s$^{-1}$ and 6900–13000 km s$^{-1}$ may be fitted by an effective index $n=-\partial \ln \rho / \partial \ln r$ of 7 and 9.5, respectively, as seen from the density distribution with respect to the expansion velocity (Fig. \[fig:denicl\]). At a velocity of $\sim$ 13000 kmc$^{-1}$, there is another dense shell with a density contrast of $\sim$ 3 originated during the adiabatic cooling phase. Note that both dense shells slightly change their density profiles with time. For example, the evolution of the $^{56}$Ni bubble shell is clearly demonstrated by Fig. \[fig:crwdnt\]a.

Cooling and recombination wave {#sec:dmd-crw}
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As the envelope expands, cooling by radiation – a cooling and recombination wave – occurs and completely dominates the luminosity of the SN by about day 18. From this time to nearly day 94 the bolometric luminosity is mainly determined by properties of the CRW (for details see Grassberg & Nadyozhin [@gn76]; Imshennik & Nadyozhin [@in89]). A main property of the CRW consists in generating virtually the entire energy flux carried away by radiation within its front. This radiation flux exhausts the thermal and recombination energy of cooling matter by means of recombination. At the inner edge of the CRW, the radiation flux is 