Estimation of electron-electron interaction strengths for the rare-earth metals fromXαcalculations

We give a simple method within the Xα approximation to calculate various electron-electron and -hole interaction strengths U from variation in the one-electron orbital energies with respect to changes in the orbital occupancies. The values of different U’s such as $U_{\mathrm{ff}}$ and $U_{\mathrm{fc}}$, calculated within the present scheme for the rare-earth series compare well with previously obtained experimental as well as theoretical estimates, wherever available. The present estimation of $U_{\mathrm{fd}}$ is considerably lower than the values suggested earlier in the literature.