# N2: Accomplishments of the second funding period

Project N2 was submitted as a subsequent proposal in Summer 2017 and was funded starting from January 2018. During the first (not even completed) year of the grant, the following projects were accomplished.

• New analisys of the two-photon exhange correction in $$\mu$$-D
We have improved our calculations of two-photon exchange contributions to the Lamb shift of $$\mu$$-D by performing an analysis of statistical and systematic uncertainties related to the use of chiral effective field theory. We find that statistical uncertainties propagated through the low-energy constants are negligible, while systematic errors due to the cutoff dependence and the chiral convergence are below 1 %. This project is part of the PhD thesis of O. J. Hernandez, who will defend his thesis at the end of 2019. We are now working on an alternative expansion that will allow to compute the two-photon exchange corrections in a more precise way. We plan to submit this paper by the Summer of 2019.
• Review paper on muonic atoms
Being a leading group in the calculation of nuclear structure corrections with muonic atoms, we have been commissioned to write a review for Journal of Physics G: Particles and Nuclei. In this paper, we reviewed all of our computations and connected them to other theoretical methods and to the contemporary experimental issues raised by measurements in muonic and ordinary atoms.
• Electric dipole polarizablity of $$^{48}$$Ca and $$^{68}$$Ni
Using our newly developed many-body technology that allows to compute the electric polarizability $$\alpha_D$$ in coupled-cluster theory with the inclusion of high order correlations, such as triples corrections, we computed $$\alpha_D$$ for $$^{48}$$Ca. Compared to our previous computation that included less correlations, we find that triples corrections are necessary to reconcile the agreement with experimental data obtained from $$(p,p')$$ scattering. We are now extendig these studies to the neutron-rich nucleus of $$^{68}$$Ni, where we also find the effect of three-particle-three-holes correlations to be non negligible. The $$^{68}$$Ni calculations are part of the Charlie Payne's PhD studies. He just started his PhD and his defense is expected to take place during the third funding period. We plan to publish this first paper together with experimental colleagues from the Collapse collaboration at the beginning of 2019.
• Electromagnetic response functions in deuterium
In preparation for tackling neutrino-nucleus scattering, we have initiated a derivation of the electromagnetic responses in the deuteron. While the latter have been studied in the past, to the best of our knowledge, the convergence of the chiral effective field theory has never been looked at in detail, in particular for the transverse response function. B. Acharya has implemented all the electromagnetic operators up to next-to-next-to-leading order, including meson exchange currents, as part of his postdoc studies, see Fig N2.1. We plan to write a paper on this to be submitted during the first quarter of 2019. The next step, which has already been initiated, consists in extending the formalism to the axial response functions. Once these steps are done for a simple nucleus such as the deuteron, we will be prepared to implement the electro-weak operators in the many-body coupled-cluster codes and study heavier nuclei, such as $$^{16}$$O.

Figure N2.1 Double differential cross sections for electron scattering off the deuteron. Our prelimininary computations in impulse approximation and with meson exchange currents, in comparison with experimental data.

• Program/Workshop Organization
We organized a Program at the INT, from June 12 to July 13, 2018, on "Fundamental physics with electroweak probes of light nuclei''. It was attended by 82 scientists from 10 different countries and with a 20 % of female participants.
We also organized a local workshop in Mainz, October 1-3, 2018, on "Electromagnetic observables for low-energy nuclear physics''. It was attended by 40 participants, 18 % of whom were female. Several topics and possible observables to measure/calculate were discussed, which will help us shape the proposal for the third funding period.