The resonance amplitude associated with the Gamow states

Abstract

The Gamow states describe the quasinormal modes of quantum systems. It is shown that the resonance amplitude associated with the Gamow states is given by the complex delta function. It is also shown that under the near-resonance approximation of neglecting the lower bound of the energy, such resonance amplitude becomes the Breit-Wigner amplitude. This result establishes the precise connection between the Gamow states, Nakanishi's complex delta function and the Breit-Wigner amplitude. In addition, this result provides another theoretical basis for the phenomenological fact that the almost-Lorentzian peaks in cross sections are produced by intermediate, unstable particles.

References in corpus (15)

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• Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States
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Cited by in corpus (11)

• Shell Model in the Complex Energy Plane
• Isospin decomposition of $\gamma N\to N^{\ast }$ transitions within a dynamical coupled-channels model
• Dynamical coupled-channels model of $K^{-}p$ reactions (II): Extraction of ${\Lambda }^{\ast }$ and ${\Sigma }^{\ast }$ hyperon resonances
• The rigged Hilbert space approach to the Gamow states
• Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
• Toward establishing low-lying $\Lambda$ and $\Sigma$ hyperon resonances with the $\bar{K}+d\to \pi +Y+N$ reaction
• q-Gamow States as continuous linear functionals on analytical test functions
• q-Gamow States for intermediate energies
• The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
• Light-quark baryon spectroscopy from ANL-Osaka dynamical coupled-channels analysis
• Time as a dynamical variable in quantum decay