Decaying states of many-body system

The existence of particle outflow in the decay of many-body system leads to a special description with two sets of state eigenvectors and corresponding complex eigenvalues. Using such eigenvectors the general time behavior of the decaying system is obtained. As an example, we consider the problem of a particle decay of the many-body system to demonstrate the difference between this problem and the problem of a single particle in potential well. We also consider the case of particle scattering by an optical potential and show that the existence of outflow also leads to two sets of state eigenvectors, but with real energy eigenvalues.The existence of particle outflow in the decay of many-body system leads to a special description with two sets of state eigenvectors and corresponding complex eigenvalues. Using such eigenvectors the general time behavior of the decaying system is obtained. As an example, we consider the problem of a particle decay of the many-body system to demonstrate the difference between this problem and the problem of a single particle in potential well. We also consider the case of particle scattering by an optical potential and show that the existence of outflow also leads to two sets of state eigenvectors, but with real energy eigenvalues.

Physica ScriptaFeb 1, 19950 citations

Decaying States in Quantum Systems

A.P. Grécos

North-Holland mathematics studiesJan 1, 19851 citation

Decay of Atomic States

Valery S. Lisitsa

Springer eBooksJan 1, 19940 citations

Applications of nonequilibrium Green functions to time-dependent decaying systems

Songho Murmrgn Gim

We used nonequilibrium many-body Green techniques for the time varying resonant phenomena in few-body systems. By relating the transition energy shift and width to the self-energy and by applying the functional variational techniques to the transition energy shift and width, the corresponding initial state resonant wave functions are derived. Then we obtained time-dependent decaying state wave functions, evolving from these initial states by solving the time-dependent Schr\"odinger equation for the decaying system numerically. Finally, we observed the plausible time decaying behaviors of our model as predicted by real few-body systems.We used nonequilibrium many-body Green techniques for the time varying resonant phenomena in few-body systems. By relating the transition energy shift and width to the self-energy and by applying the functional variational techniques to the transition energy shift and width, the corresponding initial state resonant wave functions are derived. Then we obtained time-dependent decaying state wave functions, evolving from these initial states by solving the time-dependent Schr\"odinger equation for the decaying system numerically. Finally, we observed the plausible time decaying behaviors of our model as predicted by real few-body systems.

Physical Review ADec 5, 20070 citations

Weak decay of the positronium ion

Nishat Ul Sani, M. Jamil Aslam, Ishtiaq Ahmed

The positronium ion ( $\mathrm{Ps}^-$ ), a coulombic three-body bound state of two electrons and a positron, predominantly decays via electron-positron annihilation into electromagnetic final states. While its radiative decay channels have been extensively studied, much less attention has been given to weak processes in this system. In this work, we investigate the rare decay $\mathrm{Ps}^- \to e^- ν_μ\barν_μ$ , obtained by replacing the photon in $\mathrm{Ps}^- \to e^- γ$ with a virtual $Z$ boson. Treating the three-body process as an effective two-body transition, $\mathrm{Ps}^- \to e^- Z^*\left(\to ν_μ\barν_μ\right)$ , we compute the decay rate by explicitly evaluating all spin configurations of the initial bound state and final particles. The result agrees with that obtained using the standard spin-summation formalism of quantum field theory. We find that the branching ratio is comparable to that of the weak decay of ortho-positronium, $\mathrm{o\text{-}Ps} \to γν\barν$ .The positronium ion ($\mathrm{Ps}^-$), a coulombic three-body bound state of two electrons and a positron, predominantly decays via electron-positron annihilation into electromagnetic final states. While its radiative decay channels have been extensively studied, much less attention has been given to weak processes in this system. In this work, we investigate the rare decay $\mathrm{Ps}^- \to e^- ν_μ\barν_μ$, obtained by replacing the photon in $\mathrm{Ps}^- \to e^- γ$ with a virtual $Z$ boson. Treating the three-body process as an effective two-body transition, $\mathrm{Ps}^- \to e^- Z^*\left(\to ν_μ\barν_μ\right)$, we compute the decay rate by explicitly evaluating all spin configurations of the initial bound state and final particles. The result agrees with that obtained using the standard spin-summation formalism of quantum field theory. We find that the branching ratio is comparable to that of the weak decay of ortho-positronium, $\mathrm{o\text{-}Ps} \to γν\barν$.

hep-phCross-listedarXiv:2606.25433Jun 25, 2026

Microscopic theory of decaying many-particle systems

Stefan Hunn

Jan 1, 20130 citations

The positronium ion (

\mathrm{Ps}^-

), a coulombic three-body bound state of two electrons and a positron, predominantly decays via electron-positron annihilation into electromagnetic final states. While its radiative decay channels have been extensively studied, much less attention has been given to weak processes in this system. In this work, we investigate the rare decay

\mathrm{Ps}^- \to e^- ν_μ\barν_μ

, obtained by replacing the photon in

\mathrm{Ps}^- \to e^- γ

with a virtual

Z

boson. Treating the three-body process as an effective two-body transition,

\mathrm{Ps}^- \to e^- Z^*\left(\to ν_μ\barν_μ\right)

, we compute the decay rate by explicitly evaluating all spin configurations of the initial bound state and final particles. The result agrees with that obtained using the standard spin-summation formalism of quantum field theory. We find that the branching ratio is comparable to that of the weak decay of ortho-positronium,

\mathrm{o\text{-}Ps} \to γν\barν