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

Abstract

Metastable pionic helium (πHe + ) is a three-body atom composed of a helium nucleus, an electron occupying the 1s ground state, and a negatively charged pion π − in a Rydberg state with principaland orbital angular momentum quantum numbers of n ∼ ℓ + 1 ∼ 16. We calculate the spinindependent energies of the π 3 He + and π 4 He + isotopes in the region n = 15-19. These include relativistic and quantum electrodynamics corrections of orders R∞α 2 and R∞α 3 in atomic units, where R∞ and α 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 π − , and the radiative and Auger decay rates of the states are also calculated. Some states (n, ℓ) = (16, 15) and (17, 16) retain nanosecond-scale lifetimes against π − absorption into the helium nucleus. We propose to use laser pulses to induce π − transitions from these metastable states, to states with large (∼ 10 11 s −1 ) Auger rates. The πHe 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 π − . 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. A resonance curve is obtained from which the πHe + transition frequency can in principle be determined with a fractional precision of 10 −8 − 10 −6 provided that the systematic uncertainties can be controlled. By comparing the measured πHe + frequencies with the calculated values, the π − mass may be determined with a similar precision. The πHe + will be synthesized by allowing a high-intensity (> 10 8 s −1 ) beam of π − produced by a cyclotron to come to rest in a helium target. The precise time structure of the π − beam is used to ensure a sufficient rate of coincidence between the resonant laser pulses and the πHe + atoms.

Attempt at laser spectroscopy of pionic helium atoms at PSI

“…Nothing is experimentally known about the n and ℓ distribution of states which may be formed, and no atomic lines of πHe + have been detected so far. The lifetimes of some πHe + states calculated recently [1] using the complex-coordinate rotation method appear to differ by 1-2 orders of magnitude from earlier estimations made in the 1960's. Several assumptions are needed to design the laser spectroscopy experiment.…”

“…The width of this profile is predominantly caused by the Auger decay rate of the resonance daughter state (17,14), and the 14-GHz spacing between the fine structure sublines that arise from the interaction between the electron spin and the orbital angular momentum of the π − . Simulations [1] indicate that the centroid of this profile can in principle be determined with a precision of < 1 GHz, which corresponds to a fractional precision of better than ∼ 1 × 10 −6 on the πHe + transition frequency ν exp . Other laser transitions, e.g., (17, 16)→ (16,15) between metastable states are predicted to have resonance lineshapes that are much narrower.…”

“…The Rydberg πHe 2+ ion that remains after Auger decay undergoes Stark mixing with s, p, and d states (see Ref. [1] and references therein) during collisions with the helium atoms in the experimental target. As these low-ℓ states have a large overlap with the helium nucleus, the π − undergoes nuclear absorption within picoseconds.…”

“…The precise time structure of this π − beam allows the formation of πHe + to be synchronized to the arrival of the resonant laser pulses at the target [1]. The 1-ns-long laser pulses of wavelength λ = 383.8 nm will be generated by a frequency-doubled hybrid dye/Ti:Sapphire laser which is pumped by a diodepumped solid-state (DPSS) Nd:YAG laser.…”

“…The PiHe collaboration of PSI is currently attempting to carry out laser spectroscopy [1] of metastable pionic helium (πHe…”