The charge independence of nuclear forces implies that in describing nuclear structure we do not have to distinguish between neutrons and protons. This symmetry is broken by electromagnetic interaction leading to a vast field of investigation aimed at clarifying the coupling between strong and electromagnetic forces. That is why, after so many decades since the first formulation of the nuclear model, the so-called nuclear isospin must be still treated as an approximate symmetry. In this framework particle and nuclear physics join in an attempt of solving a longstanding open question involving microscopic ab-initio calculations and phenomenological spectroscopic evidence in nuclear structure. To solve this puzzle, the study of n-p, p-p and n-n interactions assume a key role. In fact, according to charge independence of nuclear forces, the scattering length should remain unchanged for all the nucleon-nucleon combinations.
Since it is not possible to produce a neutron target with a suitable density, n-n scattering length measurements have been carried out in an indirect way and is therefore affected by the largest uncertainties.
Taking advantage of the recently updated n_TOF neutron facility at CERN, we aim at studying the isospin invariance in a wide energy range . More in detail, the n-p and n-n scattering length will be deduced from neutron-induced deuteron breakup reaction 2H(n,p)nn using the same experimental set-up and for different neutron kinetic energies. Therefore, our approach makes it possible to produce a coherent data set for the two channels, possibly revealing an energy range where the isospin symmetry is restored.
It is important to remind that the cross section of the final state interaction of two nucleons is relatively small, and therefore, so far only experiments with monoenergetic neutron beams have been carried out. Placed approximately 20 m on top of the n_TOF spallation target, EAR2 provides approximately 107 MeV-neutrons per bunch, while maintaining a good energy resolution and low background conditions. Considering the important improvements of the n_TOF facility during the 2nd long shutdown period of CERN (LS2)  we are confident that the experimental area EAR2 allows the accurate measurement of the neutron-neutron scattering length over a large energy region, namely between 10 and 100 MeV.
As mentioned above, the proposed experiment is based on the detection of the three outgoing particles (one proton and 2 neutrons) in kinematic coincidence, thus leading to a full three-body kinematic reconstruction. The feasibility of this challenging experiment requires the development of an experimental setup consisting of an active target and a neutron detector with tracking capability. The active target consists of a plastic scintillator highly enriched in 2H, positioned in the neutron beam. Consequently, when 2H(n,p)nn reactions take place the energy of the emitted protons is recorded, and the interaction point can be reconstructed. On the other hand, the neutron detector is an innovative detector  which exploit neutron-proton elastic scattering to retrieve the direction of fast neutrons.
After a brief overview of the physical case, and the proposed measurement setup at n_TOF EAR2, we present the results of the in-progress experimental activity, including the possibility of implementing the active target, as well as describing the performances of the prototype of a neutron detector with innovative tracking capability.
 A. Musumarra et al., https://arxiv.org/abs/2109.11543