We have calculated analytically the time-dependent gamma-ray line fluxes, shapes, blueshifts, and widths expected from the radioactive decay of Ni-56 --> Co-56 --> Fe-56 and Co-57 --> Fe-57 synthesized in various Type I supernovae. Assuming spherically symmetric and homologous expansion and possible mixing in the ejecta, we have evaluated the fluxes for the most intense lines from deflagration models for Type Ia supernovae, detonation models for less common Type I supernovae, and core-bounce models for Type Ib supernovae, and have considered the detectability of these lines by the Gamma Ray Observatory (GRO) and the proposed Nuclear Astrophysics Explorer (NAE). The most intense and most detectable lines are the 0.847 and 1.238 MeV lines from Co-56 decay. The maximum flux of the 0.847 MeV line expected from a deflagration Type Ia supernova is 3 x 10(-3) [D(Mpc)]-2 photons cm-2 s-1. We show that this and several other gamma-ray lines from such supernovae should be measurable at the 3-sigma level or above by the GRO instruments at distances as large as 10 Mpc and by the high-resolution spectrometer on the proposed NAE out to as much as 17 Mpc. The maximum line fluxes expected from the detonation models for less common Type I supernovae are typically a factor of 3 larger than those from the Type Ia deflagration models, while the line fluxes expected from the Type Ib core-bounce models are typically a factor of 5 smaller. Measurements of these lines can enable us to test the current models and to distinguish between the processes of nuclear deflagration, nuclear detonation, and core bounce in the supernova explosion, and to study both the nucleosynthetic processes and the explosion dynamics in these supernovae, in model-independent ways. The nucleosynthetic yields, or total mass of Ni-56 produced in a supernova, can be determined, independent of the assumed model, from measurements of the late-time gamma-ray line fluxes. The mass-dependent distribution of the expansion velocity in the ejecta and the dynamics of the supernova explosion can be studied in several independent ways from time-dependent measurements of the fluxes of individual gamma-ray lines, the ratios of the fluxes of lines of different energies, and the individual gamma-ray line shapes, their blueshifted line centers, and their effective line widths. Mixing of the Ni-56 in the ejecta can also be studied both from measurements of the fluxes of the Ni-56 and Co-56 lines at early times and from measurements of the individual gamma-ray line shapes and their effective widths at late times. Although the expected line widths are all narrower than the energy resolution of the GRO detectors, we show that for the closest (less-than-or-equal-to 5 Mpc) supernovae, the GRO detectors should be able to make significant measurements of line blueshifts for both deflagration and detonation models, and to place limits on the line widths. Detailed measurements of the line shapes, however, must await high-resolution spectroscopy with NAE.
