After 50 years since the identification of Quantum Chromodynamics (QCD) as the fundamental theory of
strong interactions, there are still many challenges that confront nuclear theory, ranging from
fundamental searches of Physics beyond the Standard Model to applications in nuclear medicine and
energy production, due to the formidable complexities of the strongly correlated many-body problem
and of QCD in the low-energy domain.
The systematic approach based on EFTs has become in the last decades the standard framework to
address the nuclear interaction problem. From one side, EFTs provide a direct link to QCD by identifying
the active degrees of freedom which arise, at least ideally, from a decimation process starting from
fundamental quarks and gluons. On the other side, it offers a systematic computational scheme of
physical observables as expansions in power of the small ratio between relevant momenta and a short-
distance scale, the breakdown scale, characteristic of each specific EFT. All the short-distance effects
from the frozen degrees of freedom are effectively encoded in the values of the low-energy constants
(LECs) parametrizing contact interactions, whose values are determined through fits to experimental
data.
As an example, in the chiral EFT (ChEFT), based on the approximate chiral symmetry exhibited by
QCD, the interactions of nucleons, pions and external electroweak probes (currents) are written as a
perturbative expansion in powers of nucleon momenta and pion mass divided by chiral breakdown
scale, identified with the typical mass of hadrons unprotected by chiral symmetry. This scheme allows a
consistent derivation of many-body forces and currents, and the implementation of well defined
procedures to estimate the theoretical errors produced by the truncation of the expansion. At present
ChEFT nucleon-nucleon (NN) interactions have been constructed up to 5th order using NN scattering
data as input. The three-body force starts to contribute at the 3th order and currently its contribution at
the 4th order is under investigation. However, no accurate description of 3-body scattering observables
has been obtained at this order so far.
Electroweak nuclear charge and current transition operators have also been developed at the 4th order,
including two-body contributions. Open problems are represented by the rather poor convergence
pattern within the standard power counting, which demands dedicated studies to estimate the
theoretical uncertainty from the truncation of the chiral series.
Other EFTs, valid at much lower energies, are the pionless and Halo-cluster EFTs, where the
separation of scales is determined by the large values of the scattering lengths as compared to the
interaction ranges, and universal properties emerge, common to nuclear, atomic and molecular
systems. Power counting in these EFTs is currently the subject of a lively debate in the literature,
regarding e.g. the existence of a leading-order 4-body interaction.
Accurate numerical techniques to solve the Schroedinger equation for few-body systems make the
latter an ideal theoretical laboratory to validate and constrain nuclear interaction and transition
operators. The Hyperspherical Harmonics (HH) method is one of these techniques, in which members
of the present project are the leading experts. Active research is dedicated to the refinement and
extension of these techniques in A>4 sysyems.
On the other hand, much of the input required from nuclear theory to interpret and guide experimental
searches for BSM Physics involve heavier systems. This concerns long-baseline neutrino experiments
aimed at a precise determination of the oscillation parameters, where an accurate modeling of nuclear
effects at low, medium and relativistic energies is required for nuclei like 12C, 16O and 40Ar.
Also neutrinoless double beta decay experiments require the knowledge of matrix elements of transition
operators in nuclei starting from 48Ca. The nuclear shell model can be used to describe the structure of
these nuclei, but effective interactions have to be derived in the restricted model space, linked to the
microscopic ones.
A furhter link between microscopic interactions between nucleons and effective interactions can be
established through nucleon-nucleus optical potentials, overcoming purely phenomenological
approaches, which is especially important in the domain of exotic nuclei, to be studied at future
radioactive ion beam facilities.The components of the proposed INFN research network are fully involved in this scientific context, in
particular, in the study of two- and three-nucleon interactions in EFT and the development of the EM
and weak transition currents (Pisa, Napoli, Lecce), in the development and refinement of new accurate
techniques to study the few-body problem (Trento, Pisa and Padova), in the derivation of effective
interactions for the realistic shell model (Napoli), in the lepton-nucleus interaction (Lecce, Torino), in the
study of cluster models for light and medium-light nuclear systems (Trento, Padova), in the theoretical
support to national activities for the production of innovative radionuclides and radiolabeled compounds
for advanced medical therapies and diagnostics (Padova).
Within the scientific context described above, the objectives of our project for the next three years can
be grouped in two interdependent main areas: a) basic interactions and ab-initio methods, also involving
the exploration of quantum computing techniques, and b) applications, both in the realm of fundamental
research (BSM, neutrino experiments, reactions of astrophysical interest) and applied research (energy
production, nuclear medicine).
a) The most fundamental interaction we will be dealing with is the one described in ChEFT. We intend to
arrive at a fully consistent implementation of two- and three-nucleon forces at the 4th order of the chiral
expansion, capable of accurately describing bound and scattering observables in the three-nucleon
system, solving long-standing discrepancies like the N-d Ay puzzle. The prospects for achieving this
result are very promising, in view of the recent identification of 5 three-nucleon contact LECs arising at
this order, which were overlooked in the previous literature. The obtained three-nucleon force 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. We also plan to explore the possibility of applying a genetic algorithm developed for
quantum computers to determine the LECs of the nuclear chiral interaction and electroweak currents for
few- and many-body calculations. Proceeding to larger scales, we will study weakly bound systems by
means of the pionless, Halo/Cluster EFT and coupled channel techniques, exploring the universal
window for systems with shallow bound or virtual states and extending the description to light and
medium hypernuclei. Next, we aim at the further development of microscopic optical potentials for
nucleon-nucleus elastic and inelastic reactions, directly linked to the microscopic nuclear interaction
derived within ChEFT, including its 3-nucleon components, which will be crucial in relation to radioactive
ion beam facilities. Finally, also the relation of the fundamental NN interaction with the effective finite-
range interactions commonly used in Hartree-Fock calculations will be a subject of our investigation, as
well as the development of effective operators for the nuclear interaction with electroweak probes in the
reduced model space of the nuclear shell model.
b) Physics applications we will address with the refined microscopic ChEFT interaction and currents
include few-nucleon capture reactions of astrophysical interest, like p-d, d-d, p-3H, d-3H and d-3He.
The effective operators, arising in the reduced model space of the nuclear shell model, for the nuclear
interaction with electroweak probes will be used to calculate the nuclear matrix elements involved in
nuclear single and double beta decay both with and without neutrinos.
We also plan to further explore possible signals of the hypothetical X17 boson in reactions involving
few-nucleons.
Halo-cluster EFT will be used for the electromagnetic breakup of 9Be and 10Be. We also plan to
address in the following three years nuclear fusion reactions, like p-6Li, 3He-6Li, p-11B, 6Li-6Li, in the
context of cluster or optical models.
A further objective is the refinement of models for inclusive and semi-inclusive lepton-nucleus scattering
at low, medium, and high energies, relevant for next-generation long-baseline neutrino experiments.
On the nuclear medicine side, we plan to devise the most promising production routes for radionuclides
to be used in therapy and diagnostics, such as 155Tb, 161Tb, 186Re, 47Sc and 67Cu, by analyzing
their production cross sections, the contaminations by other radioisotopes, and particle-activation rates.
Finally, an important goal of our project is to provide a fertile environment for the growth of young PhD
students and post-docs through the organization of periodic meetings to share the work of the single
nodes.