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On the normalization of the Gamov resonant wave function in the configuration space

  • Proceedings of the International Conference “Nucleus-2007” on the Fundamental Problems of Nuclear Physics, Atomic Power Engineering, and Nuclear Technologies (LVII International Conference on Nuclear Spectroscopy and Atomic Nuclear Structure)
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Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

The regularization of the normalization integral for the resonant wave function, proposed by Zeldovich, is valid only when |Req res| > |Imq res|. A new normalization procedure is proposed and implemented, which is valid when this condition fails. First, an arbitrarily normalized vertex function g(k) is calculated using the formula with the potential V(r) in the integrand. This Fourier integral converges for a potential with the asymptotics V(r) → constr −nexp(−μr) if |Imq res| < μ/2. Then the function g(k) is normalized using the generalized normalization rule, which is independent of the resonance pole position. The proposed method is approved by the example of calculation for a virtual triton.

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991, Russia

    Yu. V. Orlov

  2. National University of Uzbekistan, Tashkent, Uzbekistan

    B. F. Irgaziev

Authors
  1. Yu. V. Orlov
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  2. B. F. Irgaziev
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Correspondence to Yu. V. Orlov.

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Original Russian Text © Yu.V. Orlov, B.F. Irgaziev, 2008, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2008, vol. 72, No. 11, pp. 1625–1629.

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Orlov, Y.V., Irgaziev, B.F. On the normalization of the Gamov resonant wave function in the configuration space. Bull. Russ. Acad. Sci. Phys. 72, 1539–1543 (2008). https://doi.org/10.3103/S106287380811021X

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  • DOI: https://doi.org/10.3103/S106287380811021X

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