$\alpha$ decay in intense laser fields: Calculations using realistic nuclear potentials

We calculate the effect of intense laser fields on nuclear $\alpha$ decay processes, using realistic and quantitative nuclear potentials. We show that $\alpha$ decay rates can indeed be modified by strong laser fields to some finite extent. We also predict that $\alpha$ decays with lower decay energies are relatively easier to be modified than those with higher decay energies, due to longer tunneling paths for the laser field to act on. Furthermore, we predict that modifications to angle-resolved penetrability are easier to achieve than modifications to angle-integrated penetrability.

Figure 1

Potentials between the $\alpha$ particle and the daughter nucleus, including the Igo $\alpha$-nucleus potential and the Coulomb potential, for three nuclear elements (a) ${}^{144}\mathrm{Nd}$, (b) ${}^{224}\mathrm{Ra}$, and (c) ${}^{212}\mathrm{Po}$. The red horizontal line in each panel is the corresponding $\alpha$ decay energy $Q$, the intersections of which with the potential energy curve give the tunneling entrance point $R_{\mathrm{in}}$ and the tunneling exit point $R_{\mathrm{out}}$.

Figure 2

Time-dependent modifications to the $\alpha$ particle penetrability, seen from three spatial angles, namely, $\theta =0^{\circ }$ (red solid), ${45}^{\circ }$ (blue dashed), and ${90}^{\circ }$ (black dash dotted). The same three nuclear elements are used as in Fig. 1. The peak intensity used is ${10}^{24}$ W/${\mathrm{cm}}^2$ for all three elements.

Figure 3

Relative changes of the penetrability $P$ seen from $\theta =0^{\circ }$ and from $\theta ={180}^{\circ }$, for three different laser intensities, namely, ${10}^{24}$ W/${\mathrm{cm}}^2$ (a), ${10}^{26}$ W/${\mathrm{cm}}^2$ (b), and ${10}^{28}$ W/${\mathrm{cm}}^2$ (c). The nuclear element used here is ${}^{144}\mathrm{Nd}$. Positive-negative asymmetry between $0^{\circ }$ and ${180}^{\circ }$ can be more clearly seen from the sum of the two, as shown by the thick black curve in each panel.

Figure 4

Angle-resolved (red squares) and angle-integrated (blue circles) modifications to the $\alpha$ decay penetrability, as a function of laser intensity. Both $\mathrm{\Delta }$ and the intensity $I$ are plotted in the logarithmic scale, with which both curves are linear. The red (square) curves have slope 0.5, due to a linear dependency on the laser field strength. The blue (circle) curves have slope 1.0, due to a quadratic dependency on the laser field strength.

Figure 5

(a) An elliptically polarized laser field $E\left(t\right)$ rotates along the polarization ellipse. (b) Asymptotic velocity distribution of the emitted $\alpha$ particle without (dashed circle) and with (solid grey circle) the laser field. With the laser field, the position of the circle will be shifted and the distribution over the circle will no longer be uniform. (c) Simulated $\alpha$ particle velocity distribution using a trapezoidal laser pulse. The velocities are in atomic units and the color scale is in arbitrary units. (d) Difference in the velocity distribution if there are no modifications to the penetrability. The color-scale units are the same as in (c).