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Charged particle scattering problem with a complex-range Gaussian basis

  • D. A. Sailaubek
  • O. A. Rubtsova
  • V. I. Kukulin
Regular Article - Theoretical Physics
  • 19 Downloads

Abstract.

A new approach towards solving quantum scattering problems with a short-range interaction and repulsive Coulomb interaction is introduced on the base of the Coulomb wave-packet formalism. The formalism allows to construct a finite-dimensional spectral expansion for the pure Coulomb resolvent and the resolvent for the Coulomb distorted short-range interaction as well. The above Coulomb wave-packet states can be approximated via the so-called complex-range Gaussian basis which is shown to be very convenient for practical calculations in continuum. As a result, the off-mass-shell elements of the Coulomb-nuclear t-matrix are found in a wide energy region from diagonalisation procedures for the total and Coulomb Hamiltonian matrices on the basis presented. The method is illustrated by few examples for calculations of partial amplitudes for local potentials and non-local coupled-channel interaction caused by an intruder state.

References

  1. 1.
    R.G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New-York, 1966)Google Scholar
  2. 2.
    S.P. Merkuriev, Ann. Phys. 130, 395 (1980)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    E.O. Alt, A.M. Mukhamedzhanov, M.M. Nishonov, A.I. Sattarov, Phys. Rev. C 65, 064613 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    A. Deltuva, Phys. Rev. C 88, 011601(R) (2013)ADSCrossRefGoogle Scholar
  5. 5.
    Z. Papp, C-.Y. Hu, Z.T. Hlousek, B. Kónya, S.L. Yakovlev, Phys. Rev. A 63, 062721 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    P. Doleschall, Z. Papp, Phys. Rev. C 72, 044003 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    I.B. Abdurakhmanov, A.S. Kadyrov, I. Bray, Phys. Rev. A 94, 022703 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    S. Quaglioni, W. Leidemann, G. Orlandini, N. Barnea, V.D. Efros, Phys. Rev. C 69, 044002 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    V.I. Kukulin, O.A. Rubtsova, Theor. Math. Phys. 145, 1711 (2005)CrossRefGoogle Scholar
  10. 10.
    O.A. Rubtsova, V.I. Kukulin, V.N. Pomerantsev, Ann. Phys. 360, 613 (2015)CrossRefGoogle Scholar
  11. 11.
    H. Bethe, Quantenmechanik der Einund Zwei-Electronenprobleme, Handbuch der Physik, Zweite Auflage, XXIV, Erster Teil (1933)Google Scholar
  12. 12.
    E. Hiyama et al., Prog. Theor. Exp. Phys. 2012, 01A204 (2012)CrossRefGoogle Scholar
  13. 13.
    Sh.I. Ohtsubo, Y. Fukushima, M. Kamimura, E. Hiyama, Prog. Theor. Exp. Phys. 2013, 073D02 (2013)CrossRefGoogle Scholar
  14. 14.
    T. Egami et al., Phys. Rev. C 70, 047604 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    H. Müther, O.A. Rubtsova, V.I. Kukulin, V.N. Pomerantsev, Phys. Rev. C 94, 024328 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    D.P. Kostomarov, V.I. Kukulin, Numerical methods for few-body quantum mechanical problem with nuclear physics applications, in Proceedings of the 5th International Conference on Mathematical Modeling, Programming, and Mathematical Methods for Solution of Physical Problems, Dubna, 1985, edited by A.A. Samarsky (Joint Institute for Nuclear Research, Dubna, 1986) p. 113Google Scholar
  17. 17.
    J.M. Almira, Surv. Approx. Theory 3, 152 (2007)MathSciNetGoogle Scholar
  18. 18.
    V.I. Kukulin, I.T. Obukhovsky, V.N. Pomerantsev, A. Faessler, J. Phys. G 27, 1851 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    S.B. Dubovichenko, Phys. At. Nucl. 73, 9 (2010)CrossRefGoogle Scholar
  20. 20.
    L.C. McIntyre, W. Haeberli, Nucl. Phys. A 91, 382 (1967)ADSCrossRefGoogle Scholar
  21. 21.
    L.G. Keller, W. Haeberli, Nucl. Phys. A 156, 465 (1970)ADSCrossRefGoogle Scholar
  22. 22.
    W. Gruebler et al., Nucl. Phys. A 242, 265 (1975)ADSCrossRefGoogle Scholar
  23. 23.
    P.A. Schmelzbach et al., Nucl. Phys. A 184, 193 (1972)ADSCrossRefGoogle Scholar
  24. 24.
    S. Sack, L. Biedenharn, G. Breit, Phys. Rev. 93, 321 (1954)ADSCrossRefGoogle Scholar
  25. 25.
    R.A. Arndt, W.J. Briscoe, I.I. Strakovsky, R.L. Workman, Phys. Rev. C 76, 025209 (2007)ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • D. A. Sailaubek
    • 1
  • O. A. Rubtsova
    • 2
  • V. I. Kukulin
    • 2
  1. 1.Faculty of Physics and Technical SciencesGumilyov Eurasian National UniversityAstanaKazakhstan
  2. 2.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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