Calculation of low-energy-electron lifetimes

The effect of the density of states on the lifetime of low-energy electrons in metals has been studied using a golden rule approach. Simple approximations to the real density of states of metals have been used allowing analytical results, which show that the free-electron scaling $(E-E_F{)}^{-2}$ of the lifetime is affected above the onset of $d$-electron contributions. Hence, in noble metals a scaling with $(E-E_F-{\omega }_d{)}^{-2},$ where ${\omega }_d$ is the energy distance from the Fermi energy to the top of the $d$ band, appears once $d$ electrons can be excited. In ferromagnetic Co, the ratio between the lifetimes of majority and minority spin electrons is found energy independent below the threshold for the excitation of majority $d$ electrons while this ratio increases with energy above that point.