The nonadiabatic corrections to the self-energy part sum_s (q,#omega#) of the phonon Green's function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and sum_s (q,#omega#) are calculated for arbitrary vectors q and energy #omega# in the BCS approximation. The results obtained for q = 0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and sum_s (q,#omega#) possesses a logarithmic singularity at #omega# = 2#DELTA#, where #DELTA# is the negligible superconducting gap. It is also shown that in systems with nesting, sum_s (Q,#omega#) (where Q is the nesting vector) possesses a square-root singularity at #omega# = 2#DELTA#, i. e., exactly of the same type as at q = 0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional in the phonon spectral function S (q,#omega#) approx= -#pi#~(-1)Im D_s(q,#omega#) where D_s(q,#omega#) is the phonon Green's function, at temperatures T < T_c.
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