Constrained local plasma density approximation for the calculation of the stopping power for slow ions in solids

A constrained local plasma density approximation is presented for the calculation of the stopping power of solids for slow ions. Using the density-functional theory with the local density approximation for exchange-correlation in the scattering potential and the constrained local plasma density approximation for averaging over effective solid-state electron densities, the stopping power for slow hydrogen and helium projectiles in different solids are calculated. The obtained results of the stopping powers for slow H and He projectiles, and the stopping power ratio $R=\left(\frac{1}{4}\right)\left[\right(-{dE/dx)}_{\mathrm{He}}/\left(-{dE/dx)}_{\mathrm{H}}\right]$ in some solids are in agreement with recent experimental predictions.