Nonperturbative analysis of nuclear shape effects on the bound electron g factor

Abstract

The theory of the g factor of an electron bound to a deformed nucleus is considered nonperturbatively and results are presented for a wide range of nuclei with charge numbers from Z=16 up to Z=98. We calculate the nuclear deformation correction to the bound electron g factor within a numerical approach and reveal a sizable difference compared to previous state-of-the-art analytical calculations. We also note particularly low values in the region of filled proton or neutron shells, and thus a reflection of the nuclear shell structure both in the charge and neutron number. PACS numbers: 31.30.js, 21.10.FtThe electron's g factor characterizes its magnetic moment in terms of its angular momentum. For an electron bound to an atomic nucleus, the g factor can be predicted in the framework of bound state quantum electrodynamics (QED) as well as measured in Penning traps, both with a very high degree of accuracy. This enables extraction of information on fundamental interactions, constants and nuclear structure. For example, the combination of theory and precise measurements of the bound electron g factor has recently provided an enhanced value for the electron mass [1], and bound state QED in strong fields was tested with unprecedented precision [2][3][4][5]. It also enables measurement on characteristics of nuclei such as electric charge radii, as shown for Si 13+ ion [6], or the isotopic mass difference as demonstrated for 48 Ca and 40 Ca in [7], or, as proposed theoretically, magnetic moments [8]. Also, it was argued that g-factor experiments with heavy ions could result in a value for the fine-structure constant which is more accurate than the presently established one [9]. With planned experiments involving high Z nuclei [10,11] and current experimental accuracies on the 10 −10 level for low Z, it is important to keep track also of higher order effects. In this context, the influence of nuclear size and deformation is critical. In [12], the nuclear shape correction to the bound electron g factor was introduced and calculated for spinless nuclei using the perturbative effective radius method [13,14]. This effect takes the influence of a deformed nuclear charge distribution into account, and changes the g factor on a 10 −6 level for heavy nuclei, thus being potentially visible in future experiments. Therefore, a comparison of experiment and theory for heavy nuclei demands a critical scrutiny of the validity of the previously used perturbative methods, as pointed out in [15].In this paper, we present non-perturbative calculations of the nuclear deformation correction to the bound electron g factor and show the corresponding values for nuclei across the entire nuclear chart, quantifying the nonperturbative corrections and especially observing the appearance of nuclear shell closure effects in the values of the bound electron g factor.Relativistic units with =c=1 are used throughout this work, as well as the Heavyside unit of charge with α=e 2 /4π, where α is the fine structure constant and the elementary charge e is neg...

Access to the Kaon Radius with Kaonic Atoms

“…Then, the FNS effect has be calculated using tabulated nuclear data [ 40 ] for root‐mean‐square radius values, with a Fermi or even with a deformed Fermi nuclear potential, [ 28,41 ] or with more realistic predictions based on the Skyrme‐type nuclear potential, [ 42 ] not forgetting about the nuclear deformation correction. [ 38 ] There is room for an improvement in the evaluation of the FKS effect as well, from a simple two‐sphere model to a more sophisticated and realistic one. The higher‐order QED effects, such as self‐energy, Wichmann–Kroll, Källén–Sabry, muonic and hadronic Uehling potentials [ 16,41,43 ] should be also included.…”

“…[ 36 ] For kaonic atoms the FNS correction has a much stronger impact, and therefore one should take into account also higher‐order terms in $$\alpha Z$$ (see, e.g., refs. [37, 38]). As an outcome, the sensitivity coefficients depend significantly on the specific ion and transition, and can vary considerably.…”

Skyrme-type nuclear interaction as a tool for calculating the finite nuclear size correction to atomic energy levels and the bound-electron $g$ factor

“…Hence, in order to perform more precise calculations of the FNS correction, it is necessary to use a more realistic nuclear-structure description and go beyond the simple Fermi model. As for other nuclear-structure corrections, we note that significant improvements in the evaluation of nuclear deformation and nuclear polarization effects have been made in recent years [30][31][32][33][34].…”

Tests of physics beyond the Standard Model with single-electron ions

“…Since the leading-order finite nuclear size correction cancels out in the reduced g factor, the total finite nuclear size correction, which can be calculated numerically, following, for instance, the method developed in Refs. [35][36][37][38], is synonymous with the higher-order finite nuclear size correction. The uncertainty on this contribution is dominated by that on the nuclear radius, and was estimated for various H-like ions in Ref.…”