Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

Abstract

We provide an up to date summary of the theory contributions to the 2S → 2P Lamb shift and the fine structure of the 2P state in the muonic helium ion (µ 4 He) + . This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the 3 He-4 He isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of n = 2 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.

Precision spectroscopy of helium in a magic wavelength optical dipole trap

“…In the immediate future, we aim to improve the measurement of the 2 3 S 1,F =3/2 → 2 1 S 0,F =1/2 transition in 3 He, which may bring the uncertainty on δr 2 down to < 0.002 fm 2 . This is actually better than the expected accuracy from muonic helium, which will be limited to 0.0031 fm 2 because of theoretical uncertainty in calculating the two-photon exchange contribution to the Lamb shift [48].…”

Vacuum polarization corrections to the n=2 and n=3 levels in muonic HeRepko1, Radford2, Dicus3 2020Phys. Rev. D0000View full textAdd to dashboardCite

“…The result for helium with r N = 1.681 ± 0.004 fm [13] is given in Table I. There is very little dependence on the power of the form factor, but the correction is of order r N /a and its coefficient could be introduced as a parameter.…”

“…The case of muonic 4 He is considerably simpler since the nucleus is spinless and there is only one nuclear form factor and a single spin [12,13]. The underlying potential that describes a muon interacting with a point nucleus is…”

Paving the way for fundamental physics tests with singly-ionized helium

“…However, the CREMA collaboration has performed a more precise measurement of r α in muonic helium which is expected to be published soon. Since the nuclear charge radius extracted from muonic helium will be strongly limited by theory (mainly due to the nuclear polarizability contribution), we can use the theory uncertainty of r α of 0.0008 fm [16] to estimate the effect on the uncertainty of the 1S-2S transition frequency in He + , which then yields an uncertainty of about 60 kHz. An improvement on the calculation of the nuclear polarizability in muonic helium will result in a direct reduction of this uncertainty.…”