Perturbation Theory Using a Reduced Set of States

A method is given whereby a second-order calculation of the energy due to a perturbation $H_{\mathrm{en}}$ of the zero-order Hamiltonian $H_e+H_p+H_{\mathrm{ep}}$ can be evaluated approximately using only the eigenstates ${\psi }_e$ and relaxation times ${\tau }_{\mathrm{ep}}$. As an example the Ruderman-Kittel formula for the exchange-type coupling of nuclear spins is re-evaluated.