A Pedestrian Approach to the Theory of Transfer Reactions: Application to Weakly-Bound and Unbound Exotic Nuclei

  • Joaquín Gómez CamachoEmail author
  • Antonio M. Moro
Part of the Lecture Notes in Physics book series (LNP, volume 879)


The present status of the theoretical description of transfer reactions is pedagogically presented. It is shown how transfer, from a complicated many-body problem, can be reduced to a three-body problem, introducing spectroscopic amplitudes. The quantum three-body scattering process is described increasing the complexity, starting from Distorted Wave Born Approximation, introducing implicitly break-up effects in Adiabatic Wave Approximation, introducing explicitly break-up effects in Continuum Discretized Coupled channels, and introducing rearrangement couplings in Coupled Reaction Channels. The two latter formalisms are expressed as approximations to the rigorous three-body Faddeev treatment. The application of these formalisms to transfer to weakly bound and unbound exotic nuclei is discussed.


Elastic Scattering Adiabatic Approximation Halo Nucleus Faddeev Equation Halo Neutron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been partially supported by Spanish national projects FPA2009-08848 and FPA2009-07653 and by the Consolider Ingenio 2010 Program CPAN (CSD2007-00042).


  1. 1.
    G.R. Satchler, Direct Nuclear Reactions (Clarendon Press, Oxford, 1983) Google Scholar
  2. 2.
    N. Austern, R.M. Drisko, E.C. Halbert, G.R. Satchler, Theory of finite-range distorted-waves calculations. Phys. Rev. 133, B3 (1964) ADSCrossRefGoogle Scholar
  3. 3.
    N. Austern, Direct Nuclear Reaction Theories (Wiley, New York, 1970) Google Scholar
  4. 4.
    T. Tamura, Compact reformulation of distorted-wave and coupled-channel born approximations for transfer reactions between nuclei. Phys. Rep. 14, 59 (1974) ADSCrossRefGoogle Scholar
  5. 5.
    N.K. Glendenning, Direct Nuclear Reactions (World Scientific, Singapore, 2004) CrossRefzbMATHGoogle Scholar
  6. 6.
    J. Sharpey-Schafer, The mean square radius of nuclear matter and spectroscopic factors from the DWBA. Phys. Lett. B 26, 652 (1968) ADSCrossRefGoogle Scholar
  7. 7.
    J.L.C. Ford, K.S. Toth, G.R. Satchler, D.C. Hensley, L.W. Owen, R.M. DeVries, R.M. Gaedke, P.J. Riley, S.T. Thornton, Single-nucleon transfer reactions induced by 11B ions on 208Pb: a test of the distorted-wave Born approximation. Phys. Rev. C 10, 1429 (1974) ADSCrossRefGoogle Scholar
  8. 8.
    K.S. Toth, J.L.C. Ford, G.R. Satchler, E.E. Gross, D.C. Hensley, S.T. Thornton, T.C. Schweizer, Measurements and analysis of the 208Pb(12C, 13C), (12C, 11B), and (12C, 14C) reactions. Phys. Rev. C 14, 1471 (1976) ADSCrossRefGoogle Scholar
  9. 9.
    T. Tamura, T. Udagawa, M.C. Mermaz, Direct reaction analyses of heavy-ion induced reactions leading to discrete states. Phys. Rep. 65, 345 (1980) ADSCrossRefGoogle Scholar
  10. 10.
    R.C. Johnson, P.J.R. Soper, Contribution of deuteron breakup channels to deuteron stripping and elastic scattering. Phys. Rev. C 1, 976 (1970) ADSCrossRefGoogle Scholar
  11. 11.
    H. Amakawa, S. Yamaji, A. Mori, K. Yazaki, Adiabatic treatment of elastic deuteron-nucleus scattering. Phys. Lett. B 82, 13 (1979) ADSCrossRefGoogle Scholar
  12. 12.
    H. Amakawa, K. Yazaki, Adiabatic treatment of deuteron break-up on a nucleus. Phys. Lett. B 87, 159 (1979) ADSCrossRefGoogle Scholar
  13. 13.
    R.C. Johnson, P.C. Tandy, An approximate three-body theory of deuteron stripping. Nucl. Phys. A 235, 56 (1974) ADSCrossRefGoogle Scholar
  14. 14.
    J.D. Harvey, R.C. Johnson, Influence of breakup channels on the analysis of deuteron stripping reactions. Phys. Rev. C 3, 636 (1971) ADSCrossRefGoogle Scholar
  15. 15.
    G.R. Satchler, Adiabatic deuteron model and the 208Pb(p,d) reaction at 22 MeV. Phys. Rev. C 4, 1485 (1971) ADSCrossRefGoogle Scholar
  16. 16.
    G.L. Wales, R.C. Johnson, Deuteron break-up effects in (p,d) reactions at 65 MeV. Nucl. Phys. A 274, 168 (1976) ADSCrossRefGoogle Scholar
  17. 17.
    N.K. Timofeyuk, R.C. Johnson, Deuteron stripping and pick-up on halo nuclei. Phys. Rev. C 59, 1545 (1999) ADSCrossRefGoogle Scholar
  18. 18.
    M. Kawai, Chapter II. Formalism of the method of coupled discretized continuum channels. Prog. Theor. Phys. Suppl. 89(Suppl. 1), 11 (1986) ADSCrossRefGoogle Scholar
  19. 19.
    N. Austern, Y. Iseri, M. Kamimura, M. Kawai, G. Rawitscher, M. Yahiro, Continuum-discretized coupled-channels calculations for three-body models of deuteron-nucleus reactions. Phys. Rep. 154, 125 (1987) ADSCrossRefGoogle Scholar
  20. 20.
    G.H. Rawitscher, Effect of deuteron breakup on (d,p) cross sections. Phys. Rev. C 11, 1152 (1975) ADSCrossRefGoogle Scholar
  21. 21.
    Y. Iseri, M. Yahiro, M. Nakano, Investigation of adiabatic approximation of deuteron-breakup effect on (d,p) reactions. Prog. Theor. Phys. 69, 1038 (1983) ADSCrossRefGoogle Scholar
  22. 22.
    H. Amakawa, N. Austern, Adiabatic-approximation survey of breakup effects in deuteron-induced reactions. Phys. Rev. C 27, 922 (1983) ADSCrossRefGoogle Scholar
  23. 23.
    A. Laid, J.A. Tostevin, R.C. Johnson, Deuteron breakup effects in transfer reactions using a Weinberg state expansion method. Phys. Rev. C 48, 1307 (1993) ADSCrossRefGoogle Scholar
  24. 24.
    N.B. Nguyen, F.M. Nunes, R.C. Johnson, Finite-range effects in (d,p) reactions. Phys. Rev. C 82, 014611 (2010) ADSCrossRefGoogle Scholar
  25. 25.
    M. Kawai, M. Kamimura, K. Takesako, Chapter V. Coupled-channels variational method for nuclear breakup and rearrangement processes. Prog. Theor. Phys. Suppl. 89(Suppl 1), 118 (1986) ADSCrossRefGoogle Scholar
  26. 26.
    T. Ohmura, B. Imanishi, M. Ichimura, M. Kawai, Study of deuteron stripping reaction by coupled channel theory. II properties of interaction kernel and method of numerical solution. Prog. Theor. Phys. 43, 347 (1970) ADSCrossRefGoogle Scholar
  27. 27.
    I.J. Thompson, F.M. Nunes, in Nuclear reactions for astrophysics, Nuclear Reactions for Astrophysics, ed. by I.J. Thompson, F.M. Nunes (Cambridge University Press, Cambridge, 2009), p. 1 CrossRefGoogle Scholar
  28. 28.
    L.D. Faddeev, Scattering theory for a three-particle system. Zh. Eksp. Teor. Fiz. 39, 1459 (1960) MathSciNetGoogle Scholar
  29. 29.
    N. Austern, M. Yahiro, M. Kawai, Continuum discretized coupled-channels method as a truncation of a connected-kernel formulation of three-body problems. Phys. Rev. Lett. 63, 2649 (1989) ADSCrossRefGoogle Scholar
  30. 30.
    N. Austern, M. Kawai, M. Yahiro, Three-body reaction theory in a model space. Phys. Rev. C 53, 314 (1996) ADSCrossRefGoogle Scholar
  31. 31.
    A. Deltuva, A.M. Moro, E. Cravo, F.M. Nunes, A.C. Fonseca, Three-body description of direct nuclear reactions: comparison with the continuum discretized coupled channels method. Phys. Rev. C 76, 064602 (2007) ADSCrossRefGoogle Scholar
  32. 32.
    A. Deltuva, Spin observables in three-body direct nuclear reactions. Nucl. Phys. A 821, 72 (2009) ADSCrossRefGoogle Scholar
  33. 33.
    A. Deltuva, Deuteron stripping and pickup involving the halo nuclei 11Be and 15C. Phys. Rev. C 79, 054603 (2009) ADSCrossRefGoogle Scholar
  34. 34.
    A. Deltuva, Three-body direct nuclear reactions: nonlocal optical potential. Phys. Rev. C 79, 021602 (2009) ADSCrossRefGoogle Scholar
  35. 35.
    N.J. Upadhyay, A. Deltuva, F.M. Nunes, Testing the continuum-discretized coupled channels method for deuteron-induced reactions. Phys. Rev. C 85, 054621 (2012) ADSCrossRefGoogle Scholar
  36. 36.
    W.R. Coker, Gamow-state analysis of 54Fe(d,n) to proton resonances in 55Co. Phys. Rev. C 9, 784 (1974) ADSCrossRefGoogle Scholar
  37. 37.
    R. Huby, J.R. Mines, Distorted-wave born approximation for stripping to virtual levels. Rev. Mod. Phys. 37, 406 (1965) ADSCrossRefGoogle Scholar
  38. 38.
    C.M. Vincent, H.T. Fortune, New method for distorted-wave analysis of stripping to unbound states. Phys. Rev. C 2, 782 (1970) ADSCrossRefGoogle Scholar
  39. 39.
    H.B. Jeppesen, A.M. Moro, U.C. Bergmann, M.J.G. Borge, J. Cederkall, L.M. Fraile, H.O.U. Fynbo, J. Gomez-Camacho, H.T. Johansson, B. Jonson, M. Meister, T. Nilsson, G. Nyman, M. Pantea, K. Riisager, A. Richter, G. Schrieder, T. Sieber, O. Tengblad, E. Tengborn, M. Turrion, F. Wenander, Study of 10Li via the 9Li(2H, p) reaction at REX-ISOLDE. Phys. Lett. B 642, 449 (2006) ADSCrossRefGoogle Scholar
  40. 40.
    I.J. Thompson, Computer code fresco. Comput. Phys. Rep. 7, 167 (1988) ADSCrossRefGoogle Scholar
  41. 41.
    A.M. Moro, R. Crespo, F. Nunes, I.J. Thompson, 8B breakup in elastic and transfer reactions. Phys. Rev. C 66, 024612 (2002) ADSCrossRefGoogle Scholar
  42. 42.
    A.M. Moro, R. Crespo, F.M. Nunes, I.J. Thompson, Breakup and core coupling in 14N(7Be,8B)13C. Phys. Rev. C 67, 047602 (2003) ADSCrossRefGoogle Scholar
  43. 43.
    K. Ogata, M. Yahiro, Y. Iseri, M. Kamimura, Determination of S 17 from the 7Be(d,n)8B reaction. Phys. Rev. C 67, 011602 (2003) ADSCrossRefGoogle Scholar
  44. 44.
    B. Zwieglinski, W. Benenson, R.G.H. Robertson, W.R. Coker, Study of the 10Be(d,p)11Be reaction at 25 MeV. Nucl. Phys. A 315, 124 (1979) ADSCrossRefGoogle Scholar
  45. 45.
    S. Fortier, S. Pita, J.S. Winfield, W.N. Catford, N.A. Orr, J.V. de Wiele, Y. Blumenfeld, R. Chapman, S.P.G. Chappell, N.M. Clarke, N. Curtis, M. Freer, S. Galès, K.L. Jones, H. Langevin-Joliot, H. Laurent, I. Lhenry, J.M. Maison, P. Roussel-Chomaz, M. Shawcross, M. Smith, K. Spohr, T. Suomijarvi, A. de Vismes, Core excitation in 11Be(gs) via the p (11Be, 10Be) d reaction. Phys. Lett. B 461, 22 (1999) ADSCrossRefGoogle Scholar
  46. 46.
    A.M. Moro, F.M. Nunes, Transfer to the continuum and breakup reactions. Nucl. Phys. A 767, 138 (2006) ADSCrossRefGoogle Scholar
  47. 47.
    A.M. Moro, F.M. Nunes, R.C. Johnson, Theory of (d, p) and (p, d) reactions including breakup: comparison of methods. Phys. Rev. C 80, 064606 (2009) ADSCrossRefGoogle Scholar
  48. 48.
    J.S. Winfield, S. Fortier, W.N. Catford, S. Pita, N.A. Orr, J.V. de Wiele, Y. Blumenfeld, R. Chapman, S.P.G. Chappell, N.M. Clarke, N. Curtis, M. Freer, S. Galès, H. Langevin-Joliot, H. Laurent, I. Lhenry, J.M. Maison, P. Roussel-Chomaz, M. Shawcross, K. Spohr, T. Suomij, Single-neutron transfer from 11Begs via the (p,d) reaction with a radioactive beam. Nucl. Phys. A 683, 48 (2001) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Centro Nacional de AceleradoresUniversidad de Sevilla/Junta de Andalucía/CSICSevilleSpain
  2. 2.Departamento de FAMNUniversidad de SevillaSevilleSpain

Personalised recommendations