Abstract
A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schr\"{o}dinger equation, it preserves the total energy but not the kinetic energy in the intermediate-time region of a decay process where those of the parent and daughters overlap. The decay rate computed with Fermi's golden rule requires corrections that vary with the distance between the initial and final states, and the energy distribution of the daughter is distorted from that of plane waves. The corrections have universal properties in relativistically invariant systems and reveal macroscopic quantum phenomena for light particles. The implications for precision experiments in beta decays and various radiative transitions are presented.
Highlights
A many-body interaction transforms a many-body state to a sum of the same kinetic energy, and the waves behave like free particles and do not show diffraction at the asymptotic region, t = ∞
We study problems connected with the wave zone and find that a new length E /m2, where m and E are the observed particle’s mass and energy, appears for the coherence length and becomes much longer than the de Broglie wave length in relativistically invariant systems
The finite-size correction becomes large in the situation where the wave functions of the initial and final states overlap over a wide area
Summary
In a physical system described by a Hamiltonian H composed of a free term H0 and an interaction term Hint,. The free part H0 is a bi-linear field form and the interaction part Hint is a higher field polynomial. Hint causes a change in the particle number such as a decay of a pion into a charged lepton and a neutrino
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
