Nuclear polarization corrections to the μ4He+ Lamb shift.

Area of Science:

• Atomic Physics
• Nuclear Physics
• Quantum Electrodynamics

Background:

• The proton radius conundrum highlights discrepancies in measurements of the proton's size.
• Precise Lamb shift measurements in light muonic atoms are essential for resolving this puzzle.
• Nuclear polarization corrections are a key limiting factor in extracting precise charge radii.

Purpose of the Study:

• To perform an ab initio calculation of nuclear polarization for the muonic helium-4 ion (μ(4)He(+)).
• To reduce uncertainties in Lamb shift measurements for μ(4)He(+).
• To provide crucial theoretical data for upcoming experimental measurements at PSI.

Main Methods:

• Employed ab initio few-body methods, specifically the Lorentz integral transform with hyperspherical harmonics expansion.
• Utilized two distinct state-of-the-art nuclear Hamiltonians.
• Included leading multipole contributions, Coulomb, relativistic, and finite-nucleon-size corrections.

Main Results:

• Calculated the nuclear polarization energy correction for 2S-2P transitions in μ(4)He(+) as δ(pol)(A)=-2.47 meV ±6%.
• Significantly reduced the uncertainty compared to previous estimates.
• Identified the nuclear Hamiltonian as the primary source of remaining uncertainty.

Conclusions:

• The calculated nuclear polarization provides a more accurate theoretical value for μ(4)He(+).
• This result is instrumental for the planned μ(4)He(+) Lamb shift experiment.
• Further improvements in nuclear Hamiltonians are needed to enhance accuracy.