Theory of exchange via double-occupation states in crystallineHe3

Recent theories of exchange in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have yielded results for the exchange integral $J$ which are considerably smaller than experimental values. A new mode of exchange is suggested, based on a virtual excited state composed of a vacancy plus doubly occupied cell, which may yield somewhat larger values of $J$. Preliminary calculations based on a variational approach are presented. Numerical results are indicative but can likely be improved with a better trial function. Arguments are given to support the claim that future computations of the exchange integral via this mechanism should give results larger than in previous theories.