Abstract
Based on the Shell-Model, and the linear response theory, we discuss the influence of strong electron screening (SES) on the $\gamma$ -ray heating rates (GRHR) by beta decay for several typical iron group nuclei. We calculate the screening potential caused by the relativistically degenerate electron. We also investigate the effect of SES on beta decay Q-value, electron chemical potential, as well as the shell and pair effects. We find that the GRHR increase by several orders magnitude and the screening enhancement factor can get to 76.83 due to SES.
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