7 q/p$_{F}$  0  0.05  0.1  0.15  0.2  0.25  0.3 B( ,q)  0  0.05  0.1  0.15  0.2  0.25  1  2  3  4  5  6  7 q/p$_{F}$  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8 B( ,q)  0.05  0.1  0.15  0.2  0.25  1  2  3  4  5  6  7 -0.2 -0.1 0 0 0.02 0.04 0.06 0.08 0.1 -0.08 -0.04 0 0.04 Re  Im  FIG. 3: Dependence of the real (solid lines) and imaginary (dashed lines) parts of the scattering polarization tensor in units of density of states on the energy transfer in units of threshold energy 2Δ(0) for fixed momentum transfer q = 0 . 1 p F , with p F = 0 . 1 fm − $^{1}$, and two temperatures T = 0 . 2 T c (upper panel) and T = 0 . 9 T c (lower panel). The zero temper- ature gap is taken to be Δ(0) = 1 MeV, T c = Δ(0) / 1 . 76. FIG. 2: The spectral function of density fluctuations at T = 0 . 2 T c (upper panel) and T = 0 . 9 T c (lower panel). The parameters are as in Fig. 1. tensors Π ′ XX ′ ( q ) are similar to Eq. (46), but involve dif- ferent combinations of coherence factors. The real parts are obtained from the dispersion relation (44). Figure 3 shows the real and imaginary parts of the scattering polarization tensor at two temperatures and for fixed momentum transfer. Figure 4 shows the spec- tral function derived from the scattering polarization ten- sor. It is seen that the modes with energies within the breaking threshold ω ≤ 2Δ(0) are relevant for scattering processes, as opposed to the pair breaking case where only the modes with ω ≥ 2Δ(0) emerge. This justifies the separation of the modes into two classes. The peak values are larger at higher temperatures T ≤ T$_{c}$ , as is the case for the pair breaking response. described in Ref. [20]. On carrying out the angular inte- grals we are left with a one-dimensional integral over the energy. As an example, we give the expression for the elementary loop Here we wish to obtain the unpaired ( T > T$_{c}$ ) limit of the polarization function (18). This amounts to setting the coherence factors in Eq. (19)–(22) to their values in the normal state C. Unpaired and uncorrelated limits ImΠ ′ $_{GG}$( q ) ν ( p$_{F}$ ) − $^{1}$, = − πp$_{F}$ T 4 qµ$_{0}$ ∫ ∞ − µ/T dξ$_{p}$ T [ u 2 $_{p}$u 2 p + q ϵ$_{p}$$_{+}$$_{q}$ ξ$_{p}$$_{+}$$_{q}$ ∣ x = x + 0 [ f ( ϵ$_{p}$ ) − f ( ϵ$_{p}$ + ω )] θ (1 − | x + 0 | ) − v 2 $_{p}$v 2 p + q ϵ$_{p}$$_{+}$$_{q}$ ξ$_{p}$$_{+}$$_{q}$ ∣ x = x − 0 [ f ( ϵ$_{p}$ ) − f ( ϵ$_{p}$ − ω )] θ (1 − | x − 0 | ) ] , (46) u$_{p}$ = 1 , v$_{p}$ = 0 . (47) Π$_{RPA}$( q ) = A ( q ) 1 − v$_{ph}$ A ( q ) , (48) It follows then from Eq. (20) that Π$_{FG}$ = 0 = Π$_{GF}$ and, therefore, B = 0. Setting B = 0 in Eq. (18) and noting that C ̸ = 0, since Π$_{G}$ $^{†}$G = 0, we obtain where θ is the Heaviside step function, x = ( p · q ) / | p || q | , and x ± 0 is the x value satisfying the equation ± ω + ϵ$_{p}$ − ϵ$_{p}$$_{+}$$_{q}$ = 0 and the prime refers to the scattering part. The expressions for the scattering parts of the polarization