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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., Comment: Submission to SciPost, 10 pages, 4 figure, Proceedins of the 24th European conference on few-body problems in physics (EFB24) at the University of Surrey, Guildford, United Kingdom, from 2 to 6 September 2019

We analyse the Coulomb breakup of 19C measured at 67A MeV at RIKEN. We use the Coulomb-Corrected Eikonal (CCE) approximation to model the reaction and describe the one-neutron halo nucleus 19C within Halo Effective Field Theory (EFT). At leading order we obtain a fair reproduction of the measured cross section as a function of energy and angle. The description is insensitive to the choice of optical potential, as long as it accurately represents the size of 18C. It is also insensitive to the interior of the 19C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of 19C: these data put constraints on the one-neutron separation energy of this nucleus and, for a given binding energy, can be used to extract an asymptotic normalisation coefficient (ANC). These results are confirmed by CCE calculations employing next-to-leading order Halo EFT descriptions of 19C: at this order the results for the Coulomb breakup cross section are completely insensitive to the choice of the regulator. Accordingly, this reaction can be used to constrain the one-neutron separation energy and ANC of 19C., 19 pages, 5 figures