Dynamical Screening of $\alpha$-$\alpha$ Resonant Scattering and Thermal Nuclear Scattering Rate in a Plasma

We use effective field theory and thermal field theory to study the dynamical screening effect in the QED plasma on the $\alpha$-$\alpha$ scattering at the $^8$Be resonance. Dynamical screening leads to an imaginary part of the potential which results in a thermal width for the resonance and dominates over the previously considered static screening effect. As a result, both the resonance energy and width increase with the plasma temperature. Furthermore, dynamical screening can have a huge impact on the $\alpha$-$\alpha$ thermal nuclear scattering rate. For example, when the temperature is around $10$ keV, the rate is suppressed by a factor of about $900$. We expect similar thermal suppressions of nuclear reaction rates to occur in those reactions dominated by an above threshold resonance with a thermal energy. Dynamical screening effects on nuclear reactions can be relevant to cosmology and astrophysics.