Formal solutions for response functions of superconductors and 3He(B)

Formal solutions for the autocorrelation functions of density and the transversal current are discussed in the acoustic and quasihomogeneous regime. The poles of these functions are obtained without any restrictions imposed on Landau parameters. The formula for sound dispersion at T = 0 is generalized by the inclusion of terms of the relative order of (kv2Δ)2, (k is the wave vector, v is the Fermi velocity, Δ is the energy gap, h̷ ≡ 1). The dispersion formulae for transversal and longitudinal excitations with a gap for 3He(B) are also given, with an accuracy up to the terms of the order of (kv2Δ)2, for 0 ⩽ T ⩽ Tc, and without any restrictions imposed on Landau parameters. Under these last assumptions our autocorrelation functions are calculated in the polar as well as non-polar regions. It is shown that if T > 0, the transversal function vanishes at some ω, such that 0 ⩽ ω2 ⩽ (125)Δ2. Moreover,the zero of the density autocorrelation function is distanced from its pole by an amount of the order of (kv2Δ)2.