Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential

Abstract

We express the resonant energies of the delta-shell potential in terms of the Lambert $W$ function, and we calculate their decay widths and decay constants. The ensuing numerical results strengthen the interpretation of such decay widths and constants as a way to quantify the coupling between a resonance and the continuum. We calculate explicitly the decay energy spectrum of the resonances of the delta-shell potential, and we show numerically that the lineshape of such spectrum is not the same as, and can be very different from, the Breit-Wigner (Lorentzian) distribution. We argue that the standard Golden Rule cannot describe the interference of two resonances, and we show how to describe such interference by way of the decay energy spectrum of two resonant states.

References in corpus (28)

• Big-Bang Nucleosynthesis
• Sinc approximation of algebraically decaying functions
• Shell Model in the Complex Energy Plane
• Precision decay rate calculations in quantum field theory
• Isospin decomposition of $\gamma N\to N^{\ast }$ transitions within a dynamical coupled-channels model
• A direct approach to quantum tunneling
• Observation of an anomalous line shape of the ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ mass spectrum near the $p\bar{p}$ mass threshold in $J/\psi \to \gamma {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$
• Time-reversal symmetric resolution of unity without background integrals in open quantum systems
• Resonances and antibound states of Pöschl-Teller potential: Ladder operators and SUSY partners
• Pole positions and residues from pion photoproduction using the Laurent+Pietarinen expansion method
• Observation of the decay $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ and evidence for $B^0\to \varphi {\pi }^{+}{\pi }^{-}$
• Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps
• Hermitian and non-Hermitian formulations of the time evolution of quantum decay
• On the definition of the Δmass and width
• Observation of the doubly radiative decay ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$
• Baryon transition form factors at the pole
• Nonexponential tunneling decay of a single ultracold atom
• Toward establishing low-lying $\Lambda$ and $\Sigma$ hyperon resonances with the $\bar{K}+d\to \pi +Y+N$ reaction
• The resonance amplitude associated with the Gamow states
• Time evolution of decay for purely absorptive potentials: The effect of spectral singularities
• q-Gamow States for intermediate energies
• Extracting the resonance parameters from experimental data on scattering of charged particles
• Non-Hermitian Hamilton operator in open quantum systems
• Observation of $B^{+}\to J/\psi 3{\pi }^{+}2{\pi }^{-}$ and $B^{+}\to \psi (2S){\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems
• Cross section versus time delay and trapping probability
• Underlying non-Hermitian character of the Born rule in open quantum systems
• General inner products for energy eigenstates

Cited by in corpus (6)

• Probing the Non-exponential Decay Regime in Open Quantum Systems
• An approximation to the Woods-Saxon potential based on a contact interaction
• The Gamow-state description of the decay energy spectrum of neutron-unbound ${}^{25}$O
• Winter (or delta-shell) Model at Small and Intermediate Volumes
• Thermodynamic properties of the one-dimensional Robin quantum well
• Winter Model at Finite Volume