From “strong-field atomic physics” to “strong-field nuclear physics”
Authors: Wang Xu ,   Graduate School, China Academy of Engineering Physics, Beijing 100193, China,   Southern Center for Nuclear-Science Theory, Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China
Published: November 2024

<sec>In the mid-1980s, chirped pulse amplification (Nobel Prize in Physics 2018) broke through previous limits to laser intensity, allowing intensities to exceed the atomic unit threshold (1 atomic unit of laser intensity corresponds to a power density of 3.5×10<sup>16</sup> W/cm<sup>2</sup>). These strong laser fields can cause high-order nonlinear responses in atoms and molecules, resulting in a series of novel phenomena, among which high-order harmonic generation and attosecond pulse generation (Nobel Prize in Physics 2023) are particularly important. With the development of high-power laser technology, laser intensity has now reached the order of 10<sup>23</sup> W/cm<sup>2</sup> and is constantly increasing. Now, a fundamental question has been raised: can such a powerful laser field induce similar high-order nonlinear responses in atomic nuclei, potentially transitioning “strong-field atomic physics” into “strong-field nuclear physics”?</sec><sec>To explore this, we investigate a dimensionless parameter that estimates the strength of light-matter interaction: <inline-formula><tex-math id="M1">\begin{document}$ \eta = D{E_0}/{{\Delta }}E $\end{document}</tex-math></inline-formula>, where <i>D</i> is the transition moment (between two representative levels of the system), <i>E</i><sub>0</sub> is the laser field amplitude, <i>DE</i><sub>0</sub> quantifies the laser-matter interaction energy, and Δ<i>E</i> is the transition energy. If <inline-formula><tex-math id="M2">\begin{document}$ \eta \ll 1 $\end{document}</tex-math></inline-formula>, the interaction is within the linear, perturbative regime. However, when <inline-formula><tex-math id="M3">\begin{document}$ \eta \sim 1 $\end{document}</tex-math></inline-formula>, highly nonlinear responses are anticipated. For laser-atom interactions, <i>D</i> ~ 1 a.u. and Δ<i>E</i> = 1 a.u., so if <i>E</i><sub>0</sub> ~ 1 a.u., then <inline-formula><tex-math id="M4">\begin{document}$ \eta \sim 1 $\end{document}</tex-math></inline-formula> and highly nonlinear responses are initiated, leading to the above-mentioned strong-field phenomena.</sec><sec>In the case of light-nucleus interaction, it is typical that <inline-formula><tex-math id="M5">\begin{document}$ \eta \ll 1 $\end{document}</tex-math></inline-formula>. When considering nuclei instead of atoms, <i>D</i> becomes several (~5 to 7) orders of magnitude smaller, while Δ<i>E</i> becomes several (~5) orders of magnitude larger. Consequently, the laser field amplitude <i>E</i><sub>0</sub> will need to be 10 orders of magnitude higher, or the laser intensity needs to be 20 orders of magnitude higher (~ 10<sup>36</sup> W/cm<sup>2</sup>), which is beyond existing technological limit and even exceeds the Schwinger limit, where vacuum breakdown occurs.</sec><sec>However, there exist special nuclei with exceptional properties. For instance, the <sup>229</sup>Th nucleus has a uniquely low-lying excited state with an energy value of only 8.4 eV, or 0.3 a.u. This unusually low transition energy significantly increases <i>η</i>. This transition has also been proposed for building nuclear clocks, which have potential advantages over existing atomic clocks.</sec><sec>Another key factor is nuclear hyperfine mixing (NHM). An electron, particularly the one in an inner orbital, can generate a strong electromagnetic field at the position of the nucleus, leading to the mixing of nuclear eigenstates. For <sup>229</sup>Th, this NHM effect is especially pronounced: the lifetime of the 8.4-eV nuclear isomeric state in a bare <sup>229</sup>Th nucleus (<sup>229</sup>Th<sup>90+</sup>) is on the order of 10<sup>3</sup> s, while in the hydrogenlike ionic state (<sup>229</sup>Th<sup>89+</sup>) it decreases by five orders of magnitude to 10<sup>–2</sup> s. This 1s electron greatly affects the properties of the <sup>229</sup>Th nucleus, effectively changing the nuclear transition moment from <i>D</i> for the bare nucleus to <inline-formula><tex-math id="M6">\begin{document}$ D' = D + b{\mu _{\text{e}}} $\end{document}</tex-math></inline-formula> for the hydrogenlike ion, where <i>D</i> ~ 10<sup>–7</sup> a.u., <inline-formula><tex-math id="M7">\begin{document}$ b \approx 0.03 $\end{document}</tex-math></inline-formula> is the mixing coefficient, <inline-formula><tex-math id="M8">\begin{document}$ {\mu _{\text{e}}} $\end{document}</tex-math></inline-formula> is the magnetic moment of the electron, and <inline-formula><tex-math id="M9">\begin{document}$ D'\approx b\mu_{\text{e}}\sim10^{-4}\ \text{a}\text{.u}. $\end{document}</tex-math></inline-formula> That is to say, the existence of the 1s electron increases the light-nucleus coupling matrix element by approximately three orders of magnitude, leading to the five-orders-of-magnitude reduction in the isomeric lifetime.</sec><sec>With the minimized transition energy Δ<i>E</i> and the NHM-enhanced transition moment <i>D'</i>, it is found that <inline-formula><tex-math id="M10">\begin{document}$ \eta \sim 1 $\end{document}</tex-math></inline-formula> for currently achievable laser intensities. Highly nonlinear responses are expected in the <sup>229</sup>Th nucleus. This is confirmed by our numerical results. Highly efficient nuclear isomeric excitation can be achieved: an excitation probability of over 10% is achieved per nucleus per femtosecond laser pulse at a laser intensity of 10<sup>21</sup> W/cm<sup>2</sup>. Correspondingly, the intense laser-driven <sup>229</sup>Th<sup>89+</sup> system emits secondary light in the form of high harmonics, which share similarities with those from laser-driven atoms but also have different features.</sec><sec>In conclusion, it appears feasible to extend “strong-field atomic physics” to “strong-field nuclear physics”, at least in the case of <sup>229</sup>Th. “Strong-field nuclear physics” is emerging as a new frontier in light-matter interaction and nuclear physics, providing opportunities for precisely exciting and controlling atomic nuclei with intense lasers and new avenues for coherent light emission based on nuclear transitions.</sec>