Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory

Towards Precision Muonic X-ray Measurements of Charge Radii of Light Nuclei

“…Accordingly, once the experimental accuracy of the transition energies is improved, the uncertainty in δE TPE and higher-order nuclear structure contributions [29] is expected to dominate the derived radii. Based on the calculations for the lightest nuclei (see [28] and references therein), preliminary results for 6,7 Li [83] and the recent studies on heavier systems [84], we estimate that a 5 to 10% uncertainty in the calculated δE TPE is achievable, resulting in an absolute radii with an accuracy of the order of a few times 10 −4 , similar to that for the neighboring nuclei (see Table 1). Further calculations for the nuclei of interest are in progress.…”

“…Measuring ∆r mir can thus contribute to the understanding of the variations in neutron skin with isospin, while any deviations from a linearity would indicate the role that continuum degrees of freedom play in exotic nuclei structure evolution. Light mirror pairs such as 7 Li-7 Be and 8 Li-8 B possess a large isospin asymmetry and are, hence, well-suited to testing these theoretical predictions. Differences in radii were measured with the optical isotope shifts in the Li [36,49,50] and Be [51] chains, while the measurement of 8 B [61] is ongoing.…”

“…Precise nuclear radii are needed to disentangle potentially missing QED contributions as a function of Z. To illustrate this point, let us consider 2 3 S 1 − 2 3 P j transitions in 7 Li + . Their hyperfine-averaged value was determined to within 0.4 MHz [65].…”

“…Due to the heavy mass of muons (m µ ∼ 200 m e , with m e the electron mass), the Bohr radius of muonic atoms is approximately 200 times smaller than that of electronic atoms, and thus, for low angular momentum states, the muon wavefunction has a 200 3 ≈ 10 6 times larger overlap with that of the nucleus. The nuclear properties thus lead to measurable shifts in the atomic transition energies, making muonic atom spectroscopy an effective probe of phenomena such as finite nuclear size effects [1][2][3][4][5][6][7], relativistic QED (quantum electrodynamics) contributions [4,[7][8][9], and possible short-range interactions carried by new mediators [10][11][12][13][14][15][16]. These systems are particularly well-suited to accurately determining the RMS (root mean squre) nuclear charge radius (the slope of the Sachs form factor at small momentum transfer, henceforth called 'radius' for brevity), which can be obtained using the spectroscopy of low-lying radiative transitions (mostly 2P − 1S) [1,17,18].…”

Nuclear recoil correction to the hyperfine splitting in atomic systems

“…( 6), and it can be used for analytic derivation of the Z α expansion or for direct numerical calculation. In view of the planned hyperfine splitting measurements in muonic atoms [12], this nonperturbative numerical calculation of E hfsrec would be helpful in interpretation of the measured hfs in terms of the nuclear magnetization distribution. The accurate recoil corrections to hfs are important also in view of significant disagreements for µD [13] and 6 Li [14][15][16] measured values.…”