Semiclassical description of X-ray laser induced $\alpha$-emission in odd-$A$ nuclei

Abstract: In this work, we present a theoretical study of X-ray laser-assisted $\alpha$-decay in odd-$A$ nuclei within a semiclassical framework. The interaction of the emitted $\alpha$-particle with an intense X-ray laser field is incorporated through a multiphoton absorption process, leading to the emergence of a discrete set of $\alpha$-particle's energy states. Our results reveal that such fields enhance the $\alpha$-particle's penetration probability ($\Delta P_{\mathrm{rel}}$) through the barrier to a considerable extent, exhibiting a strong dependence on the laser intensity ($I_0$) and the intrinsic nuclear structure. We propose an analytical expression relating the $\Delta P_{\mathrm{rel}}$-values to properties of the $\alpha$-radioactive parent nucleus, thereby providing a predictive framework for the laser-induced modifications. For instance, $^{247}$Cm-nucleus exhibits a relative enhancement in penetration probability of the order of $10^{-2}$\% with current laser facilities of intensity of $10^{23}$ W/cm $^2$, which can exceed more than 100\% with more intense laser fields ( $I_0 \sim$ $10^{27}$ W / cm $^2$). Furthermore, the relative changes in $\alpha$-decay half-lives ($\Delta T_{\mathrm{rel}}$) are found to be in negative correlation with $\Delta P_{\mathrm{rel}}$-values. Overall, this work establishes a theoretical basis for future experimental investigations of laser-assisted $\alpha$-radioactivity.