Coulomb-nuclear potential resonances for oscillatory structure in second energy derivative of fusion cross section times energy

Regular Article - Theoretical Physics


In a nucleus-nucleus collision, resonances depicted by larger values of reaction cross section (σ R) at specific energies are generated by the combined Coulomb-nuclear potential by virtue of well-developed pocket in it. The generation of such resonance is ascertained by the peak value of phase-shift time or dwell time at the resonance energy. We extract the results of fusion cross section (σ F) from σ R in the presence of such resonances and present them in the form of a quantity D F(E) = (d2( F)/dE 2): the second energy derivative of the product of σ F and energy E. In principle the variation of the quantity D F(E) as a function of energy shows two peaks and a negative dip between them around each resonance energy stated above. There can be several resonances in a given angular momentum trajectory denoted by partial wave ℓ. Hence each ℓ would carry a number of peaks and dips for the result of D F(E) over a range of energy. These results of D F(E) from a large number of ℓs involved in a heavy-ion collision shall be added together and, after some mutual cancellation and/or addition, the final result of D F(E) will show an oscillatory structure with a large number of residual peaks and dips present over the range of energy of variation. These calculated results of D F(E) give successful explanation of the corresponding results extracted from the experimental results of σ F at different energies in the cases of heavy-ion system of reactions, namely 16O + 208Pb, 36S + 110Pd, 58Ni + 60Ni and thereby it is confirmed that peaks and dips found in the variation of D F(E) extracted from the measured results of σ F as a function of the energy are critically influenced by the potential pocket resonances generated in the reactions.


Partial Wave Reaction Cross Section Fusion Cross Section Lower Energy Region 208Pb System 
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.
    C.L. Jiang, B.B. Back, H. Esbensen, R.V.F. Janssens, K.E. Rehm, Phys. Rev. C 73, 014613 (2006).CrossRefADSGoogle Scholar
  2. 2.
    M. Dasgupta, D.J. Hinde, A. Diaz-Torres, B. Bouriquet, Catherine I. Low, G.J. Milburn, J.O. Newton, Phys. Rev. Lett. 99, 192701 (2007).CrossRefADSGoogle Scholar
  3. 3.
    C.R. Morton, A.C. Berriman, M. Dasgupta, D.J. Hinde, J.O. Newton, K. Hagino, I.J. Thompson, Phys. Rev. C 60, 044608 (1999).CrossRefADSGoogle Scholar
  4. 4.
    C.L. Jiang et al., Phys. Rev. Lett. 89, 052701 (2002).CrossRefADSGoogle Scholar
  5. 5.
    C.L. Jiang, H. Esbensen, B.B. Back, R.V.F. Janssens, K.E. Rehm, Phys. Rev. C 69, 014604 (2004).CrossRefADSGoogle Scholar
  6. 6.
    C.L. Jiang et al., Phys. Rev. Lett. 93, 012701 (2004).CrossRefADSGoogle Scholar
  7. 7.
    C.L. Jiang et al., Phys. Rev. C 71, 044613 (2005).CrossRefADSGoogle Scholar
  8. 8.
    M. Dasgupta, D.J. Hinde, N. Rowley, A.M. Stefanini, Annu. Rev. Nucl. Part. Sci. 48, 401 (1998).CrossRefADSGoogle Scholar
  9. 9.
    J.O. Newton, R.D. Butt, M. Dasgupta, D.J. Hinde, I.I. Gontchar, C.R. Morton, K. Hagino, Phys. Rev. C 70, 024605 (2004).CrossRefADSGoogle Scholar
  10. 10.
    H. Esbensen, C.L. Jiang, Phys. Rev. C 79, 064619 (2009).CrossRefADSGoogle Scholar
  11. 11.
    T. Udagawa, T. Tamura, Phys. Rev. C 29, 1922 (1984).CrossRefADSGoogle Scholar
  12. 12.
    B. Sahu, L. Satpathy, C.S. Shastry, Phys. Lett. A 303, 105 (2002).MathSciNetCrossRefMATHADSGoogle Scholar
  13. 13.
    Basudeb Sahu, Bidhubhusan Sahu, Int. J. Mod. Phys. E 21, 1250067 (2012).CrossRefGoogle Scholar
  14. 14.
    Basudeb Sahu, G.S. Mallick, B.B. Sahu, S.K. Agarwalla, C.S. Shastry, Phys. Rev. C 77, 024604 (2008).CrossRefADSGoogle Scholar
  15. 15.
    C.E. Fröberg, Rev. Mod. Phys. 27, 399 (1955).MathSciNetCrossRefMATHADSGoogle Scholar
  16. 16.
    F. Videback, R.B. Goldstein, L. Grodzins, S.G. Steadman, T.A. Belote, J.D. Garrett, Phys. Rev. C 15, 954 (1977).CrossRefADSGoogle Scholar
  17. 17.
    J.X. Wei, J.R. Leigh, J.O. Newton, R.C. Lemmon, S. Elfstrom, J.X. Chen, N. Rowley, Phys. Rev. Lett. 67, 3368 (1991).CrossRefADSGoogle Scholar
  18. 18.
    A.M. Stefanini et al., Phys. Rev. C 52, 1727 (1995).CrossRefADSGoogle Scholar
  19. 19.
    A.M. Stefanini et al., Phys. Rev. Lett. 74, 864 (1995).CrossRefADSGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Kalinganagar (K8/636)BhubaneswarIndia
  2. 2.Department of PhysicsNorth Orissa UniversityBaripadaIndia

Personalised recommendations