Quadrupolar contact terms and Hyperfine Structure

Abstract

In the interaction of two electric quadrupoles, there is at short distances a contact term proportional to the second derivative of a delta function. This contact term contributes to the hyperfine splitting of bound states of two particles with spin one or higher-for example the bound states of Omega minus and a nucleus of spin one.The contact hyperfine splitting occurs in states with orbital angular momentum one(p-wave), in contrast to the Fermi contact interaction which is in s-states.We find that these contact splittings will be observable with Omega minus atoms and help measure the quadrupole moment and charge radius of the hyperon.