Abstract

We study the ionization of atomic hydrogen by a fast positron in the presence of an external linearly polarized laser field. We concentrate on the limit of a small momentum transfer and describe the fast positron’s continuum states by Volkov wave functions. The ejected electron is described by a Coulomb–Volkov wave function. We are limited to small laser intensities such that the dressed state of the target is treatable within the time-dependent perturbation theory, even though the laser intensity is still quite high by laboratory standards. Numerical results for the triply differential cross sections and their dependencies on laser-field parameters are discussed and compared with the results of laser-assisted ionization by electron impact.

© 2007 Optical Society of America

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  1. J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
    [CrossRef]
  2. C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
    [CrossRef] [PubMed]
  3. C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
    [CrossRef] [PubMed]
  4. P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
    [CrossRef] [PubMed]
  5. D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
    [CrossRef]
  6. A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
    [CrossRef]
  7. S.-M. Li, J. Chen, and Z.-F. Zhou, J. Phys. B 35, 557 (2002).
    [CrossRef]
  8. S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
    [CrossRef]
  9. A. Chattopadhyay and C. Sinha, Phys. Rev. A 72, 053406 (2005).
    [CrossRef]
  10. C. Arcidiacono, Á. Kövér, and G. Laricchia, Phys. Rev. Lett. 95, 223202 (2005).
    [CrossRef] [PubMed]
  11. Á. Kövér and G. Laricchia, Phys. Rev. Lett. 80, 5309 (1998).
    [CrossRef]
  12. J. Berakdar, Phys. Rev. Lett. 81, 1393 (1998).
    [CrossRef]
  13. J. Berakdar, Nucl. Instrum. Methods Phys. Res. B 171, 204 (2000).
    [CrossRef]
  14. J. Fiol, V. D. Rodríguez, and R. O. Barrachina, J. Phys. B 34, 933 (2001).
    [CrossRef]
  15. J. Fiol and R. E. Olson, J. Phys. B 35, 1173 (2002).
  16. L. Sarkadi, Phys. Rev. A 68, 032706 (2003).
    [CrossRef]
  17. D. Ghosh and C. Sinha, J. Phys. B 38, 61 (2005).
    [CrossRef]
  18. J. Berakdar and H. Klar, J. Phys. B 26, 3891 (1993).
    [CrossRef]
  19. D. M. Volkov, Z. Phys. 94, 250 (1935).
    [CrossRef]
  20. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitzevskii, Course of Theoretical Physics. Vol. 4: Quantum Electrodynamics, 2nd ed. (Pergamon, 1982).
  21. P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B 13, 4495 (1980).
    [CrossRef]
  22. A. S. Kornev and B. A. Zon, J. Phys. B 35, 2451 (2002).
    [CrossRef]
  23. M. Abramowitz and I. Stegun, A Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Department of Commerce, 1972).
  24. S.-M. Li, J. Chen, and Z.-F. Zhou, Eur. Phys. J. D 19, 157 (2002).
    [CrossRef]
  25. H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
    [CrossRef]

2005 (5)

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
[CrossRef]

A. Chattopadhyay and C. Sinha, Phys. Rev. A 72, 053406 (2005).
[CrossRef]

C. Arcidiacono, Á. Kövér, and G. Laricchia, Phys. Rev. Lett. 95, 223202 (2005).
[CrossRef] [PubMed]

D. Ghosh and C. Sinha, J. Phys. B 38, 61 (2005).
[CrossRef]

2003 (2)

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

L. Sarkadi, Phys. Rev. A 68, 032706 (2003).
[CrossRef]

2002 (4)

A. S. Kornev and B. A. Zon, J. Phys. B 35, 2451 (2002).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, Eur. Phys. J. D 19, 157 (2002).
[CrossRef]

J. Fiol and R. E. Olson, J. Phys. B 35, 1173 (2002).

S.-M. Li, J. Chen, and Z.-F. Zhou, J. Phys. B 35, 557 (2002).
[CrossRef]

2001 (1)

J. Fiol, V. D. Rodríguez, and R. O. Barrachina, J. Phys. B 34, 933 (2001).
[CrossRef]

2000 (1)

J. Berakdar, Nucl. Instrum. Methods Phys. Res. B 171, 204 (2000).
[CrossRef]

1999 (1)

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

1998 (2)

Á. Kövér and G. Laricchia, Phys. Rev. Lett. 80, 5309 (1998).
[CrossRef]

J. Berakdar, Phys. Rev. Lett. 81, 1393 (1998).
[CrossRef]

1997 (1)

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

1993 (1)

J. Berakdar and H. Klar, J. Phys. B 26, 3891 (1993).
[CrossRef]

1989 (1)

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

1988 (1)

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

1986 (1)

H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
[CrossRef]

1980 (1)

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B 13, 4495 (1980).
[CrossRef]

1935 (1)

D. M. Volkov, Z. Phys. 94, 250 (1935).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. Stegun, A Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Department of Commerce, 1972).

Arcidiacono, C.

C. Arcidiacono, Á. Kövér, and G. Laricchia, Phys. Rev. Lett. 95, 223202 (2005).
[CrossRef] [PubMed]

Barrachina, R. O.

J. Fiol, V. D. Rodríguez, and R. O. Barrachina, J. Phys. B 34, 933 (2001).
[CrossRef]

Berakdar, J.

S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
[CrossRef]

J. Berakdar, Nucl. Instrum. Methods Phys. Res. B 171, 204 (2000).
[CrossRef]

J. Berakdar, Phys. Rev. Lett. 81, 1393 (1998).
[CrossRef]

J. Berakdar and H. Klar, J. Phys. B 26, 3891 (1993).
[CrossRef]

Berestetskii, V. B.

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitzevskii, Course of Theoretical Physics. Vol. 4: Quantum Electrodynamics, 2nd ed. (Pergamon, 1982).

Cavaliere, P.

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B 13, 4495 (1980).
[CrossRef]

Chattopadhyay, A.

A. Chattopadhyay and C. Sinha, Phys. Rev. A 72, 053406 (2005).
[CrossRef]

Chen, J.

S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, Eur. Phys. J. D 19, 157 (2002).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, J. Phys. B 35, 557 (2002).
[CrossRef]

Dorn, A.

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Dörner, R.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Ehrhardt, H.

H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
[CrossRef]

Ferrante, G.

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B 13, 4495 (1980).
[CrossRef]

Fiol, J.

J. Fiol and R. E. Olson, J. Phys. B 35, 1173 (2002).

J. Fiol, V. D. Rodríguez, and R. O. Barrachina, J. Phys. B 34, 933 (2001).
[CrossRef]

Fischer, D.

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

Franchen, P.

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

Franken, P.

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

Ghosh, D.

D. Ghosh and C. Sinha, J. Phys. B 38, 61 (2005).
[CrossRef]

Höhr, C.

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

Joachain, C. J.

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

Jung, K.

H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
[CrossRef]

Khail, D.

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

Klar, H.

J. Berakdar and H. Klar, J. Phys. B 26, 3891 (1993).
[CrossRef]

Knoth, G.

H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
[CrossRef]

Kornev, A. S.

A. S. Kornev and B. A. Zon, J. Phys. B 35, 2451 (2002).
[CrossRef]

Kövér, Á.

C. Arcidiacono, Á. Kövér, and G. Laricchia, Phys. Rev. Lett. 95, 223202 (2005).
[CrossRef] [PubMed]

Á. Kövér and G. Laricchia, Phys. Rev. Lett. 80, 5309 (1998).
[CrossRef]

Laricchia, G.

C. Arcidiacono, Á. Kövér, and G. Laricchia, Phys. Rev. Lett. 95, 223202 (2005).
[CrossRef] [PubMed]

Á. Kövér and G. Laricchia, Phys. Rev. Lett. 80, 5309 (1998).
[CrossRef]

Leone, C.

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B 13, 4495 (1980).
[CrossRef]

Li, S.-M.

S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, Eur. Phys. J. D 19, 157 (2002).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, J. Phys. B 35, 557 (2002).
[CrossRef]

Lifshitz, E. M.

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitzevskii, Course of Theoretical Physics. Vol. 4: Quantum Electrodynamics, 2nd ed. (Pergamon, 1982).

Makhoute, A.

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

Maquet, A.

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

Martin, P.

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

Moshammer, R.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Najjari, B.

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

Olson, R. E.

J. Fiol and R. E. Olson, J. Phys. B 35, 1173 (2002).

Pitzevskii, L. P.

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitzevskii, Course of Theoretical Physics. Vol. 4: Quantum Electrodynamics, 2nd ed. (Pergamon, 1982).

Rodríguez, V. D.

J. Fiol, V. D. Rodríguez, and R. O. Barrachina, J. Phys. B 34, 933 (2001).
[CrossRef]

Sarkadi, L.

L. Sarkadi, Phys. Rev. A 68, 032706 (2003).
[CrossRef]

Schlemmer, P.

H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
[CrossRef]

Schmidt, L. Ph. H.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Schmidt-Böcking, H.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Schröter, C. D.

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

Sinha, C.

A. Chattopadhyay and C. Sinha, Phys. Rev. A 72, 053406 (2005).
[CrossRef]

D. Ghosh and C. Sinha, J. Phys. B 38, 61 (2005).
[CrossRef]

Stegun, I.

M. Abramowitz and I. Stegun, A Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Department of Commerce, 1972).

Taïeb, R.

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

Ullrich, J.

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Veniad, V.

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

Veniard, V.

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

Volkov, D. M.

D. M. Volkov, Z. Phys. 94, 250 (1935).
[CrossRef]

Zhang, S.-T.

S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
[CrossRef]

Zhou, Z.-F.

S.-M. Li, J. Chen, and Z.-F. Zhou, J. Phys. B 35, 557 (2002).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, Eur. Phys. J. D 19, 157 (2002).
[CrossRef]

Zon, B. A.

A. S. Kornev and B. A. Zon, J. Phys. B 35, 2451 (2002).
[CrossRef]

Eur. Phys. J. D (1)

S.-M. Li, J. Chen, and Z.-F. Zhou, Eur. Phys. J. D 19, 157 (2002).
[CrossRef]

J. Phys. B (9)

P. Cavaliere, G. Ferrante, and C. Leone, J. Phys. B 13, 4495 (1980).
[CrossRef]

A. S. Kornev and B. A. Zon, J. Phys. B 35, 2451 (2002).
[CrossRef]

A. Makhoute, D. Khail, A. Maquet, C. J. Joachain, and R. Taïeb, J. Phys. B 32, 3255 (1999).
[CrossRef]

S.-M. Li, J. Chen, and Z.-F. Zhou, J. Phys. B 35, 557 (2002).
[CrossRef]

S.-M. Li, J. Berakdar, S.-T. Zhang, and J. Chen, J. Phys. B 38, 1291 (2005).
[CrossRef]

J. Fiol, V. D. Rodríguez, and R. O. Barrachina, J. Phys. B 34, 933 (2001).
[CrossRef]

J. Fiol and R. E. Olson, J. Phys. B 35, 1173 (2002).

D. Ghosh and C. Sinha, J. Phys. B 38, 61 (2005).
[CrossRef]

J. Berakdar and H. Klar, J. Phys. B 26, 3891 (1993).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (1)

J. Berakdar, Nucl. Instrum. Methods Phys. Res. B 171, 204 (2000).
[CrossRef]

Phys. Rev. A (4)

L. Sarkadi, Phys. Rev. A 68, 032706 (2003).
[CrossRef]

A. Chattopadhyay and C. Sinha, Phys. Rev. A 72, 053406 (2005).
[CrossRef]

P. Martin, V. Veniard, A. Maquet, P. Franchen, and C. J. Joachain, Phys. Rev. A 39, 6178 (1989).
[CrossRef] [PubMed]

D. Khail, A. Maquet, R. Taïeb, C. J. Joachain, and A. Makhoute, Phys. Rev. A 56, 4918 (1997).
[CrossRef]

Phys. Rev. Lett. (5)

C. Höhr, A. Dorn, B. Najjari, D. Fischer, C. D. Schröter, and J. Ullrich, Phys. Rev. Lett. 94, 153201 (2005).
[CrossRef] [PubMed]

C. J. Joachain, P. Franken, A. Maquet, P. Martin, and V. Veniad, Phys. Rev. Lett. 61, 165 (1988).
[CrossRef] [PubMed]

C. Arcidiacono, Á. Kövér, and G. Laricchia, Phys. Rev. Lett. 95, 223202 (2005).
[CrossRef] [PubMed]

Á. Kövér and G. Laricchia, Phys. Rev. Lett. 80, 5309 (1998).
[CrossRef]

J. Berakdar, Phys. Rev. Lett. 81, 1393 (1998).
[CrossRef]

Rep. Prog. Phys. (1)

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph. H. Schmidt, and H. Schmidt-Böcking, Rep. Prog. Phys. 66, 1463 (2003).
[CrossRef]

Z. Phys. (1)

D. M. Volkov, Z. Phys. 94, 250 (1935).
[CrossRef]

Z. Phys. D (1)

H. Ehrhardt, K. Jung, G. Knoth, and P. Schlemmer, Z. Phys. D 13, 3 (1986).
[CrossRef]

Other (2)

M. Abramowitz and I. Stegun, A Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Department of Commerce, 1972).

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitzevskii, Course of Theoretical Physics. Vol. 4: Quantum Electrodynamics, 2nd ed. (Pergamon, 1982).

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Figures (4)

Fig. 1
Fig. 1

Top panel shows a schematic of the scattering geometry. Other panels show the photon-number-summed TDCS versus the ejection angle θ e of the electron. In (a), we choose E 0 k i , whereas in (b) E 0 k i . The kinetic energies of the impinging positron (electron) and of the ejected electron are, respectively, E i = 150 eV and E e = 3 eV . The laser amplitude is E 0 = 5.0 × 10 7 V cm 1 , and the frequency is ω = 1.17 eV (Nd:YAG laser). The scattering angle θ f of the scattered positron (electron) is θ f = 4 ° . Solid curves, result for positron impact ( Z p = + 1 ) ; dashed curves, result for electron impact ( Z p = 1 ) .

Fig. 2
Fig. 2

Photon-number-summed TDCS versus the impact energy for θ f = 4 ° , θ e = 45 ° , and E e = 3 eV . The laser parameters are the same as in Fig. 1. Panel (a) shows the results for E 0 k i , whereas in (b) the results for E 0 k i are depicted. Solid curve, result for positron impact; dashed curve, result for electron impact.

Fig. 3
Fig. 3

Photon-number-summed TDCS for E 0 k i versus the laser’s electronic field amplitude of a Nd:YAG laser ( ω = 1.17 eV ) . The impact energy, the kinetic energy of ejected electron, and the particles’ emission angles are the same as in Fig. 2. Solid curve, result for positron impact; dashed curve, result for electron impact.

Fig. 4
Fig. 4

Photon-number-summed TDCS versus the angle Θ between the laser polarization axis and the incident direction. The parameters are the same as in Fig. 1. Solid curve, result for positron impact; dashed curve, result for electron impact.

Equations (5)

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

S = i d t χ k f ( r 0 , t ) χ k e ( r 1 , t ) Z p r 0 Z p r 01 χ k i ( r 0 , t ) ψ 0 ( r 1 , t ) .
χ k e ( r 1 , t ) = ( 2 π ) 3 2 e π ξ 2 Γ ( 1 + i ξ ) 1 F 1 ( i ξ , 1 , i ( k e r 1 + k e r 1 ) ) exp { i [ k e r 1 k e α 0 sin ω t E e t ( 1 2 c 2 ) t A 2 ( t ) d t ] } ,
ψ 0 ( r 1 , t ) = ( 1 ( i ω ) E 0 r 1 cos ω t ) ϕ 0 ( r 1 ) exp [ i W 0 t ( i 2 c 2 ) t A 2 ( t ) d t ] ,
T l = 1 2 π 3 J l ( D α 0 ) e π ξ 2 Γ ( 1 i ξ ) Z p q 2 λ { ( 1 + l ω D E 0 E 0 γ ) × [ γ 2 + ( λ i k e ) 2 ] i ξ [ ( γ + k e ) 2 + λ 2 ] 1 i ξ ( 1 l ω D E 0 E 0 q ) [ q 2 + ( λ i k e ) 2 ] i ξ [ ( q k e ) 2 + λ 2 ] 1 i ξ } γ = 0 , λ = 1 ,
d 3 σ d Ω f d Ω e d E e = ( 2 π ) 4 l = + ( k f k e k i ) T l 2 .

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