Experimental and theoretical multi-channel study of direct nuclear reactions: a tool to provide data driven information on the 76Ge neutrino-less double-beta decay

The study of heavy-ions induced double charge-exchange (HI-DCE) nuclear reactions is a promising way to access data-driven information on neutrino-less double-beta decay nuclear matrix elements. In the following, particular attention is given to the (18O,18Ne) and (20Ne,20O) HI-DCE reactions as tools for β + β + and β − β − decays, respectively. The experiments are performed in Catania at the Laboratori Nazionali del Sud of the Istituto Nazionale di Fisica Nucleare (INFN-LNS). The MAGNEX magnetic spectrometer is used to momentum analyse the ejectiles of a large network of nuclear reactions. New preliminary experimental data for the 76Se(18O,18F)76As and 76Ge(20Ne,20F)76As single charge exchange (SCE) and for the 76Se(18O,18Ne)76Ge and 76Ge(20Ne,20O)76Se DCE nuclear reactions were also investigated.

Neutrino-less double-beta decay is considered the experimentum crucis to reveal the Majorana nature of neutrinos and the lepton-number violation, being a link between the current and next-generation physics beyond the standard model [1].The role of nuclear matrix elements (NMEs) in 0νββ research is crucial to design the next-generation experiments and to access the neutrino effective mass, if the process will be actually observed [2].Due to that, the present spread in the results of about a factor of three for the NMEs calculated among different nuclear structure theories need to be overcome [3].In order to constraint the NMEs values, experiments adopting a broad variety of nuclear probes have been performed in the past decades [2].Although interesting, all these measurements revealed to be still not conclusive for the 0νββ-decay NMEs.
Heavy-ion Double Charge-Exchange reactions (HI-DCE) have been recently proposed to stimulate in the laboratory the same g.s. to g.s.nuclear transition occurring in the 0νββdecay and to access the nuclear response to the second order isospin operator, in analogy to the 0νββ-decay second order weak process.This analogy is the leitmotiv of the NUMEN (Nuclear Matrix Elements for neutrino-less double-beta decay) and NURE projects [4,5,6,7,8] proposing the idea to constrain the NMEs calculations using a new data-driven approach, based on the study of HI-DCE reactions.Promising results regarding the possibility to extract the DCE NME from the experimental cross-section measurements have been achieved in the last few years [9].Recently, the linear correlation between the DCE double Gamow-Teller (DGT) NMEs and the 0νββ DGT and total NMEs was demonstrated using both the interacting-boson model and the large-scale shell-model nuclear structure approaches [10].
The NUMEN project aims to study the ( 18 O, 18 Ne) DCE reaction as a probe for the β + β + transitions and the ( 20 Ne, 20 O) one for the β − β − , with the aim to explore the DCE mechanism in both directions [7,9].Since NMEs are time invariant quantities, they are common to a DCE and to its inverse, so the contextual measurements of both directions in the DCE represent a useful test of the procedure to extract NME from the measured DCE cross-section.The hard task to extract the NMEs from the DCE cross-section measurements could be accomplished provided that the complete description of the DCE reaction mechanism is completely under control [9].From the experimental side, the full understanding of all the nuclear structure and reaction properties makes it necessary to study a wide network of reaction channels including the elastic and inelastic scattering [11,12,13], the one and two-nucleon transfer [14,15,16,17,18], the SCE [19,20] and DCE [21,22] nuclear reactions.
The newly proposed multi-channel approach can be applied to the study of the ββ-decay candidates.During the conference, new experimental data and the relative theoretical analysis were presented for the networks of nuclear reactions involving the 76 Ge ↔ 76 Se ββ-decay partners.In particular, the elastic and inelastic scattering, the SCE and the DCE nuclear reaction channels.
The 18 O + 76 Se and the 20 Ne + 76 Ge collisions at 15.3 AMeV incident energy were performed at the LNS-INFN using the 18 O 8+ and the 20 Ne 10+ beams accelerated by the K800 Superconducting Cyclotron.The beam ions impinged on the 76 Se and 76 Ge targets evaporated on nat C backing layers and located in the object point of the MAGNEX magnetic spectrometer [23,24,25,26], inside its scattering chamber.The ejectiles were momentum analysed in different runs in which the optical axis of MAGNEX was oriented, compared to the beam direction, at several θ opt angles.During the 76 Se( 18 O, 18 Ne) 76 Ge and the 76 Ge( 20 Ne, 20 Ne) 76 Se DCE reaction cross-section measurements, the MAGNEX spectrometer was placed at θ opt = +3 • and -3 • , respectively, including zero degree in the full acceptance mode (≃ 50 msr), and the total covered angular range was 0 • ≤ θ lab ≤ 9 • .In these configuration, the beam enters in the spectrometer acceptance and the magnetic fields guide it to a place in the focal plane region away from the detectors [27].A Faraday cup of 0.8 cm entrance diameter and 3 cm depth, mounted 15 cm downstream of the target, was used to stop the beam and collect the charge during the nonzero degree measurements.An electron suppressor polarized at -200 V and a low noise charge integrator allowed to keep the charge collection accuracy better than 10% in all the experiment runs.
The beam current was optimized at each optical angle configuration in order to reach event rates tolerable by the focal plane detector (FPD) [28].The magnetic fields of the dipole and quadrupole magnets were set in order to transport the ions of interest in the region of momenta covered by the FPD.The data reduction strategy includes the position calibration of the FPD, identification of the ejectiles and reconstruction of the momentum vector at the target by inversion of the transport equations following the guidelines presented in previous publications [29].Target thicknesses, covered scattering angles, spectrometer optical angles and explored solid angles are listed in Table 1 for each of the presented reaction channels.
The accurate set-up and the advanced data reduction have allowed to produce high resolution energy spectra and angular distributions for all the analysed channels.The excitation energy E x was calculated as the difference Q 0 -Q where the Q 0 is the ground to ground state Q-value and Q is the Q-value obtained by the missing mass technique based on relativistic kinematic transformations.E x measured spectra are shown in Figs. 1 of Refs.[11] and [13] for the 18 O + 76 Se and 20 Ne + 76 Ge elastic and inelastic scattering at 15.3 AMeV, respectively.In these cases, the achieved energy resolution is about 0.5 MeV.Slightly better values are obtained for the other reaction channels, depending on the different energy straggling produced by the ejectile/target interaction.Absolute cross-section angular distributions were extracted for the several structures clearly visible in the spectra.Theoretical analysis is in progress and will be presented in forthcoming papers.
The new multi-channel experimental and theoretical approach was applied to a wide network of nuclear reactions involving the 76 Ge and 76 Se ββ decay partners.Two experiments were dedicated to this scope and many nuclear reaction channels were studied, including the 76 Ge ↔ 76 Se transition populated in both directions through the ( 18 O, 18 Ne) and the ( 20 Ne, 20 O) DCE reactions.During the conference, the results of the study on the elastic and inelastic scattering published in Refs.[11] and [13] were discussed.The preliminary 76 As spectra populated in the new ( 18 O, 18 F) and ( 20 Ne, 20 F) heavy-ion SCE reactions' measurements were compared to the results obtained in the (d, 2 He) and ( 3 He,t) from Refs.[30] and [31], respectively.Preliminary results on the zero-degree 76 Se( 18 O, 18 Ne) 76 Ge and the 76 Ge( 20 Ne, 20 O) 76 Se DCE cross-sections measurements were presented, although further theoretical investigations are needed in order to master the difficult matter of extracting a nuclear matrix element.All of these results will be published in forthcoming works including the theoretical analyses.

Table 1 .
Main parameters characterizing the experimental set-up of each explored reaction channel: target, and carbon backing thicknesses, covered scattering angles [θ min lab ; θ max lab ], MAGNEX central angle θ opt , magnetic rigidity Bρ, quadrupole field BQ and MAGNEX solid angle acceptance are given.