Three-body Coulomb description of pionic helium

Abstract

The three-body Schrödinger equation of the system composed of an α particle He 2+ , a negatively charged pion π − , and an electron interacting through Coulomb forces is solved in perimetric coordinates with the Lagrangemesh method. The ground state, quasibound states, and resonances are obtained for total orbital momenta L = 0 − 20. Mean distances between the particles allow for identifying the structure of these states. The widths of resonances broader than 10 −5 atomic units are derived with the complex scaling method. A transition from atomic to molecular structure occurs between L = 10 and L = 13. Excited levels obtained for L = 0 − 5 display hydrogenlike properties for both the α-pion system and the electron excitations. Excited levels with L 14 correspond to a vibrational excitation of the relative motion of the heavy particles. The validity of the Born-Oppenheimer approximation is found to be fair over the whole range of total orbital momenta.

Laser spectroscopy of three-body antiprotonic and pionic helium atoms at CERN and PSI

“…The PiHe collaboration at PSI recently carried out laser spectroscopy of the analogous pionic helium atom ( 4 He + ≡ − + 4 He 2+ + − ) [18][19][20][21][22]. In this three-body system, a negatively-charged pion occupies a highly excited state with ≈ ℓ + 1 ≈ 17.…”

Laser spectroscopy of long-lived pionic and antiprotonic helium in superfluid helium

“…The PiHe collaboration carried out laser spectroscopy of three-body pionic helium atoms (𝜋 4 He + ≡ 𝜋 − + 4 He 2+ + 𝑒 − ) [1][2][3][4][5][6] at the 590 MeV cyclotron facility of the Paul Scherrer Institute.…”

Recent progress of laser spectroscopy measurements of pionic helium

“…Metastable pionic helium atoms (π 4 He + ≡ π − + 4 He 2+ +e − ) [1][2][3][4][5] consist of a helium nucleus, an electron in the ground state, and a negatively-charged pion in a state with high principal and orbital angular momentum quantum numbers n ≈ + 1 ≈ 16. Atoms populating such states possess nanosecond-scale lifetimes against π − nuclear absorption because the pionic orbitals have very small overlap with the helium nucleus.…”