Proposed method for laser spectroscopy of pionic helium atoms to determine the charged-pion mass

Abstract

Metastable pionic helium ($\pi {\mathrm{He}}^{+}$) is a three-body atom composed of a helium nucleus, an electron occupying the $1s$ ground state, and a negatively charged pion ${\pi }^{-}$ in a Rydberg state with principal- and orbital angular momentum quantum numbers of $n\sim \ell +1\sim 16$. We calculate the spin-independent energies of the $\pi {{}^3\mathrm{He}}^{+}$ and $\pi {{}^4\mathrm{He}}^{+}$ isotopes in the region $n=15$--19. These include relativistic and quantum electrodynamics corrections of orders $R_{\infty }{\alpha }^2$ and $R_{\infty }{\alpha }^3$ in atomic units, where $R_{\infty }$ and $\alpha$ denote the Rydberg and fine structure constants. The fine-structure splitting due to the coupling between the electron spin and the orbital angular momentum of the ${\pi }^{-}$, and the radiative and Auger decay rates of the states are also calculated. Some states $(n,\ell )=(16,15)$ and $(17,16)$ retain nanosecond-scale lifetimes against ${\pi }^{-}$ absorption into the helium nucleus. We propose to use laser pulses to induce ${\pi }^{-}$ transitions from these metastable states, to states with large ($\sim 10^{11}$ s${}^{-1}$) Auger rates. The $\pi {\mathrm{He}}^{2+}$ ion that remains after Auger emission of the $1s$ electron undergoes Stark mixing with the $s$, $p$, and $d$ states during collisions with the helium atoms in the experimental target. This leads to immediate nuclear absorption of the ${\pi }^{-}$. The resonance condition between the laser beam and the atom is thus revealed as a sharp spike in the rates of neutrons, protons, deuterons, and tritons that emerge....(continued)

Comments: 25 pages, 3 tables, 11 figures