Hyperfine structure of muonic lithium ions

• Main Authors: Alexey P. Martynenko, Aleksandr A. Ulybin
• Format: Article
• Language: English
• Published: Samara State Technical University 2015-06-01
• Series: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
• Subjects: quantum electrodynamics; hyperfine splitting; quasipotential method
• Online Access: http://mi.mathnet.ru/eng/vsgtu1375

On the basis of perturbation theory in fine structure constant $\alpha$ and the ratio of electron to muon masses we calculate recoil corrections of order $\alpha^4 (M_e/M_\mu)$, $\alpha^4 (M_e/M_\mu)^2\ln(M_e/M_\mu)$, $\alpha^4 (M_e/M_\mu)^2$, $\alpha^5(m_e/m_\mu)\ln(m_e/m_\mu)$ to hyperfine splitting of the ground state in muonic lithium ions $(\mu e ^6_3\mathrm{Li})^+$ and $(\mu e ^7_3\mathrm{Li})^+$. We obtain total results for the ground state small hyperfine splittings in $(\mu e ^6_3\mathrm{Li})^+$ $\Delta\nu_1=14153.03$ MHz and $\Delta\nu_2=21571.26$ MHz and in $(\mu e ^7_3\mathrm{Li})^+$ $\Delta\nu_1=13991.97$ MHz and $\Delta\nu_2=21735.03$ MHz which can be considered as a reliable estimate for a comparison with future experimental data.