Generalization of Gamow states to multi-particle decay

TL;DR

This paper extends the concept of Gamow states from single-particle to multi-particle decay scenarios, deriving their exact form and behavior, including relativistic cases, to better understand metastable quantum systems.

Contribution

The paper generalizes Gamow states to multi-particle decays and derives their exact form, including relativistic effects, enhancing the theoretical framework for metastable quantum states.

Findings

Derived the exact form of the expanding wavefront for multi-particle Gamow states

Extended Gamow states to relativistic outgoing particles

Provided the non-relativistic limit of the multi-particle Gamow state contribution

Abstract

For single-particle nonrelativistic quantum mechanics, a Gamow state is an eigenfunction of the Hamiltonian with complex eigenvalue. Gamow states are not normalizable; they depend on time via the usual multiplier exp(-iEt) supplemented by a cutoff at an expanding wavefront. Gamow states have been used to extend nuclear shell models; they are to metastable states as normalizable eigenfunctions are to bound states. In this paper we generalize Gamow states to decays with multiple outgoing particles. We derive the exact form of the expanding wavefront, even for relativistic outgoing particles. In the non-relativistic limit we derive the exact form of the multi-particle Gamow state contribution to the system propagator (Green's function).