Neutrinos and antineutrinos are emitted in great quantity in supernova explosions. In a previous paper they were linked to a hypothetical acceleron field and the variations in this acceleron field as the blast reached earth were investigated as a cause for accelerated nuclear decays. In this paper, the nuclear decays, which are thought to be primarily decays of Nickel-56 and Cobalt-56, which power the light curves of supernovae are investigated. The half-lives and other properties of Nickel-56 and Cobalt-56 have been measured in the laboratory, and the theory of the ground state and other levels of these nuclei are investigated to see if they are sensitive to changes in the acceleron field. One cannot induce stars to explode, but supernovae are often observed in distant galaxies and their study may be used to infer what the possible behaviors are. Nuclear theory is examined to see what the characteristics of Ni-56 and Co-56 might be, including whether the ground states of these nuclei have a pairing gap in their energy states. The calculations indicate that Ni-56 has no pairing gap and the neutrons in Co-56 have no pairing gap. There is a weak pairing gap for protons in Co-56. The implications of this for whether accelerated decay would result for these nuclei, and hence whether accelerated decay would be compatible with the observed light curves if the acceleron mechanism is adopted.