Both conductivities can be expressed in terms of the corresponding effective scattering frequency, calculated in the preceding section as
where the electron effective mass is given by Equation (1).In the relaxation time approximation and for strongly degenerate electrons we get
so that the Wiedemann–Franz law is satisfied: Let us remind ourselves, that the equality (204) is violated when the scattering is not negligible compared to electron scattering by nuclei and by impurities. This and other effects leading to violation of the Wiedemann–Franz law are discussed in [339].

The role of neutron gas in the inner crust deserves comment. Its normal component contributes to , so that
However, there are actually two contributions to . The first one results from the scattering and is therefore of a standard “diffusive” nature. This contribution to is where is the number density of the gas of “neutron excitations” (neutrons are strongly degenerate and moreover superfluid), is their effective mass, and is their scattering frequency. Neutron excitations scatter by nuclear clusters and by themselves via strong interactions, However, due to a much smaller neutronneutron cross section as compared to the neutroncluster one, and due to the low density of neutron excitations, we get , so that . The second contribution to is characteristic of superfluids and has a convective character (“convective counterflow”, see, e.g., Tilley & Tilley [403]); we denote it by .It can be noted that for “neutron excitations” scatter by the lattice phonons. Complete calculation of , taking due account of the effect of the crystal lattice on neutron scattering and neutron superfluidity remains to be done.
The presence of impurities considerably decreases electrical and thermal conductivities at low temperature and high density; see Figure 54. At , 5% of impurities with reduces and at by two orders of magnitude. Accreted crusts are characterized by nuclides with lower values of and than those in the groundstate crust. Accordingly, accreted crusts have higher electrical and thermal conductivities than the groundstate crust of the same and . This is illustrated in Figure 55. Notice the differences between the and plots at 10^{8} K and 10^{9} K. They are due to an additional factor in , reflected in the Wiedermann–Franz law (205).
Recent calculations of , taking into account the Landau damping of transverse plasmons, give a much larger contribution from scattering than the previous ones, using the static screening, on which Figures 54 and 55 are based. As shown by Shternin and Yakovlev [378], the Landau damping of transverse plasmons strongly reduces in the inner crust at .
The contribution of ions to was recently calculated by Chugunov and Haensel [100], who also quote older papers on this subject. As a rule, can be neglected compared to . A notable exception, relevant for magnetized neutron stars, is discussed in Section 9.5.
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