Explosions of Type Ic Supernovae (SNe Ic) are investigated using a relativistic hydrodynamic code to study the role of their outermost layers of the ejecta in light-element nucleosynthesis through spallation reactions as a possible mechanism of the "primary" process. We have confirmed that the energy distribution of the outermost layers with a mass fraction of only 0.001% follows the empirical formula proposed by previous work when the explosion is furious. In such explosions, a significant fraction of the ejecta (>0.1% in mass) have energy greater than the threshold energy for spallation reactions. On the other hand, we find that the outermost layers of ejecta become more energetic than the empirical formula would predict when the explosion energy per unit ejecta mass is smaller than ∼1.3 × 1051 ergs M⊙ -1. As a consequence, it is necessary to numerically calculate explosions to estimate light-element yields from SNe Ic. The usage of the empirical formula would overestimate the yields by a factor of ≳3 for energetic explosions, such as SN 1998bw, and underestimate the yields by a similar factor for less energetic explosions, such as SN 1994I. The yields of the light elements Li, Be, and B (LiBeB) from SNe Ic are estimated by solving the transfer equation of cosmic rays originated from ejecta of SNe Ic and compared with observations. The abundance ratios Be/O and B/O produced by each of our SNe Ic models are consistent with those of metal-poor stars. The total amounts of these elements estimated from observations indicate that energetic SNe Ic, such as SN 1998bw, could be candidates for a production site of Be and B in the Galactic halo only when the fraction of this type out of all the SNe was more than a factor of 100 higher than the value estimated from current observational data. This primary mechanism would predict that there are stars significantly deficient in light elements that were formed from the interstellar medium not affected by SNe Ic. Since this has no support from current observations, other primary mechanisms, such as the light-element formation in superbubbles, are needed for other types of SNe. The observed abundance pattern of all elements including heavy elements in metal-poor stars suggests that these two mechanisms should have supplied similar amounts of Be and B. Our calculations show that SNe Ic can not produce an appreciable amount of Li.
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