Nonlocal contributions to theρ−ωmixing charge-symmetry-breaking force

Nonlocal contributions of order ${\left(\frac{1}{m}\right)}^2$ to the $\rho -\omega$ mixing charge-symmetry-breaking nucleon-nucleon force are derived, including several aspects not previously considered. Numerical results for scattering lengths and effective ranges are generated which indicate a slightly larger effect than that found recently by others. The relativistic aspects of this force and its relationship to the electromagnetic Breit interaction are developed. The total correction due to all the $\left(\frac{1}{m^2}\right)$ terms is approximately 10%. We estimate that $\Delta E({}_{}{}^3{}_{}{}^{}\mathrm{He}-{}_{}{}^3{}_{}{}^{}\mathrm{H})=+{40}_{-15\mathrm{}}^{+45\mathrm{}}$ keV is due to the $\rho -\omega$ force.