Screening and Electron Correlation Effects on the ElectronPhonon Interaction in Monovalent Metal
Abstract
The frequency and lifetime of the phonon and the electron correlation effect in monovalent metal are formulated simultaneously using the twotime Green'sfunction method, and the screening of the electronphonon interaction is studied. It is shown that when only the direct Coulomb force is taken into account, the contribution of the electronphonon interaction to the dispersion relation and halfwidth formula is proportional to the first and the second powers of the screening factor ∊^{1}, respectively. The halfwidth formula becomes complicated when the exchange Coulomb force is taken into account, and the effective electronphonon interaction is not a welldefined concept in this case. The electroncorrelation effect is taken into account by increasing the order at which the hierarchy equation is decoupled to one higher than the HartreeFock approximation. The correlation effect including the nonadiabatic effects is obtained and is compared with the results of Bailyn, Hone, and Vosco. The numerical calculation of the dispersion and lifetime of the phonon for sodium metal is carried out and is compared with the results of Toya and DayalSrivastava. The Kohn anomaly in the phonon width appears in the transverse branches T_{1} and T_{2} in the [110] direction.
 Publication:

Physical Review
 Pub Date:
 August 1968
 DOI:
 10.1103/PhysRev.172.747
 Bibcode:
 1968PhRv..172..747T