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 (1In 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
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The role of neutron gas in the inner crust deserves comment. Its normal component contributes to ,
so that
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 [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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