Influence of electronic environment on $\alpha$ decay

The influence of atomic and conductivity electrons in the metal matrices on the $\alpha$-decay rate is analyzed. The Coulomb interaction of inner atomic electrons and free electrons with the nuclei is treated in the adiabatic approximation and as a shake-off process, respectively. The role of conductivity electrons is analyzed in the framework of strict collision theory. Simple formulas are derived for the exponential tunneling probability $P$ in the approximation of a short tunneling path compared to characteristic electronic dimensions. It is shown that the pre-exponential factor in the decay rate depends on the energy absorbed by electrons during decay, whereas $P$ is independent of it. The half-life of the nucleus surrounded by electrons is a bit larger $(\sim 1\%)$ than that of the bare nucleus.

Figure 1

Sketch of the $\alpha$-decay energies. Drawn are the potential energy of the relative motion of the $\alpha$ particle and a bare daughter nucleus $V_{\text{B}}\left(r\right)$ (full line) and the effective potential energy for the nucleus “dressed in the electron cloud” $V_{\text{eff}}\left(r\right)$ (dashed). The $Q$ and $E=Q-\Delta Q$ are the corresponding kinetic energies at infinity, and $\Delta Q$ is a part of the nuclear energy absorbed by electrons.