Skip to main content
Log in

Different Methods for the Two-Nucleon T-Matrix in the Operator Form

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

We compare three methods to calculate the nucleon–nucleon t-matrix based on the three-dimensional formulation of Golak et al. (Phys Rev C 81:034006, 2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon–nucleon scattering observables using a chiral next-to-next-to-leading-order neutron–proton potential. We also apply our three-dimensional framework to the demanding problem of proton–proton scattering, using a corresponding version of the nucleon–nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton–proton scattering.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Golak J., Glöckle W., Skibiński R., Witała H., Rozpędzik D., Topolnicki K., Fachruddin I., Elster Ch., Nogga A.: Two-nucleon systems in three dimensions. Phys. Rev. C 81, 034006 (2010)

    Article  ADS  Google Scholar 

  2. Glöckle W., Witała H., Hüber D., Kamada H., Golak J.: The three-nucleon continuum: achievements, challenges and applications. Phys. Rep. 274, 107 (1996)

    Article  ADS  Google Scholar 

  3. Nogga A., Kamada H., Glöckle W.: Modern nuclear force predictions for the alpha particle. Phys. Rev. Lett. 85, 944 (2000)

    Article  ADS  Google Scholar 

  4. Elster Ch., Thomas J.H., Glöckle W.: Two-body T-matrices without angular-momentum decomposition: energy and momentum dependences. Few-Body Syst. 24, 55 (1998)

    Article  ADS  Google Scholar 

  5. Fachruddin I., Elster Ch., Glöckle W.: New forms of deuteron equations and wave function representations. Phys. Rev. C 63, 054003 (2001)

    Article  ADS  Google Scholar 

  6. Ramalho G., Arriaga A., Peña M.T.: Solution of the spectator equation for relativistic NN scattering without partial wave expansion. Few-Body Syst. 39, 123 (2006)

    Article  ADS  Google Scholar 

  7. Caia G., Pascalutsa V., Wright L.E.: Solving potential scattering equations without partial wave decomposition. Phys. Rev. C 69, 034003 (2004)

    Article  ADS  Google Scholar 

  8. Rodriguez-Gallardo M., Deltuva A., Cravo E., Crespo R., Fonseca A.C.: Two-body scattering without angular-momentum decomposition. Phys. Rev. C 78, 034602 (2008)

    Article  ADS  Google Scholar 

  9. Elster Ch., Schadow W., Nogga A., Glöckle W.: Three body bound state calculations without angular momentum decomposition. Few-Body Syst. 27, 83 (1999)

    Article  ADS  Google Scholar 

  10. Liu H., Elster Ch., Glöckle W.: Three-body scattering at intermediate energies. Phys. Rev. C 72, 054003 (2005)

    Article  ADS  Google Scholar 

  11. Bayegan S., Hadizadeh M.R., Harzchi M.: Three-nucleon bound state in a spin-isospin dependent three dimensional approach. Phys. Rev. C 77, 064005 (2008)

    Article  ADS  Google Scholar 

  12. Bayegan S., Shalchi M.A., Hadizadeh M.R.: Three dimensional calculations of NN bound and scattering states with a chiral potential up to N3LO. Phys. Rev. C 79, 057001 (2009)

    Article  ADS  Google Scholar 

  13. Hadizadeh M.R., Tomio L., Bayegan S.: Solutions of the bound-state Faddeev-Yakubovsky equations in three dimensions by using NN and 3N potential models. Phys. Rev. C 83, 054004 (2011)

    Article  ADS  Google Scholar 

  14. Glöckle W., Elster Ch., Golak J., Skibiński R., Witała H., Kamada H.: A new treatment of 2N and 3N bound states in three dimensions. Few-Body Syst. 47, 25 (2010)

    Article  ADS  Google Scholar 

  15. Golak, J., Topolnicki, K., Skibiński, R., Glöckle, W., Kamada, H., Nogga, A.: A Three-dimensional treatment of the three-nucleon bound state. Few-Body Syst. doi:10.1007/s00601-012-0472-5

  16. Glöckle W., Fachruddin I., Elster Ch., Golak J., Skibiński R., Witała H.: 3N scattering in a three-dimensional operator formulation. Eur. Phys. J. A43, 339 (2010)

    ADS  Google Scholar 

  17. Glöckle W.: The Quantum Mechanical Few-Body Problem. Springer, Berlin (1983)

    Book  Google Scholar 

  18. Epelbaum E., Glöckle W., Meißner Ulf-G.: The two-nucleon system at next-to-next-to-next-to-leading order. Nucl. Phys. A 747, 362 (2005)

    Article  ADS  Google Scholar 

  19. Epelbaum E.: Few-nucleon forces and systems in chiral effective field theory. Prog. Part. Nucl. Phys. 57, 654 (2006)

    Article  ADS  Google Scholar 

  20. Epelbaum E., Hammer H.W., Meißner U.-G.: Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773 (2009)

    Article  ADS  Google Scholar 

  21. Wolfenstein L.: Possible triple scattering experiments. Phys. Rev. 96, 1654 (1954)

    Article  ADS  MATH  Google Scholar 

  22. Press W., Flannery B., Teukolsky S., Vetterling W.: Numerical Recipes. Cambridge University Press, Cambridge (1989)

    MATH  Google Scholar 

  23. Machleidt R.: The meson theory of nuclear forces and nuclear structure. Adv. Nucl. Phys. 19, 189 (1989)

    Article  Google Scholar 

  24. Stadler A., Glöckle W., Sauer P.U.: Faddeev equations with three-nucleon force in momentum space. Phys. Rev. C 44, 2319 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  25. Epelbaum, E.: Private communication

  26. ScaLAPACK Home Page: http://www.netlib.org/scalapack/scalapack_home.html

  27. Skibiński R., Golak J., Witała H., Glöckle W.: Proton-proton scattering without Coulomb force renormalization. Eur. Phys. J. A40, 215 (2009)

    ADS  Google Scholar 

  28. Skibiński R., Golak J., Witała H.: Numerical investigations of the three-dimensional proton-proton screened Coulomb t-matrix. Acta Phys. Polon. B41, 875 (2010)

    Google Scholar 

  29. Vincent C.M., Phatak S.C.: Accurate momentum-space method for scattering by nuclear and Coulomb potentials. Phys. Rev. C 10, 391 (1974)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Golak.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golak, J., Skibiński, R., Witała, H. et al. Different Methods for the Two-Nucleon T-Matrix in the Operator Form. Few-Body Syst 53, 237–252 (2012). https://doi.org/10.1007/s00601-012-0480-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-012-0480-5

Keywords

Navigation