The Gamow Golden Rule of Multichannel Resonances

Abstract

We construct the Gamow Golden Rule of multichannel scattering, and use it to obtain the decay distributions, the partial decay constants, the partial decay widths, and the branching fractions of a resonance that has several decay modes. We exemplify the results using two coupled-channel square well potentials.

Figures (8)

• Figure 1: Bound state wave function of energy $E_{\rm b}=-0.407101$.
• Figure 2: Real and imaginary parts of the Gamow eigenfunction of the resonance of energy $E_{\rm res}=12.7131- i\, 12.9422$.
• Figure 3: Decay energy spectrum of the resonance of energy $E_{\rm res}=12.7131- i\, 12.9422$.
• Figure 4: Channel-1 and -2 components of the bound state of energy $E_{\rm b}=-0.486193$.
• Figure 5: Real and imaginary parts of the channel-1 component of the Gamow state of energy $E_{\rm res}=3.66303-i\,0.0581467$.