Metastable pionic helium ($\pi{ \rm He}^+$) 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 $\pi{ \rm ^3He}^+$ and $\pi{ \rm ^4He}^+$ 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 $\pi{ \rm He}^{ 2+}$ 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)
Categories: physics.atom-ph hep-ex hep-ph nucl-ex nucl-th