Electron-phonon interaction and damping of phonons in simple metals application to aluminum

The theory of the electron-phonon interaction and of its influence on the damping of phonons is presented. The basic quantity entering into the theory, the matrix element of the effective electron-phonon interaction, will be obtained from an integral equation which is derived without making any simplifying assumptions about the wave functions and the energy spectrum of the Bloch electrons. Also for the matrix element of the ion-electron interaction a formula is given which allows an extension of the present calculation to metals with a complicated band structure. For the purpose of numerical computation in the metal Al the phonon lifetimes are determined in the free-electron model. The calculated values are compared with the experimental data of Nilsson and Stedman and with the theoretical results of Björkmanet al.