The Decay Process: An Exactly Soluble Example and its Implications

  • Gaston García-Calderón
  • Gerardo Loyola
  • Marcos Moshinsky
Conference paper


There is agreement on the exponential decay law for unstable states in a certain range of times but not on what happens for very long or very short times. In particular for the latter a paradox appears from the contradictory results of two very straightforward calculations. To understand the matter better we consider s-states limited by a δ function radial potential of infinite height at a distance r = a. At time t = 0 we lower the height of the δ toa finite value b and obtain in an explicit analytic form the decay amplitude as a function of time in the full interval 0 ≤ t ≤ ∞. Our results support one of the calculations for very short times based on a schematic theory of nuclear reactions.


Peris Sine 


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  1. [1]
    G. Gamow, Z. Phys. 51, 204 (1928).CrossRefADSGoogle Scholar
  2. [2]
    W. Gurney and E.U. Condon, Phys. Rev. 33, 127 (1929).CrossRefADSGoogle Scholar
  3. [3]
    M. Moshinsky, Phys. Rev. 84, 525 (1951).CrossRefMATHADSMathSciNetGoogle Scholar
  4. [4]
    G. García-Calderón, in these Proceedings. Google Scholar
  5. [5]
    G. Breit and E.P. Wigner, Phys. Rev. 49, 519, 642 (1936).Google Scholar
  6. [6]
    A. Peres, Ann. Phys. (N.Y.) 129, 33 (1980)CrossRefADSMathSciNetGoogle Scholar
  7. [6a]
    Grotza and H.V. Klapdor, Phys. Rev. C 30, 2098 (1984).ADSGoogle Scholar
  8. [7]
    M. Moshinsky, G. Loyola, and J.L. Mateos, “Time dependent model for heavy ion collision with a single resonance”, Proceedings of the XIV Symposium on Nuclear Physics, Oaxtepec, México (World Scientific 1991, Singapore).Google Scholar
  9. [8]
    G. Beck and H.M. Nussenzveig, N. Cimento 16, 441 (1960). See also the contribution of H.M. Nussenzveig in these Proceedings. MathSciNetGoogle Scholar
  10. [9]
    M. Moshinsky, G. Loyola, and C. Villegas, Rev. Mex. Fís. 37, 369 (1991).Google Scholar
  11. [10]
    I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, New York 1980) p. 931, Formula 8.254.Google Scholar
  12. [11]
    M.L. Goldberger and K.M. Watson, Collision Theory (John Wiley & Sons, New York, 1964) Chapter VIII and in particular p. 450.MATHGoogle Scholar
  13. [12]
    G. García-Calderón and M. Berrondo, Lett. N. Cimento, Serie 2, 26, 562 (1979).CrossRefGoogle Scholar
  14. [13]
    M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover Publications Inc., New York, 1972) p. 297, formula 7.1.4.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Gaston García-Calderón
  • Gerardo Loyola
    • 1
  • Marcos Moshinsky
    • 2
  1. 1.Instituto de FísicaUNAMMéxico
  2. 2.El Colegio NacionalMéxico

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