Yukawa Bound States of a Large Number of Fermions

Understand

We consider the bound state problem for a field theory that contains a Dirac fermion $\chi$ that Yukawa couples to a (light) scalar field $\phi$.

• We are interested in bound states with a large number $N$ of $\chi$ particles.
• A Fermi gas model is used to numerically determine the dependence of the radius $R$ of these bound states on $N$ and also the dependence of the binding energy on $N$.
• Since scalar interactions with relativistic $\chi$'s are suppressed two regimes emerge.