Geiger-Nuttall Law for Nuclei in Strong Electromagnetic Fields

We investigate the influence of a strong laser electromagnetic field on the $\alpha$-decay rate by using the Hennenberger frame of reference. We introduce an adimensional parameter $D=S_0/R_0$, where $R_0$ is the geometrical nuclear radius and $S_0\sim \sqrt{I}/{\omega }^2$ is a length parameter depending on the laser intensity $I$ and frequency $\omega$. We show that the barrier penetrability has a strong increase for intensities corresponding to $D>D_{\text{crit}}=1$, due to the fact that the resulting Coulomb potential becomes strongly anisotropic even for spherical nuclei. As a consequence, the contribution of the monopole term increases the barrier penetrability by 2 orders of magnitude, while the total contribution has an effect of 6 orders of magnitude at $D\sim 3D_{\text{crit}}$. In the case of deformed nuclei, the electromagnetic field increases the penetrability by an additional order of magnitude for a quadrupole deformation ${\beta }_2\sim 0.3$. The influence of the electromagnetic field can be expressed in terms of a shifted Geiger-Nuttal law by a term depending on $S_0$ and deformation.

Figure 1

Logarithm of the penetrability given by Eq. (16) normalized to its maximal value versus the angle between the emitted particle and laser beam $\mathrm{\Theta }$ for $D=S_0/R_0=1/\sqrt{10}$ (stars), $D=1$ (triangles), and $D=\sqrt{10}$ (circles) from ${}^{212}\mathrm{Po}$.

Figure 2

Logarithm of the total penetrability versus $D=S_0/R_0$ for various quadrupole deformations of ${}^{232}\mathrm{Pu}$.

Figure 3

Logarithm of penetrability versus the Coulomb-Sommerfeld parameter for Po istopes in the absence of the laser field (crosses), by considering only the monopole component (circles) and the full contribution (triangles) for $D=\sqrt{10}$. The corresponding linear fits, expressing the Geiger-Nuttall law, are plotted by red lines.

Figure 4

Same as in Fig. 3 but for Pu isotopes.