Both conductivities can be expressed in terms of the corresponding effective scattering frequency, calculated in the preceding section as
In the relaxation time approximation and for strongly degenerate electrons we getWiedemann–Franz law is satisfied: .
The role of neutron gas in the inner crust deserves comment. Its normal component contributes to , so that); 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 ground-state crust. Accordingly, accreted crusts have higher electrical and thermal conductivities than the ground-state crust of the same and . This is illustrated in Figure 55. Notice the differences between the and plots at 108 K and 109 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 , 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 , 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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