Theoretical study on spectroscopic properties of 10 Λ-S and 26 Ω states for AlH molecule
Authors: Xing Wei , Li Sheng-Zhou , Sun Jin-Feng , Cao Xu , Zhu Zun-Lue , Li Wen-Tao , Li Yue-Yi , Bai Chun-Xu ,   College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China,   School of Physics, Henan Normal University, Xinxiang 453000, China,   Weifang University of Science and Technology, Shouguang 262700, China
Published: June 2023

On the basis of correcting various errors caused by spin-orbit coupling effects, scalar relativity effects, core-valence correlation effects and basis set truncation, the potential energy curves of 10 Λ-S states and 26 Ω states of AlH molecule are calculated by using icMRCI + <i>Q</i> method. The transition dipole moments of 6 pairs of transitions between the <inline-formula><tex-math id="Z-20230730142000">\begin{document}${\rm X}{}^1\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142000.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142000.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="Z-20230730142022">\begin{document}$ {\rm a^3}{\Pi _{{0^ + }}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142022.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142022.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="Z-20230730142040">\begin{document}${\rm a^3}{\Pi _1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142040.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142040.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="Z-20230730142100">\begin{document}${\rm a^3}{\Pi _2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142100.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142100.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="Z-20230730142117">\begin{document}${\rm A^1}{\Pi _1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142117.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142117.png"/></alternatives></inline-formula> states are calculated by using the icMRCI/AV6Z* theory with the consideration of spin-orbit coupling effects. The spectral and transition data obtained here for AlH molecule are in very good agreement with the available experimental measurements. The findings are below. 1) The transition intensities are relatively strong of the Q(<i>J″</i>) branches for the (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4) and (1, 5) bands of the A<sup>1</sup>Π<sub>1</sub> – <inline-formula><tex-math id="Z-20230730142409">\begin{document}${\rm X}{}^1\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142409.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142409.png"/></alternatives></inline-formula> transition, with the increase of <i>J″</i>; the Einstein <i>A</i> coefficients and vibrational branching ratio gradually decrease, and the weighted absorption oscillator strength gradually increases of Δ<i>υ</i> = 0 band, the Einstein <i>A</i> coefficient, vibrational branching ratio, and weighted absorption oscillator strength gradually increase for the Δ<i>υ</i> ≠ 0 bands. 2) The radiation lifetimes of A<sup>1</sup>Π<sub>1</sub>(<i>υ'</i> = 0, 1) increases slowly as the <i>J'</i> increases. 3) The A<sup>1</sup>Π<sub>1</sub>(<i>υ'</i> = 0 and 1, <i>J'</i> = 1, +) →<inline-formula><tex-math id="Z-20230730142155">\begin{document}${\rm X}{}^1\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142155.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142155.png"/></alternatives></inline-formula>(<i>υ''</i> = 0–3, <i>J'</i>′ = 1, –) transition of AlH molecule satisfies the criteria for laser cooling of diatomic molecules, that is, the vibrational branching ratio of the highly diagonal distribution, the extremely short radiation lifetimes of the A<sup>1</sup>Π<sub>1</sub>(<i>υ'</i> = 0 and 1, <i>J'</i> = 1, +) states, and the intermediate electronic states <inline-formula><tex-math id="Z-20230730142244">\begin{document}$ {\rm a^3}{\Pi _{{0^ + }}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142244.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142244.png"/></alternatives></inline-formula>, a<sup>3</sup>Π<sub>1</sub>, and a<sup>3</sup>Π<sub>2</sub> do not interfere with laser cooling. Therefore, based on the cyclic transition A<sup>1</sup>Π<sub>1</sub>(<i>υ'</i> = 0 and 1, <i>J'</i> = 1, +) ↔ <inline-formula><tex-math id="Z-20230730142341">\begin{document}${\rm X}{}^1\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142341.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230615_Z-20230730142341.png"/></alternatives></inline-formula>(<i>υ'</i>′ = 0–3, <i>J''</i> = 1, –), we propose a feasible scheme for laser cooling of AlH molecule. When cooled, 2.541 × 10<sup>4</sup> photons can be scattered by four pump lasers used in the visible range, which are enough to cool AlH to the ultra-cold temperature, and the Doppler temperature and recoil temperature of the main transition are on the order of μK.