Following the idea put forward by Balseiro and Falicov, we have calculated the renor-malized spectral function A (ω) of the amplitude mode of Charge-Density-wave (CDW) phonon by electron-phonon interaction in a model system with coexisting CDW and superconductivity. The A(ω) obtained shows a havily weighted peak of delta-function type at the frequency ω≤2G, where G is the CDW band gap, and a relatively broad continuous spectrum in the region ω>2(G2十△2)1/2, where △ is the superconducting energy gap. Under the condition of fixed G, as △ decreases the intensity of the peak decreases considerably with only a small shift in its position, while the weight of the continuous spectrum raises. These characteristics are in agreement with the behavior of the Raman-active gap modes found by Sooryakumar and Klein in CDW superconductor 2H-NbSe2.
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