One- and two-electron atomic screening in fusion reactions

Recent laboratory experiments have measured fusion cross sections at center-of-mass energies low enough that the effects of atomic electrons are important. To extract the cross section for bare nuclei from these data (as required for astrophysical applications), it is necessary to understand these screening effects. We present a model in which the evolution of the electron wave function is treated dynamically in the time-dependent Hartree-Fock scheme, while the motion of the nuclei is treated classically. We have calculated screening in the d${+}^2$H and d${+}^3$He reactions and give the effective screening energy ${\mathit{U}}_{\mathit{e}}$ at small internuclear separations as a function of E. The resulting ${\mathit{U}}_{\mathit{e}}$ values do not exceed the previously established adiabatic limits, and thus cannot explain the higher screening energies derived from experiment.