Electron Effects on Barrier Penetration

The effect of the surrounding electrons on the nuclear barrier penetration probability is considered. The nuclear potential is replaced by the Fermi-Thomas potential for heavy atoms, and by a potential derived from a constant electron-density model for very light atoms. The theory is applied to the evaluation of alpha decay periods and of the rates of thermonuclear reactions including the $d-d$ reaction. It is shown that to first order the electron effect can be considered as an increase in the "effective energy" of the alpha particle. Numerical computations were made for the cases of the alpha decay of ${\mathrm{Rn}}^{222}$, ${\mathrm{Po}}^{212}$, ${\mathrm{Sm}}^{147}$, and for the rates of the $d-d$ and the $p$+${\mathrm{N}}^{14}$ reactions.