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Register a new userLamb shift in muonic ions of lithium, beryllium and boron
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Added by
Alexei P. Martynenko
Publication date
2016
fields
Physics
and research's language is
English
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We present a precise calculation of the Lamb shift $(2P_{1/2}-2S_{1/2})$ in muonic ions $(mu ^6_3Li)^{2+},~(mu ^7_3Li)^{2+}$, $(mu ^9_4Be)^{3+},~(mu ^{10}_4Be)^{3+}$, $(mu ^{10}_5B)^{4+},~(mu ^{11}_5B)^{4+}$. The contributions of orders $alpha^3divalpha^6$ to the vacuum polarization, nuclear structure and recoil, relativistic effects are taken into account. Our numerical results are consistent with previous calculations and improve them due to account of new corrections. The obtained results can be used for the comparison with future experimental data, and extraction more accurate values of nuclear charge radii.
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We make precise calculation of hyperfine structure of $S$-states in muonic ions of lithium, beryllium and boron in quantum electrodynamics. Corrections of orders $alpha^5$ and $alpha^6$ due to the vacuum polarization, nuclear structure and recoil in first and second orders of perturbation theory are taken into account. We obtain estimates of the total values of hyperfine splittings which can be used for a comparison with future experimental data.
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 $(mathrm{mu^4He})^+$. 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 $mathrm{^3He-^4He}$ 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.
We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic deuterium (mu d) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure and recoil effects are calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.
The measurement of the 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition in muonic hydrogen by Pohl et al. and subsequent analysis has led to the conclusion that the rms radius of the proton differs from the accepted (CODATA) value by approximately 4%, corresponding to a 4.9 sigma discrepancy. We investigate the finite-size effects - in particular the dependence on the shape of the proton electric form-factor - relevant to this transition using bound-state QED with nonperturbative, relativistic Dirac wave-functions for a wide range of idealised charge-distributions and a parameterization of experimental data in order to comment on the extent to which the perturbation-theory analysis which leads to the above conclusion can be confirmed. We find no statistically significant dependence of this correction on the shape of the proton form-factor.
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 data that suffer from very large uncertainties. We present the first steps towards an ab initio computation of these quantities using few-body techniques.
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