Physics of Atomic Nuclei

, 74:1151 | Cite as

Novel method for solution of coupled radial Schrödinger equations

  • S. N. Ershov
  • J. S. Vaagen
  • M. V. Zhukov
Nuclei Theory


One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.


Wave Function Atomic Nucleus Couple Equation Free Solution Linear Independence 
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.
    A. B. Migdal, Yad. Fiz. 16, 427 (1972) [Sov. J. Nucl. Phys. 16, 238 (1972)].Google Scholar
  2. 2.
    P. G. Hansen and B. Jonson, Europhys. Lett. 4, 409 (1987).ADSCrossRefGoogle Scholar
  3. 3.
    M. V. Zhukov, B. V. Danilin, D. V. Fedorov, et al., Phys. Rep. 231, 151 (1993).ADSCrossRefGoogle Scholar
  4. 4.
    R. G. Gordon, J. Chem. Phys. 51, 14 (1969).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    R. A. White and E. F. Hayes, J. Chem. Phys. 57, 2985 (1972).ADSCrossRefGoogle Scholar
  6. 6.
    L. Gr. Ixaru, Comput. Phys. Commun. 20, 97 (1980).ADSCrossRefGoogle Scholar
  7. 7.
    T.N. Rescigno and A. E. Orel, Phys. Rev. A 25, 2402 (1982).ADSCrossRefGoogle Scholar
  8. 8.
    L. D. Tolsma and G. W. Veltkamp, Comput. Phys. Commun. 40, 233 (1986).ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    B. R. Johnson, J. Chem. Phys. 69, 4678 (1978).ADSCrossRefGoogle Scholar
  10. 10.
    J. M. Hutson, Comput. Phys. Commun. 84, 1 (1994).ADSzbMATHCrossRefGoogle Scholar
  11. 11.
    P. G. Burke, A. Hibbert, and W. D. Robb, J. Phys. B 4, 153 (1971).ADSCrossRefGoogle Scholar
  12. 12.
    I. J. Thompson, F. M. Nunes, and B. V. Danilin, Comput. Phys. Commun. 161, 87 (2004).ADSzbMATHCrossRefGoogle Scholar
  13. 13.
    A. Deloff, Ann. Phys. (N.Y.) 322, 1373 (2007).MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 14.
    Z. A. Anastassi and T. E. Simos, Phys. Rep. 482–483, 1 (2009).MathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions (Nat. Bur. Std., New York, 1964).zbMATHGoogle Scholar
  16. 16.
    R. A. Gonzales, S.-Y. Kang, I. Koltracht, and G. Rawitscher, J. Comput. Phys. 153, 160 (1999).MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 17.
    B. V. Danilin, N. B. Shul’gina, S. N. Ershov, and J. S. Vaagen, Yad. Fiz. 72, 1324 (2009) [Phys. At. Nucl. 72, 1272 (2009)].Google Scholar
  18. 18.
    S. N. Ershov, L. V. Grigorenko, J. S. Vaagen, and M. V. Zhukov, J. Phys. G 37, 064026 (2010).ADSCrossRefGoogle Scholar
  19. 19.
    B. V. Danilin, I. J. Thompson, M. V. Zhukov, and J. S. Vaagen, Nucl. Phys. A 632, 383 (1998).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Joint Institute for Nuclear ResearchDubnaRussia
  2. 2.Institute of Physics and TechnologyUniversity of BergenBergenNorway
  3. 3.Fundamental PhysicsChalmers University of TechnologyGöteborgSweden

Personalised recommendations