The study on high <i>n</i> Rydberg state of La II
Authors: Li Xiao-Kang , Jia Feng-Dong , Yu Fang-Chen , Li Ming-Yang , Xue Ping , Xu Xiang-Yuan , Zhong Zhi-Ping ,   College of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China,   Collaborative Innovation Center of Quantum Matter, State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China,   Department of Physics, Capital Normal University, Beijing 100037, China,   CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
Published: December 2020

We analyze ionic spectrum of lanthanum via intermediate state (Xe)<inline-formula><tex-math id="M191">\begin{document}$ 5d6d \; ^3F_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M191.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M191.png"/></alternatives></inline-formula> in the energy region 89872-91783 cm<sup>–1</sup>, and the spectrum is obtained using five-laser resonance excitation in combination with a method of sequential ionization by a pulsed electric field and a constant electric field, and has been recalibrate in this work. Both of one strong and one weak autoionization Rydberg series converging to the La<sup>2+</sup> state are determined. Meanwhile, the two autoionization Rydberg series are assigned by relativistic multichannel theory (RMCT) within the framework of multi-channel quantum defect theory (MQDT). More specifically, the strong autoionization Rydberg series is assigned to <inline-formula><tex-math id="M192">\begin{document}$ 5dnp\left(\dfrac{5}{2},\dfrac{1}{2}\right)_3 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M192.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M192.png"/></alternatives></inline-formula> and/or <inline-formula><tex-math id="M193">\begin{document}$ 5dnp\left(\dfrac{5}{2},\dfrac{1}{2}\right)_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M193.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M193.png"/></alternatives></inline-formula>, and the weak autoionization Rydberg series is assigned to <inline-formula><tex-math id="M194">\begin{document}$ 5dnf\left(\dfrac{5}{2},\dfrac{5}{2}\right)_3 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M194.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M194.png"/></alternatives></inline-formula> and/or <inline-formula><tex-math id="M195">\begin{document}$ 5dnf\left(\dfrac{5}{2},\dfrac{5}{2}\right)_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M195.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M195.png"/></alternatives></inline-formula>. We focus on the behavior of quantum defect with excitation energy for high <inline-formula><tex-math id="M196">\begin{document}$ n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M196.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M196.png"/></alternatives></inline-formula> Rydberg states, which are sensitive to the existence of a external field. We find the breakdown of quantum defect regular behavior for a specific Rydberg series and autoionization Rydberg series of La<sup>+</sup> as the effective quantum number <inline-formula><tex-math id="M197">\begin{document}$ n^\star>67 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M197.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M197.png"/></alternatives></inline-formula>. Due to that our calculations, which are obtained by relativistic multichannel theory and included configuration interactions, are in basically agreement with that for experimental low <inline-formula><tex-math id="M198">\begin{document}$ n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M198.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M198.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M199">\begin{document}$ n^\star<67 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M199.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M199.png"/></alternatives></inline-formula>) Rydberg states as well as small stray electric fields, we suggest that plasma formed by photoionization of La atoms in the second excitation step may be responsible for the breakdown of quantum defect regular behavior.