Search results for "LAMB SHIFT"
showing 10 items of 35 documents
Theory of the n = 2 levels in muonic helium-3 ions
2017
The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several 2S → 2P transition frequencies in the muonic helium-3 ion, μ3He+. This ion is the bound state of a single negative muon μ- and a bare helium-3 nucleus (helion), 3He++. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting. These values are essential for the determination of the helion rms charge radiu…
Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
2020
We merge the dispersive relation approach and the ab initio method to compute nuclear structure corrections to the Lamb shift in muonic deuterium. We calculate the deuteron response functions and corresponding uncertainties up to next-to-next-to-next-to-leading order in chiral effective field theory and compare our results to selected electromagnetic data to test the validity of the theory. We then feed response functions calculated over a wide range of kinematics to the dispersion-theory formalism and show that an improved accuracy is obtained compared to that with the use of available experimental data in the dispersive analysis. This opens up the possibility of applying this hybrid metho…
Muonic Lithium atoms: nuclear structure corrections to the Lamb shift
2019
In view of the future plans to measure the Lamb shift in muonic Lithium atoms we address the microscopic theory of the $\mu$-$^6$Li$^{2+}$ and $\mu$-$^7$Li$^{2+}$ systems. The goal of the CREMA collaboration is to measure the Lamb shift to extract the charge radius with high precision and compare it to electron scattering data or atomic spectroscopy to see if interesting puzzles, such as the proton and deuteron radius puzzles, arise. For this experiment to be successful, theoretical information on the nuclear structure corrections to the Lamb shift is needed. For $\mu$-$^6$Li$^{2+}$ and $\mu$-$^7$Li$^{2+}$ there exist only estimates of nuclear structure corrections based on experimental dat…
THE STRUCTURE OF THE NUCLEONS
1980
Electron-proton and electron-deuteron scattering experiments in a wide four momentum range provide information about the structure of the proton and the neutron. The structure is a direct consequence of the hadronic interaction of the nucleon and reveals properties of the strong interaction. Absolute differential cross sections can be expressed in terms of electromagnetic form factors which lead to an understanding of the coupling mechanism between the electromagnetic field and the strongly interacting hadron. The structure can also be discussed in terms of charge densities, but this analysis is strongly restricted by recoil effects. The charge rms radius extracted from recent measurements …
Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution
2015
We quantify a limitation in the usual accounting of the finite-size effects, where the leading $[(Z\alpha)^4]$ and subleading $[(Z\alpha)^5]$ contributions to the Lamb shift are given by the mean-square radius and the third Zemach moment of the charge distribution. In the presence of any non-smooth behaviour of the nuclear form factor at scales comparable to the inverse Bohr radius, the expansion of the Lamb shift in the moments breaks down. This is relevant for some of the explanations of the "proton size puzzle". We find, for instance, that the de R\'ujula toy model of the proton form factor does not resolve the puzzle as claimed, despite the large value of the third Zemach moment. Withou…
Nuclear structure contribution to the Lamb shift in muonic deuterium
2013
We consider the two-photon exchange contribution to the $2P-2S$ Lamb shift in muonic deuterium in the framework of forward dispersion relations. The dispersion integrals are evaluated using experimental data on elastic deuteron form factors and inelastic electron-deuteron scattering, both in the quasielastic and hadronic range. The subtraction constant that is required to ensure convergence of the dispersion relation for the forward Compton amplitude $T_1(\nu,Q^2)$ is related to the deuteron magnetic polarizability $\beta(Q^2)$. Based on phenomenological information, we obtain for the Lamb shift $\Delta E_{2P-2S}=2.01\pm0.74$ meV. The main source of the uncertainty of the dispersion analysi…
Ab initio calculation of nuclear structure corrections in muonic atoms
2018
The measurement of the Lamb shift in muonic hydrogen and the subsequent emergence of the proton-radius puzzle have motivated an experimental campaign devoted to measuring the Lamb shift in other light muonic atoms, such as muonic deuterium and helium. For these systems it has been shown that two-photon exchange nuclear structure corrections are the largest source of uncertainty and consequently the bottleneck for exploiting the experimental precision to extract the nuclear charge radius. Utilizing techniques and methods developed to study electromagnetic reactions in light nuclei, recent calculations of nuclear structure corrections to the muonic Lamb shift have reached unprecedented precis…
The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties
2018
To shed light on the deuteron radius puzzle we analyze the theoretical uncertainties of the nuclear structure corrections to the Lamb shift in muonic deuterium. We find that the discrepancy between the calculated two-photon exchange correction and the corresponding experimentally inferred value by Pohl et al. [1] remain. The present result is consistent with our previous estimate, although the discrepancy is reduced from 2.6 $\sigma$ to 2 $\sigma$. The error analysis includes statistic as well as systematic uncertainties stemming from the use of nucleon-nucleon interactions derived from chiral effective field theory at various orders. We therefore conclude that nuclear theory uncertainty is…
The RMS charge radius of the proton and Zemach moments
2010
On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al.. De Rujula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.
Nucleon polarizabilities: From Compton scattering to hydrogen atom
2016
We review the current state of knowledge of the nucleon polarizabilities and of their role in nucleon Compton scattering and in hydrogen spectrum. We discuss the basic concepts, the recent lattice QCD calculations and advances in chiral effective-field theory. On the experimental side, we review the ongoing programs aimed to measure the nucleon (scalar and spin) polarizabilities via the Compton scattering processes, with real and virtual photons. A great part of the review is devoted to the general constraints based on unitarity, causality, discrete and continuous symmetries, which result in model-independent relations involving nucleon polarizabilities. We (re-)derive a variety of such rel…