Rayleigh scattering and power conservation

In the usual formulation of Rayleigh scattering in terms of the quasi-static dipole moments of the scatterer, the scattered field is evaluated exactly to the lowest order
(k_{0}a)^{3}
where
a
is a characteristic dimension of the scatterer. Although the scattered power may be found correctly to order
(k_{0}a)^{6}
in terms of the scattered field, power conservation does not hold. To achieve power conservation the scattered field must be determined exactly to order
(k_{0}a)^{6}
. It is shown that the term of order
(k_{0}a)^{6}
may be found by including radiation reaction as part of the polarizing field. The scattered power can then be found by using the forward scatter theorem (optical extinction theorem) and leads to power conservation correct to lowest order.