Coupled Channels Methods

  • Doru S. DelionEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 819)


The most general procedure to describe the emission of deformed fragments within a phenomenological approach is the coupled channels method. We analyze various methods to integrate the coupled channels system of differential equations describing emission processes, namely (a) numerical integration, (b) diagonalisation method, (c) analytical continuation method, (d) distorted wave approach and (e) two potential method. These methods are general, not depending upon the concrete structure of the emitted fragments. We then discuss the intrinsic system of coordinate, adiabatic approach, emission from triaxial nuclei, the coupling with rotation and vibration of the heavy fragment.


Wave Function Decay Width Daughter Nucleus Partial Decay Width Proton Emission 
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.


  1. 1.
    Fröman, P.P.: Alpha decay from deformed nuclei. Mat. Fys. Skr. Dan. Vid. Selsk. 1(3) (1957)Google Scholar
  2. 2.
    Gyarmati, B., Vertse, T.: On the normalisation of Gamow functions. Nucl. Phys. A 160, 523–528 (1971)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Vertse, T., Pál, K.F., Balogh, A.: GAMOW, a program for calculating the resonant state solution of the Radial Schrödinger Equation in an arbitrary optical potential. Comput. Phys. Commun. 27, 309–322 (1982)ADSCrossRefGoogle Scholar
  4. 4.
    Ixaru, L., Rizea, M., Vertse, T.: Piecewiese perturbation methods for calculating Eigensolutions of complex optical potential. Comput. Phys. Commun. 85, 217–230 (1995)ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Ferreira, L.S., Maglione, E., Liotta, R.J.: Nucleon resonances in deformed nuclei. Phys. Rev. Lett. 78, 1640–1643 (1997)ADSCrossRefGoogle Scholar
  6. 6.
    Kukulin, V.I., Krasnopol’sly, V.M., Horáček, J.: Theory of Resonances. Kluwer Academic Press, Dordrecht (1989)zbMATHGoogle Scholar
  7. 7.
    Tanaka, N., Suzuki, Y., Varga, K.: Exploration of resonances by analytic continuation in the coupling constant. Phys. Rev. C 56, 562–565 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    Tanaka, N., Suzuki, Y., Varga, K., Lovas, R.G.: Unbound states by analytic continuation in the coupling constant. Phys. Rev. C 59, 1391–1399 (1999)ADSCrossRefGoogle Scholar
  9. 9.
    Taylor, J.R.: Scattering Theory. Wiley, New York (1972)Google Scholar
  10. 10.
    Cattapan, G., Maglione, E.: From bound states to resonances: analytic continuation of the wave function. Phys. Rev. C 61, 067301/1–4 (2000)Google Scholar
  11. 11.
    Davids, C.N., Esbensen, H.: Decay rates of spherical and deformed proton emitters. Phys. Rev. C 61, 044302/1–5 (2000)Google Scholar
  12. 12.
    Satchler, G.R.: Direct Nuclear Reactions. Clarendon Press, Oxford (1983)Google Scholar
  13. 13.
    Bugrov, V.P., Kadmensky, S.G., Furman, V.I., Khlebostroev, V.G.: Multiparticle variant of proton and neutron radioactivity—the case of diagonal transitions. Yad. Fiz. 41, 1123 (1985) [Sov. J. Nucl. Phys. 41, 717–723 (1985)]Google Scholar
  14. 14.
    Bugrov, V.P., Kadmensky, S.G.: Proton decay of deformed nuclei. Yad. Fiz. 49, 1562 (1989) [Sov. J. Nucl. Phys. 49, 967–972 (1989)]Google Scholar
  15. 15.
    Kadmensky, S.G.: On absolute values of α-widths for heavy spherical nuclei. Z. Phys. A 312, 113–120 (1983)ADSCrossRefGoogle Scholar
  16. 16.
    Becchetti, F.D. Jr., Greenlees, G.W.: Nucleon-nucleon optical-model parameters, A > 40, E < 50 MeV. Phys. Rev. 182, 1190–1209 (1969)ADSCrossRefGoogle Scholar
  17. 17.
    Kadmensky, S.G., Bugrov, V.P.: Yad. Fiz. 59, 424 (1996) [Phys. At. Nucl. 59, 399 (1996)]Google Scholar
  18. 18.
    Gurvitz, S.A., Kalbermann, G.: Decay width and shift of a quasistationary state. Phys. Rev. Lett. 59, 262–265 (1987)ADSCrossRefGoogle Scholar
  19. 19.
    Gurvitz, S.A.: New approach to tunneling problems. Phys. Rev. A 38, 1747–1759 (1988)ADSCrossRefGoogle Scholar
  20. 20.
    Jackson, D.F., Rhoades-Brown, M.: Theories of alpha-decay. Ann. Phys. 105, 151 (1977)ADSCrossRefGoogle Scholar
  21. 21.
    Berggren, T., Olanders, P.: Alpha decay from deformed nuclei: (I) formalism and application to ground-state cedays. Nucl. Phys. A 473, 189–220 (1987)ADSCrossRefGoogle Scholar
  22. 22.
    Berggren, T.: Anisotropic alpha decay from oriented odd-mass isotopes of some light actinides. Phys. Rev. C 50, 2494–2507 (1994)ADSCrossRefGoogle Scholar
  23. 23.
    Esbensen, H., Davids, C.N.: Coupled-channels treatment of deformed proton emitters. Phys. Rev. C 63, 014315/1–13 (2000)Google Scholar
  24. 24.
    Nilsson, S.G.: Binding state of individual nucleons in strongly deformed nuclei. Kgl. Danske Videnskab. Selskab Mat. Fys. Medd. 29(16) (1955)Google Scholar
  25. 25.
    Fiorin, G., Maglione, E., Ferreira, L.S.: Theoretical description of deformed proton emitters: nonadiabatic quasiparticle method. Phys. Rev. C 67, 054302/1–4 (2003)Google Scholar
  26. 26.
    Maglione, E., Ferreira, L.S., Liotta, R.J.: Nucleon decay from deformed nuclei. Phys. Rev. Lett. 81, 538–541 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    Maglione, E., Ferreira, L.S., Liotta, R.J.: Proton emission from deformed nuclei. Phys. Rev. C 59, R589–R592 (1999)ADSCrossRefGoogle Scholar
  28. 28.
    Cwiok, S., Dudek, J., Nazarewicz, W., Skalski, J., Werner, T.: Single-particle energies, wave functions, quadrupole moments and g-factors in an axially deformed Woods-Saxon potential with applications to the two-centre-type nuclear problem. Comput. Phys. Commun. 46, 379–399 (1987)ADSCrossRefGoogle Scholar
  29. 29.
    Ferreira, L.S., Maglione, E.: 151Lu: spherical or deformed? Phys. Rev. C 61, 021304(R)/1–3 (2000)Google Scholar
  30. 30.
    Möller, P., Nix, R.J., Myers, W.D., Swiatecki, W.: Nuclear ground-state masses and deformations. At. Data Nucl. Data Tables 59, 185–381 (1995)ADSCrossRefGoogle Scholar
  31. 31.
    Maglione, E., Ferreira, L.S.: Fine structure in proton emission from deformed 131Eu. Phys. Rev. C 61, 047307/1–3 (2000)Google Scholar
  32. 32.
    Sonzogni, A.A., Davids, C.N., Woods, P.J., et al.: Fine structure in the decay of the highly deformed proton emitter 131Eu. Phys. Rev. Lett. 83, 1116–1118 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    Ferreira, L.S., Maglione, E., Fernandes, D.E.P.: Dependence of the decay widths for proton emission on the single particle potential. Phys. Rev. C 65, 024323/1–9 (2002)Google Scholar
  34. 34.
    Cherpunov, V.A.: Yad. Fiz. 6, 955 (1967)Google Scholar
  35. 35.
    Blomqvist, J., Wahlborn, S.: Shell model calculations in the Lead region with a diffuse nuclear potential. Ark. Fys. 16, 545–566 (1960)Google Scholar
  36. 36.
    Rost, E.: Protron shell-model potentials for Lead and the stability of superheavy nuclei. Phys. Lett. 26 B, 184–187 (1968)Google Scholar
  37. 37.
    Dudek, J., Szymanski, Z., Werner, T., Faessler, A., Lima, C.: Description of high spin states in 146Gd using the optimized Woods-Saxon potential. Phys. Rev. C 26, 1712–1718 (1982)ADSCrossRefGoogle Scholar
  38. 38.
    Kruppa, A.T., Barmore, B., Nazarewicz, W., Vertse, T.: Fine structure in the decay of deformed proton emitters: nonadiabatic approach. Phys. Rev. Lett. 84, 4549–4552 (2000)ADSCrossRefGoogle Scholar
  39. 39.
    Barmore, B., Kruppa, A.T., Nazarewicz, W., Vertse, T.: Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method. Phys. Rev. C 62, 054315/1–12 (2000)Google Scholar
  40. 40.
    Barmore, B., Kruppa, A.T., Nazarewicz, W., Vertse, T.: A new approach to deformed proton emitters: non-adiabatic coupled-channels. Nucl. Phys. A 682, 256c–263c (2001)ADSCrossRefGoogle Scholar
  41. 41.
    Delion, D.S., Liotta, R.J., Wyss, R.: High-spin proton emitters in odd-odd nuclei and shape changes. Phys. Rev. C 68, 054603(R)/1–5 (2003)Google Scholar
  42. 42.
    Ferreira, L.S., Maglione, E.: Odd-odd deformed proton emitters. Phys. Rev. Lett. 86, 1721–1724 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    Bohr, A., Mottelson, B.: Nuclear Structure. Benjamin, New York (1975)Google Scholar
  44. 44.
    Davids, C.N., Esbensen, H.: Decay rate of triaxially deformed proton emitters. Phys. Rev. C 69, 043314/1–9 (2004)Google Scholar
  45. 45.
    Davids, C.N., Woods, P.J., Mahmud, H., et al.: Proton decay of the highly deformed odd-odd nucleus 130Eu. Phys. Rev. C 69, 011302(R)/1–3 (2004)Google Scholar
  46. 46.
    Delion, D.S., Wyss, R., Karlgren, D., Liotta, R.J.: Proton emission from triaxial nuclei. Phys. Rev. C 70, 061301(R)/1–5 (2004)Google Scholar
  47. 47.
    Kruppa, A.T., Nazarewicz, W.: Gamow and R-Matrix approach to proton emitting nuclei. Phys. Rev. C 69, 054311/1–11 (2004)Google Scholar
  48. 48.
    Kadmensky, S.G., Sonzogni, A.A.: Proton angular distributions from oriented proton-emitting nuclei. Phys. Rev. C 62, 054601/1–5 (2000)Google Scholar
  49. 49.
    Rafiqullah, A.K.: Alpha decay of nonaxial nuclei. Phys. Rev. 127, 905–913 (1962)ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Theoretical Physics DepartmentInstitute of Physics and Nuclear EngineeringBucharest-MagureleRomania

Personalised recommendations