( t ) = d p′ C p′ ( t ) U ˜ ( p′ p ) exp [ i ħ ( E p E p′ ) t ]
C p ( t ) t = 0 C p ( 0 ) = d r exp ( i ħ p · r ) Ψ ( 0 ) ( r ) .
U ˜ ( q ) = 1 ( 2 πħ ) 3 d r U ( r ) exp ( i q · r ħ ) .
C p ( t ) = C p ( 0 ) + C p ( 1 ) ( t ) + C p ( 2 ) ( t ) +
C p ( 1 ) ( t ) = i ħ 0 t dt d p′ C p′ ( 0 ) U ˜ ( p′ p ) exp [ i ħ ( E p E p′ ) t′ ]
C p ( 0 ) = ( Δ r 0 ) 3 / 2 π 3 / 4 ħ 3 / 2 exp [ ( Δ r 0 ) 2 2 ħ 2 ( p p 0 ) 2 i ħ r 0 ] ,
Δ r ( t ) = ( Δ r 0 ) 2 + ( ħ t m Δ r 0 ) 2
p x ¯ ( ρ ) = p x C p ( t ) 2 d p ( 2 πħ ) 3 .
θ ¯ ( ρ ) = sin 1 ( p x ¯ ( ρ ) p 0 ) p x ¯ ( ρ ) p 0 .
θ ¯ ( 1 ) = 1 p 0 p x ( C p ( 0 ) C p ( 1 ) * + C p ( 1 ) C p ( 0 ) * ) d p ( 2 πħ ) 3 =
= 1 π 3 / 2 p 0 0 t dt′ 1 [ Δ r ( t′ ) ] 3 d r U x exp { ( r r 0 v 0 t ) 2 [ Δ r ( t′ ) ] 2 } .
θ ¯ ( 1 ) = 1 p 0 0 t dt′ [ x U eff ( r , t ) ] r = r 0 + v 0 t .
U eff ( r , t ) = d r U ( r + r ) Ψ c . m . ( 0 ) ( r , t ) 2 ,
Ψ c . m . ( 0 ) ( r , t ) 2 = 1 π 3 / 2 [ Δ r ( t ) ] 3 exp [ r 2 [ Δ r ( t ) ] 2 ] .
U eff ( r , t ) = α r Erf ( r Δ r ( t ) ) ,
U eff ( 0 , t ) = 2 α π Δ r ( t ) .
θ ¯ ( 1 ) = θ cl ( 1 ) [ 1 exp ( ρ 2 Δ r 0 2 ) ] ,
θ ( 1 ) Δ r 0 >> ρ ρ 2 Δ r 0 2 θ cl ( 1 ) .
θ ( 1 ) Δ r 0 > > ρ , d = 8 ρ m v 0 2 Δ r 0 4 0 r 2 dr U ( r ) .
θ ¯ ( 1 ) Δ r 0 > > ρ , d = 8 αρ d 2 m v 0 2 Δ r 0 4 = ( 2 ρ d Δ r 0 2 ) 2 θ cl ( 1 ) .
t spr > > t int = md p 0 .
( ƛ dB d ) 1 / 2 < < Δ r 0 < < d ,
( ƛ dB ρ ) 1 / 2 < < Δ r 0 < < ρ ,
10 2 cm < < Δ r 0 < < 10 5 cm .

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