Magnetic Field Dependence of the Ruderman-Kittel-Kasuya-Yosida Exchange Interaction

The interaction between two spins interacting with a gas of independent electrons by a $\delta$-function interaction in the presence of a uniform magnetic field has been calculated in the effective-mass approximation. The interaction has both steady and oscillatory dependence on the magnetic field, and is such as to contribute a field dependence to the nuclear magnetic line shape in metals having low-mass carriers.