The present project merges the former INFN project on few-body systems (FBS) with a part of the project on many-body physics (MANYBODY). The project consists of five units, the four FBS units (Lecce, Padova, Pisa and Trento) and two from MANYBODY merged in the Torino-Pavia unit; the intention is to optimize the theoretical resources discussing different aspects of atomic nuclei in a single project. Though the units collaborate in some cases, they produce independent work sharing common methodologies; the FBS units use ab-initio methods in the description of light nuclei, whereas the MANYBODY units have a long tradition in describing electromagnetic processes on medium and heavy nuclei, turning in the last years to describe neutrino-nucleus collisions. The study of the nucleus with electroweak probes is a common aspect of the present project. Most of the units investigate electron and photodisintegration, beta-decay and electron and neutrino scattering on light, medium and heavy nuclei. Moreover, the project includes applicative research in one of its units, using its background on coupled channel solutions, giving theoretical support to activities regarding the national programs for the production of innovative radionuclides and radiolabeled compounds for advanced medical therapies and diagnostics. All together, the project investigates structure, reactions and applications of the atomic nucleus.

The project takes inspiration from recent developments in the theoretical description of nuclei based on Effective Field Theory (EFT) for the construction of the nuclear interaction. The purpose is to provide a link to the underlying theory of strong interactions, Quantum Chromo-Dynamics (QCD), as the relevant degrees of freedom emerge, at least ideally, from a decimation process starting from fundamental quarks and gluons. At present the most widely used framework is the chiral EFT (ChEFT), based on the approximate chiral symmetry exhibited by QCD. The interactions of nucleons among themselves and with external electroweak probes (currents) are written as a perturbative expansion in powers of nucleon momenta and pion mass known as chiral perturbation theory (ChPT). Achievements of this scheme are the consistency between many-body forces and currents, and the possibility of implementing well defined procedures to estimate the theoretical errors produced by the truncation of the expansion. At present the ChEFT NN interactions have been constructed up to 5th order using NN scattering data as input. The progress in extending this approach to three- and many-body forces is slower due to complexities arising both in the chiral perturbative series and in the exact resolution of the quantum many-body problem.

Few-nucleon systems, studied with ab-initio methods, are a theoretical laboratory to validate and

constrain the above theories. In particular:

(A) An open issue in the ChEFT framework is the determination of the three-nucleon force (3NF),

whose practical implementation is at present limited to next-to-next-to leading order (N2LO). Work to

implement the 3NF up to N4LO is in progress but this appears a rather formidable task. At this order the

three-nucleon contact interaction component has been recently derived showing that it contains a

certain number of unconstrained low-energy constants (LECs). Their determination will allow to

increase the predictive capability of the nuclear interaction and, hopefully, help to solve longstanding

discrepancies in low-energy scattering of three and four nucleons as the Ay puzzle. The new LECs can

be determined by fitting them to specific three-nucleon data. One part of the present project is to

develop a procedure to fit these parameters to three-nucleon scattering data at several energies, with

particular reference to the very precise cross section and polarization data available for p-d elastic

scattering between 2 and 30 MeV lab energies. The obtained three-nucleon force, including the

subleading terms, will be tested in the four-nucleon system studying N-3He and N-3H scattering at low

energies and in the description of light nuclei. This will constitute a stringent test for the spin structure of

the new terms included in the 3NF.

(B) EFTs are the natural framework to study dynamical processes in which a separation of scales is

well verified. The large values of the singlet and triplet neutron-proton scattering lengths provide such

an opportunity, by locating light nuclear systems close to the unitary point, a point in which those large

values diverge. The relevant EFT, describing nucleons interacting by contact interactions, is known as

pionless EFT, and it is the rationale to explain the appearance of universal properties characterizing the

Efimov physics. A further domain of application of the same paradigm is provided by nuclei in which a

few number of nucleons are weakly bound to a core nucleus (cluster EFT). The parameters of the

theory are determined by a proper location of the bound states and low energy resonances present in

the binary system. However, three-body forces have to be considered too. Specific examples within this

framework are represented by the determination of the alpha-alpha and alpha-nucleon interaction.

(C) Nuclear processes of astrophysical interest involving few-nucleon systems are significant

applications of the presented theoretical framework, as for example the A=3-6 radiative captures, of

relevance for the theory of the Big Bang Nucleosynthesis. Theoretical predictions and uncertainty

estimates are of particular importance due to the experimental difficulties to perform measurements in

this particular low energy regime.

The research on medium and heavy nuclei of the present project covers two main aspects. The

construction of a microscopic nucleon- and antinucleon-nucleus optical potential from chiral forces and

the theoretical support to the next-generation long-baseline neutrino experiments, aimed at the precise

determination of the oscillation parameters. An accurate modeling of nuclear effects in heavier nuclei at

relativistic energies is required. In particulra:

(D) The description of nuclear reactions in medium and heavy nuclei requires a good knowledge of the

optical potential. The uncertainties produced by the usually adopted phenomenological potentials can

be reduced by microscopic optical potentials. The Pavia unit of the collaboration has recently derived a

microscopic optical potential for elastic proton-nucleus scattering from NN chiral nuclear potentials. The

convergence and the theoretical errors associated with the truncation of the chiral expansion have been

investigated. The optical potential has been tested reproducing isotopic chains against

phenomenological predictions. The model has been extended to describe antinucleon scattering,

where, with a chiral antiproton-nucleon interaction, it is able to provide a microscopic description of the

LEAR data.

(E) Nuclear uncertainties represent one of the main sources of systematic error in the analysis of

neutrino oscillation experiments (T2K/HT2K, NOvA, DunE) aimed at the precise measurements of

neutrino properties, and in particular at the observation of leptonic CP violation. The neutrino beam

energy involved in such experiments ranges from hundreds of MeV to a few GeV, thus requiring a

relativistic description of the nuclear dynamics. The main processes that need to be modeled are

quasi-elastic scattering, two-nucleon emission and excitation of nucleonic resonances, although the low

energy part of the spectrum also plays a non-negligible role. The challenge is to develop a relativistic

nuclear model able to describe consistently these different energy regimes, to be implemented in the

Monte Carlo generators used in experimental analyses. Such generators were mostly based on the

Relativistic Fermi Gas model, which is clearly inadequate to describe the complexity of the nuclear

response to an electroweak probe. A model has been developed in recent years by the Torino group in

collaboration with groups at MIT and Universities of Seville, Granada and Madrid, based on the

connection between neutrino and electron-scattering processes. The model (called SuSAv2) exploits

the scaling properties of the nuclear responses and is based on a Relativistic Mean Field description of

the nucleus. It also includes fully relativistic two-body currents through an extension to the weak sector

of a calculation performed in the past by the Torino group for electron scattering.

Finally we discuss aspects regarding fundamental symmetries and applications:

(F) Parity-violating observables can be used to better understand the quark-quark weak interaction, a

part of the Standard Model still not well known. Time-reversal violating observables, like the electric

dipole moment of light nuclei, could be useful to shed some light on physics beyond the Standard

Model. In particular there are proposed experiments for measurements of gamma asymmetries in pd

electromagnetic capture. Ab initio methods are perfectly suited for a theoretical support to this activity.

(G) At Legnaro Labs a new facility (SPES) will be soon put into operation dedicated to RIB science and

fundamental nuclear research on neutron rich systems. A large part of the new cyclotron will be devoted

to production and research on new innovative radio pharmaceuticals for Nuclear Medicine and patients'

treatment. Legnaro is building up a large interdisciplinary group for development of novel radionuclides.

An important role is played by nuclear reaction theory to guide experiments for novel routes of their

production through simulation test to find optimized conditions for production. An important aspect

concerns calculation of yields and specific activity. A strategic collaboration is in progress with INFN

Pavia where two research and health-care centers, LENA and CNAO, are located.