Abstract
We investigate the behavior of the critical charge for spontaneous pair production, ${Z}_{C}$, defined as the charge at which the total energy of a $K$-shell electron is $E=\ensuremath{-}{m}_{e}$, as a function of the radius $R$ of the charge distribution. Our approach is to solve the Dirac equation for a potential $V(r)$ consisting of a spherically symmetrical charge distribution of radius $R$ and a Coulomb tail. For a spherical shell distribution of the type usually associated with color-flavor locked strange quark nuggets, we confirm the relation ${Z}_{C}=0.71R\text{ }\text{ }(\mathrm{fm})$ for sufficiently large $R$ obtained by Madsen, who used an approach based on the Thomas-Fermi model. We also present results for a uniformly charged sphere and again find that ${Z}_{C}\ensuremath{\sim}R$ for large enough $R$. Also discussed is the behavior of ${Z}_{C}$ when simple ad hoc modifications are made to the potential for $0\ensuremath{\le}r<R$.
Sign-in/Register to access full text options 
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
