# Recent results on Heavy-Ion induced reactions of interest for $0\nu\beta\beta$ decay

C. Agodi, F. Cappuzzello, L. Acosta, C. Altana, P. Amador-Valenzuela, N. Auerbach, J. Barea, J.I. Bellone, R. Bijker, D. Bonanno, et al.

► To cite this version:

C. Agodi, F. Cappuzzello, L. Acosta, C. Altana, P. Amador-Valenzuela, et al. Recent results on Heavy-Ion induced reactions of interest for $0\nu\beta\beta$ decay. 42nd Symposium on Nuclear Physics, Jan 2019, Cocoyoc, Mexico. pp.012002, 10.1088/1742-6596/1308/1/012002. [hal-02327693](https://hal.science/hal-02327693)

HAL Id: hal-02327693

https://hal.science/hal-02327693

Submitted on 30 May 2024

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# Recent results on Heavy-Ion induced reactions of interest for $0\nu\beta\beta$ decay

C. Agodi, F. Cappuzzello, L. Acosta, C. Altana, P. Amador-Valenzuela, N. Auerbach, J. Barea, J.I. Bellone, R. Bijker, D. Bonanno, et al.

► To cite this version:

C. Agodi, F. Cappuzzello, L. Acosta, C. Altana, P. Amador-Valenzuela, et al. Recent results on Heavy-Ion induced reactions of interest for $0\nu\beta\beta$ decay. 42nd Symposium on Nuclear Physics, Jan 2019, Cocoyoc, Mexico. pp.012002, 10.1088/1742-6596/1308/1/012002. [hal-02327693](https://hal.science/hal-02327693v1)

HAL Id: hal-02327693

https://hal.science/hal-02327693v1

Submitted on 30 May 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
PAPER • OPEN ACCESS

# Recent results on Heavy-Ion induced reactions of interest for $0\nu\beta\beta$ decay

To cite this article: C. Agodi et al 2019 J. Phys.: Conf. Ser. 1308 012002

View the [article online](#) for updates and enhancements.

You may also like

- [Double beta decay experiments](#)
  K Zuber

- [Recent results on heavy-ion direct reactions of interest for $0\nu\beta\beta$ decay at INFN - LNS](#)
  M. Cavallaro, L. Acosta, P. Adsley et al.

- [Neutrinoless double-beta decay and physics beyond the standard model](#)
  Frank F Deppisch, Martin Hirsch and Heinrich Päs

<figure><img src="image_2.png" /></figure>

The
Electrochemical
Society

Advancing solid state &
electrochemical science & technology

<figure><img src="image_3.png" /></figure>

DISCOVER
how sustainability
intersects with
electrochemistry & solid
state science research

<figure><img src="image_4.png" /></figure>
PAPER • OPEN ACCESS

# Recent results on Heavy-Ion induced reactions of interest for $0\nu\beta\beta$ decay

To cite this article: C. Agodi et al 2019 J. Phys.: Conf. Ser. 1308 012002

View the [article online](#) for updates and enhancements.

You may also like

- [Double beta decay experiments](#)
  K Zuber

- [Recent results on heavy-ion direct reactions of interest for $0\nu\beta\beta$ decay at INFN - LNS](#)
  M. Cavallaro, L. Acosta, P. Adsley et al.

- [Neutrinoless double-beta decay and physics beyond the standard model](#)
  Frank F Deppisch, Martin Hirsch and Heinrich Päs

<figure><img src="image_2.png" /></figure>

The
Electrochemical
Society

Advancing solid state &
electrochemical science & technology

<figure><img src="image_3.png" /></figure>

DISCOVER
how sustainability
intersects with
electrochemistry & solid
state science research

<figure><img src="image_4.png" /></figure>
Recent results on Heavy-Ion induced reactions of interest for
0vββ decay

C. Agodi¹, F. Cappuzzello¹,³, L. Acosta²⁰, C. Altana¹, P. Amador-Valenzuela²¹,
N. Auerbach²⁷, J. Barea³⁴, J.I. Bellone¹, R. Bijker²², D. Bonanno², T. Borello-
Lewin¹⁴, I. Boztosun²⁵, V. Branchina²,³, S. Brasolin⁴, G. Brischetto¹,³,⁵, O.
Brunasso⁴, S. Burrello¹, S. Calabrese¹,³, L. Calabretta¹, D. Calvo⁴, V.
Capirossi⁴,⁶, D. Carbone¹, M. Cavallaro¹, R. Chen³³, L.E. Charon Garcia²⁰, E .R.
Chávez Lomelí²⁰, I. Ciraldo¹,³, M. Colonna¹, G. D'Agostino¹, H. Djapo²⁵, G. De
Geronimo³², F. Delaunay⁴,⁶,¹², K. De Los Rios²⁰, N. Deshmukh³⁰, C. Ferraresi⁴,⁷,
J.L. Ferreira¹⁵, J. Ferretti⁸,¹³, P. Finocchiaro¹, S. Firat²⁵, M. Fisichella⁴, A. Foti²,
G. Gallo¹,³, H. Garcia-Tecocoatzi⁸,⁹, A. Hacisalihoglu²⁶, A. Huerta-Hernandez²⁰,
J. Kotila³¹, Y. Kucuk²⁵, F. Iazzi⁴,⁶, L. La Fauci¹,³, G. Lanzalone¹,¹⁰, F. La Via¹¹,
J.A. Lay²⁸, H. Lenske²³, R. Linares¹⁵,D. Lo Presti²,³, J. Lubian¹⁵, J. Ma³³, D.
Marín-Lámbarri²⁰, J. Mas Ruiz²⁰, N. H. Medina¹⁴, D.R. Mendes¹⁵, P. Mereu⁴, M.
Moralles¹⁶, L. Neri¹, J. R. B. Oliveira¹⁴, A. Pakou¹⁸, L. Pandola¹, H. Petrascu²⁹,
N. Pietralla²⁴, F. Pinna⁴,⁶, S. Reito², P. Ries²⁴, M.R.D. Rodrigues¹⁴, A. D. Russo¹,
G. Russo²,³, E. Santopinto⁸, R.B.B. Santos¹⁷, L. Serbina²⁹, O. Sgouros¹, M.A.G.
da Silveira¹⁷, S.O. Solakci²⁵, G. Souliotis¹⁹,V. Soukeras¹, A. Spatafora¹,³, D.
Torresi¹, S. Tudisco¹, R.I.M. Vsevolodovna⁸,⁹, H. Vargas Hernandez²⁰, J.S.
Wang³³, V. Werner²⁴, Y.Y. Yang³³, A. Yildirim²⁵, V.A.B. Zagatto¹⁵ for the
NUMEN collaboration

¹ Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Italy

² Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Italy

³ Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catania, Italy

⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Italy

⁵ Centro Siciliano di Fisica Nucleare e Struttura della Materia, Italy

⁶ DISAT, Politecnico di Torino, Italy

⁷ DIMEAS, Politecnico di Torino, Italy

⁸ Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Italy

⁹ Dipartimento di Fisica, Università di Genova, Italy

¹⁰ Università degli Studi di Enna "Kore", Italy

<figure><img src="image_5.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Recent results on Heavy-Ion induced reactions of interest for
0vββ decay

C. Agodi<fnref n="1" />, F. Cappuzzello<fnref n="1" />,<fnref n="3" />, L. Acosta²⁰, C. Altana<fnref n="1" />, P. Amador-Valenzuela²¹,
N. Auerbach²⁷, J. Barea³⁴, J.I. Bellone<fnref n="1" />, R. Bijker²², D. Bonanno<fnref n="2" />, T. Borello-
Lewin¹⁴, I. Boztosun²⁵, V. Branchina<fnref n="2" />,<fnref n="3" />, S. Brasolin<fnref n="4" />, G. Brischetto<fnref n="1" />,<fnref n="3" />,<fnref n="5" />, O.
Brunasso<fnref n="4" />, S. Burrello<fnref n="1" />, S. Calabrese<fnref n="1" />,<fnref n="3" />, L. Calabretta<fnref n="1" />, D. Calvo<fnref n="4" />, V.
Capirossi<fnref n="4" />,<fnref n="6" />, D. Carbone<fnref n="1" />, M. Cavallaro<fnref n="1" />, R. Chen³³, L.E. Charon Garcia²⁰, E .R.
Chávez Lomelí²⁰, I. Ciraldo<fnref n="1" />,<fnref n="3" />, M. Colonna<fnref n="1" />, G. D'Agostino<fnref n="1" />, H. Djapo²⁵, G. De
Geronimo³², F. Delaunay<fnref n="4" />,<fnref n="6" />,¹², K. De Los Rios²⁰, N. Deshmukh³⁰, C. Ferraresi<fnref n="4" />,<fnref n="7" />,
J.L. Ferreira¹⁵, J. Ferretti<fnref n="8" />,¹³, P. Finocchiaro<fnref n="1" />, S. Firat²⁵, M. Fisichella<fnref n="4" />, A. Foti<fnref n="2" />,
G. Gallo<fnref n="1" />,<fnref n="3" />, H. Garcia-Tecocoatzi<fnref n="8" />,<fnref n="9" />, A. Hacisalihoglu²⁶, A. Huerta-Hernandez²⁰,
J. Kotila³¹, Y. Kucuk²⁵, F. Iazzi<fnref n="4" />,<fnref n="6" />, L. La Fauci<fnref n="1" />,<fnref n="3" />, G. Lanzalone<fnref n="1" />,<fnref n="10" />, F. La Via¹¹,
J.A. Lay²⁸, H. Lenske²³, R. Linares¹⁵,D. Lo Presti<fnref n="2" />,<fnref n="3" />, J. Lubian¹⁵, J. Ma³³, D.
Marín-Lámbarri²⁰, J. Mas Ruiz²⁰, N. H. Medina¹⁴, D.R. Mendes¹⁵, P. Mereu<fnref n="4" />, M.
Moralles¹⁶, L. Neri<fnref n="1" />, J. R. B. Oliveira¹⁴, A. Pakou¹⁸, L. Pandola<fnref n="1" />, H. Petrascu²⁹,
N. Pietralla²⁴, F. Pinna<fnref n="4" />,<fnref n="6" />, S. Reito<fnref n="2" />, P. Ries²⁴, M.R.D. Rodrigues¹⁴, A. D. Russo<fnref n="1" />,
G. Russo<fnref n="2" />,<fnref n="3" />, E. Santopinto<fnref n="8" />, R.B.B. Santos¹⁷, L. Serbina²⁹, O. Sgouros<fnref n="1" />, M.A.G.
da Silveira¹⁷, S.O. Solakci²⁵, G. Souliotis¹⁹,V. Soukeras<fnref n="1" />, A. Spatafora<fnref n="1" />,<fnref n="3" />, D.
Torresi<fnref n="1" />, S. Tudisco<fnref n="1" />, R.I.M. Vsevolodovna<fnref n="8" />,<fnref n="9" />, H. Vargas Hernandez²⁰, J.S.
Wang³³, V. Werner²⁴, Y.Y. Yang³³, A. Yildirim²⁵, V.A.B. Zagatto¹⁵ for the
NUMEN collaboration

<figure><img src="image_5.png" /></figure>

<footnote n="1">¹ Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Italy</footnote>

<footnote n="2">² Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Italy</footnote>

<footnote n="3">³ Dipartimento di Fisica e Astronomia "Ettore Majorana", Università di Catania, Italy</footnote>

<footnote n="4">⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Italy</footnote>

<footnote n="5">⁵ Centro Siciliano di Fisica Nucleare e Struttura della Materia, Italy</footnote>

<footnote n="6">⁶ DISAT, Politecnico di Torino, Italy</footnote>

<footnote n="7">⁷ DIMEAS, Politecnico di Torino, Italy</footnote>

<footnote n="8">⁸ Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Italy</footnote>

<footnote n="9">⁹ Dipartimento di Fisica, Università di Genova, Italy</footnote>

<footnote n="10">¹⁰ Università degli Studi di Enna "Kore", Italy</footnote>
¹¹ CNR-IMM, Sezione di Catania, Italy

¹² LPC Caen, Normandie Université, ENSICAEN, UNICAEN, CNRS/INP3, France

¹³ Department of Physics, Yale University, USA

¹⁴ Instituto de Fisica, Universidade de Sao Paulo, Brazil

¹⁵ Instituto de Fisica, Universidade Federal Fluminense, Brazil

¹⁶ Instituto de Pesquisas Energeticas e Nucleares IPEN/CNEN, Brazil

¹⁷ Centro Universitario FEI Sao Bernardo do Campo, Brazil

¹⁸ Department of Physics and HINP, University of Ioannina, Greece

¹⁹ Department of Chemistry, National and Kapodistrian University of Athens, Greece

²⁰ Instituto de Fisica, Universidad Nacional Autónoma de México, Mexico

²¹ Instituto Nacional de Investigaciones Nucleares, Mexico

²² Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico

²³ Department of Physics, University of Giessen, Germany

²⁴ Institut fur Kernphysik, Technische Universitat Darmstadt, Germany

²⁵ Department of Physics, Akdeniz University, Turkey

²⁶ Institute of Natural Sciences, Karadeniz Teknik University, Turkey

²⁷ School of Physics and Astronomy, Tel Aviv University, Israel

²⁸ Departamento de FAMN, University of Seville, Spain

²⁹ Department of Nuclear Physics, Horia Hubulei National Institute of Physics and Nuclear Engineering, IFIN-HH, Romania

³⁰ Nuclear Physics Division, Saha Institute of Nuclear Physics, India

³¹ University of Jyväskylä, Finland

³² Stony Brook University, USA

³³ Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China

³⁴ Departamento de Física, Universidad de Conception, Chile

agodi@lns.infn.it

**Abstract.** An updated overview of recent results on Heavy-Ion induced reactions of interest for neutrinoless double beta decay is reported in the framework of the NUMEN project. The NUMEN idea is to study heavy-ion induced Double Charge Exchange (DCE) reactions with the aim to get information on the nuclear matrix elements for neutrinoless double beta (0vββ) decay. Moreover, to infer the neutrino average masses from the possible measurement of the half-life of 0vββ decay, the knowledge of the nuclear matrix elements is a crucial aspect.
¹¹ CNR-IMM, Sezione di Catania, Italy

¹² LPC Caen, Normandie Université, ENSICAEN, UNICAEN, CNRS/INP3, France

¹³ Department of Physics, Yale University, USA

¹⁴ Instituto de Fisica, Universidade de Sao Paulo, Brazil

¹⁵ Instituto de Fisica, Universidade Federal Fluminense, Brazil

¹⁶ Instituto de Pesquisas Energeticas e Nucleares IPEN/CNEN, Brazil

¹⁷ Centro Universitario FEI Sao Bernardo do Campo, Brazil

¹⁸ Department of Physics and HINP, University of Ioannina, Greece

¹⁹ Department of Chemistry, National and Kapodistrian University of Athens, Greece

²⁰ Instituto de Fisica, Universidad Nacional Autónoma de México, Mexico

²¹ Instituto Nacional de Investigaciones Nucleares, Mexico

²² Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico

²³ Department of Physics, University of Giessen, Germany

²⁴ Institut fur Kernphysik, Technische Universitat Darmstadt, Germany

²⁵ Department of Physics, Akdeniz University, Turkey

²⁶ Institute of Natural Sciences, Karadeniz Teknik University, Turkey

²⁷ School of Physics and Astronomy, Tel Aviv University, Israel

²⁸ Departamento de FAMN, University of Seville, Spain

²⁹ Department of Nuclear Physics, Horia Hubulei National Institute of Physics and Nuclear Engineering, IFIN-HH, Romania

³⁰ Nuclear Physics Division, Saha Institute of Nuclear Physics, India

³¹ University of Jyväskylä, Finland

³² Stony Brook University, USA

³³ Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China

³⁴ Departamento de Física, Universidad de Conception, Chile

agodi@lns.infn.it

**Abstract.** An updated overview of recent results on Heavy-Ion induced reactions of interest for neutrinoless double beta decay is reported in the framework of the NUMEN project. The NUMEN idea is to study heavy-ion induced Double Charge Exchange (DCE) reactions with the aim to get information on the nuclear matrix elements for neutrinoless double beta (0vββ) decay. Moreover, to infer the neutrino average masses from the possible measurement of the half-life of 0vββ decay, the knowledge of the nuclear matrix elements is a crucial aspect.
# 1. Introduction

The search for neutrinoless double beta decay ($0\nu\beta\beta$) addresses fundamental questions in physics, related to the absolute neutrinos mass scale, whether neutrinos are Majorana particles or how many neutrino species are there. Moreover $0\nu\beta\beta$ search has implications for the understanding of the matter-antimatter asymmetry in the universe. The design of the $0\nu\beta\beta$ search experiments themselves require detailed understanding of nuclear physics, as background critically depend on nuclear decay chain and nuclear matrix elements are needed to link observed rates to neutrino properties.

In this framework the NUMEN project propose an innovative and original tool: to use Heavy-Ions Double Charge Exchange Reactions (HI-DCE) to access quantitative information for Nuclear Matrix Element towards $0\beta\beta$ decay.

# 2. The NUMEN Project

The NUMEN main goal is the extraction from measured cross-sections of “data-driven” information on Nuclear Matrix Elements for all the systems candidate for $0\nu\beta\beta$. Crucial for the experimental challenges is the INFN Laboratori Nazionali del Sud (LNS) facility, made up by the Superconducting Cyclotron (CS) and the MAGNEX magnetic spectrometer. The experimental measurements of HI-DCE reactions present a number of challenging aspects, since they are characterized by very low cross sections and, in the same experimental conditions, they must be identified with respect to competitive reaction channels.

It is well known that the $0\nu\beta\beta$ half-life can be factorized in three terms at different physics scale: the phase-space factor, connected with Atomic physics, the Matrix Element (NME) related with Nuclear physics and a term, related to Particle physics, in which it is supposed there are the answers to the unsolved questions, related to new physics beyond the Standard Model. For evaluation of NME several methods have been used, based on different nuclear models, an updated comparison of the results of NME calculations, obtained within various nuclear structure frameworks [1-4], indicates that significant differences are indeed found. In addition, some assumption common to different competing approaches could cause overall systematic uncertainties.

NUMEN [5, 6] propose a novel way to address experimentally-driven information on the NMEs of $0\nu\beta\beta$, based on DCE cross section measurements. These reactions are characterized by the transfer of two charge units, leaving the mass number unchanged, and can proceed either by a sequential multi-nucleon-transfer mechanism or by meson-exchange. Despite $0\nu\beta\beta$ decays and HI-DCE reactions are mediated by different interactions, they present a number of similarities. The main ones are:

i) the initial and final state wave functions in the two processes are the same,

ii) the transition operators are similar, in both cases Fermi, Gamow-Teller and rank-two tensor components are present,

iii) a large linear momentum (100 MeV/c) is available in the virtual intermediate channel,

iv) the two processes are non-local and are characterized by two vertices localized in a pair of valence nucleons,

v) they take place in the same nuclear medium,

vi) a relevant off-shell propagation through virtual intermediate channels is present.

The descriptions of NMEs for DCE and $0\nu\beta\beta$ decay present the same degree of complexity, with the advantage for DCE to be “accessible” in laboratory. However, a simple relation between DCE cross sections and $0\nu\beta\beta$ decay half-lives is not trivial and needs to be explored.

At the MAGNEX facility of the INFN-LNS we demonstrate the feasibility of this kind of DCE cross sections measurements. MAGNEX is a large acceptance magnetic system able to provide high resolution in energy, mass and angle [7] and an accurate control of the detection efficiency. The implementation of trajectory reconstruction technique is the key feature of MAGNEX, which
# 1. Introduction

The search for neutrinoless double beta decay ($0\nu\beta\beta$) addresses fundamental questions in physics, related to the absolute neutrinos mass scale, whether neutrinos are Majorana particles or how many neutrino species are there. Moreover $0\nu\beta\beta$ search has implications for the understanding of the matter-antimatter asymmetry in the universe. The design of the $0\nu\beta\beta$ search experiments themselves require detailed understanding of nuclear physics, as background critically depend on nuclear decay chain and nuclear matrix elements are needed to link observed rates to neutrino properties.

In this framework the NUMEN project propose an innovative and original tool: to use Heavy-Ions Double Charge Exchange Reactions (HI-DCE) to access quantitative information for Nuclear Matrix Element towards $0\beta\beta$ decay.

# 2. The NUMEN Project

The NUMEN main goal is the extraction from measured cross-sections of “data-driven” information on Nuclear Matrix Elements for all the systems candidate for $0\nu\beta\beta$. Crucial for the experimental challenges is the INFN Laboratori Nazionali del Sud (LNS) facility, made up by the Superconducting Cyclotron (CS) and the MAGNEX magnetic spectrometer. The experimental measurements of HI-DCE reactions present a number of challenging aspects, since they are characterized by very low cross sections and, in the same experimental conditions, they must be identified with respect to competitive reaction channels.

It is well known that the $0\nu\beta\beta$ half-life can be factorized in three terms at different physics scale: the phase-space factor, connected with Atomic physics, the Matrix Element (NME) related with Nuclear physics and a term, related to Particle physics, in which it is supposed there are the answers to the unsolved questions, related to new physics beyond the Standard Model. For evaluation of NME several methods have been used, based on different nuclear models, an updated comparison of the results of NME calculations, obtained within various nuclear structure frameworks [1-4], indicates that significant differences are indeed found. In addition, some assumption common to different competing approaches could cause overall systematic uncertainties.

NUMEN [5, 6] propose a novel way to address experimentally-driven information on the NMEs of $0\nu\beta\beta$, based on DCE cross section measurements. These reactions are characterized by the transfer of two charge units, leaving the mass number unchanged, and can proceed either by a sequential multi-nucleon-transfer mechanism or by meson-exchange. Despite $0\nu\beta\beta$ decays and HI-DCE reactions are mediated by different interactions, they present a number of similarities. The main ones are:

i) the initial and final state wave functions in the two processes are the same,

ii) the transition operators are similar, in both cases Fermi, Gamow-Teller and rank-two tensor components are present,

iii) a large linear momentum (100 MeV/c) is available in the virtual intermediate channel,

iv) the two processes are non-local and are characterized by two vertices localized in a pair of valence nucleons,

v) they take place in the same nuclear medium,

vi) a relevant off-shell propagation through virtual intermediate channels is present.

The descriptions of NMEs for DCE and $0\nu\beta\beta$ decay present the same degree of complexity, with the advantage for DCE to be “accessible” in laboratory. However, a simple relation between DCE cross sections and $0\nu\beta\beta$ decay half-lives is not trivial and needs to be explored.

At the MAGNEX facility of the INFN-LNS we demonstrate the feasibility of this kind of DCE cross sections measurements. MAGNEX is a large acceptance magnetic system able to provide high resolution in energy, mass and angle [7] and an accurate control of the detection efficiency. The implementation of trajectory reconstruction technique is the key feature of MAGNEX, which
guarantees the above mentioned performance and its relevance in the research for heavy-ion physics [8-10], also taking advantage of its coupling to the EDEN neutron detector array [11,12]. The $^{40}$Ca($^{18}$O,$^{18}$Ne)$^{40}$Ar reaction was studied at 15 MeV/u, showing that high mass, angular and energy resolution energy spectra and accurate absolute cross sections are at our reach, even at very forward angles, see ref. [13]. In addition, a schematic analysis of the reaction cross sections demonstrated that relevant quantitative information on DCE matrix elements can be extracted from the data. This result demonstrated that the previous experimental limitations are almost overcome and that high resolution and statistically significant experimental data can be measured for DCE processes.

In the present experimental conditions, due to the limitation arising from the tiny cross-sections of the processes of interest, only very few systems can be measured within the 5-years project. In order to systematically explore all the nuclei candidates for $0\nu\beta\beta$, a beam intensity at least two orders of magnitude higher than the present must be achieved.

The NUMEN project is conceived in a long-range time perspective, in view of a comprehensive study of many candidate systems for $0\nu\beta\beta$ decay. Moreover, the project promotes a renewal of the INFN-LNS research infrastructure [14] with a specific R&D activity on detectors, materials and instrumentation. As a consequence, major upgrades of the detector technologies (3D ion tracker, particle-identification wall, gamma-ray array, ...) must be developed [15, 20]. Also the target technology must be upgraded, to avoid the damage of the thin films due to the high temperature involved [21, 23]. Moreover, a deep and complete investigation of the theoretical aspects connecting nuclear reaction mechanisms and nuclear matrix elements must be carried out [24, 26].

## 2.1. *An updated overview*

NUMEN experimental activity consists of two main classes of experiments, corresponding to the exploration of the two directions of isospin transfer $\tau^- \tau^-$ and $\tau^+ \tau^+$, characteristic of $\beta-\beta^-$ and $\beta+\beta^+$ decays, respectively. In particular, the $\beta+\beta^+$ direction in the target is investigated using a $^{18}$O beam and measuring the ($^{18}$O,$^{18}$Ne) DCE induced transitions, together with the other reaction channels involving the same beam and target. Similarly, the $\beta-\beta^-$ direction is explored via the ($^{20}$Ne,$^{20}$O) reaction, using a $^{20}$Ne beam and detecting the reaction products of the DCE channel along with other open channels characterized by the same projectile and target. With the actual facility and experimental setup we perform some long run at LNS with MAGNEX, choosing few isotopes, candidates for $0\nu\beta\beta$, already at our reach in terms of energy resolution and availability of thin targets.

In particular, we performed for the first time experimental investigations of the ($^{20}$Ne,$^{20}$O) DCE reaction on $^{116}$Cd,$^{76}$Ge and $^{130}$Te targets. These are the first measurements of such a kind of reaction: no data are available in literature. A $^{20}$Ne$^{10+}$ cyclotron beam at 15 AMeV was delivered by the CS of INFN-LNS and impinged on $^{116}$Cd rolled target of 1370 µg/cm$^2$ thickness and $^{76}$Ge (386 µg/cm$^2$ thickness) and $^{130}$Te (247 µg/cm$^2$ thickness) both evaporated on a C backing of 50 µg/cm$^2$. The thickness of the various targets was carefully chosen in order to obtain an energy resolution which allows to distinguish the transition to the residual nucleus ground state from its first excited state. Indeed, the selected thickness of $^{116}$Cd is much higher than that of $^{76}$Ge and $^{130}$Te, because the first excited state in $^{116}$Sn case is at 1.293 MeV, to be compared to 0.559 MeV in $^{76}$Se and 0.536 MeV in $^{130}$Xe. The MAGNEX spectrometer was placed at forward angles including zero degrees in the full acceptance mode (50 msr). Despite the experimental limitations, we were able to measure energy spectra and absolute cross sections for the DCE reaction channel. Moreover, we measured also other reaction channels: one- and two-proton transfer, one- and two-neutron transfer and Single Charge Exchange, in order to estimate the role of the sequential multi-nucleon transfer routes on the diagonal DCE process.
guarantees the above mentioned performance and its relevance in the research for heavy-ion physics [8-10], also taking advantage of its coupling to the EDEN neutron detector array [11,12]. The $^{40}$Ca($^{18}$O,$^{18}$Ne)$^{40}$Ar reaction was studied at 15 MeV/u, showing that high mass, angular and energy resolution energy spectra and accurate absolute cross sections are at our reach, even at very forward angles, see ref. [13]. In addition, a schematic analysis of the reaction cross sections demonstrated that relevant quantitative information on DCE matrix elements can be extracted from the data. This result demonstrated that the previous experimental limitations are almost overcome and that high resolution and statistically significant experimental data can be measured for DCE processes.

In the present experimental conditions, due to the limitation arising from the tiny cross-sections of the processes of interest, only very few systems can be measured within the 5-years project. In order to systematically explore all the nuclei candidates for $0\nu\beta\beta$, a beam intensity at least two orders of magnitude higher than the present must be achieved.

The NUMEN project is conceived in a long-range time perspective, in view of a comprehensive study of many candidate systems for $0\nu\beta\beta$ decay. Moreover, the project promotes a renewal of the INFN-LNS research infrastructure [14] with a specific R&D activity on detectors, materials and instrumentation. As a consequence, major upgrades of the detector technologies (3D ion tracker, particle-identification wall, gamma-ray array, ...) must be developed [15, 20]. Also the target technology must be upgraded, to avoid the damage of the thin films due to the high temperature involved [21, 23]. Moreover, a deep and complete investigation of the theoretical aspects connecting nuclear reaction mechanisms and nuclear matrix elements must be carried out [24, 26].

## 2.1. *An updated overview*

NUMEN experimental activity consists of two main classes of experiments, corresponding to the exploration of the two directions of isospin transfer $\tau^- \tau^-$ and $\tau^+ \tau^+$, characteristic of $\beta-\beta^-$ and $\beta+\beta^+$ decays, respectively. In particular, the $\beta+\beta^+$ direction in the target is investigated using a $^{18}$O beam and measuring the ($^{18}$O,$^{18}$Ne) DCE induced transitions, together with the other reaction channels involving the same beam and target. Similarly, the $\beta-\beta^-$ direction is explored via the ($^{20}$Ne,$^{20}$O) reaction, using a $^{20}$Ne beam and detecting the reaction products of the DCE channel along with other open channels characterized by the same projectile and target. With the actual facility and experimental setup we perform some long run at LNS with MAGNEX, choosing few isotopes, candidates for $0\nu\beta\beta$, already at our reach in terms of energy resolution and availability of thin targets.

In particular, we performed for the first time experimental investigations of the ($^{20}$Ne,$^{20}$O) DCE reaction on $^{116}$Cd,$^{76}$Ge and $^{130}$Te targets. These are the first measurements of such a kind of reaction: no data are available in literature. A $^{20}$Ne$^{10+}$ cyclotron beam at 15 AMeV was delivered by the CS of INFN-LNS and impinged on $^{116}$Cd rolled target of 1370 µg/cm$^2$ thickness and $^{76}$Ge (386 µg/cm$^2$ thickness) and $^{130}$Te (247 µg/cm$^2$ thickness) both evaporated on a C backing of 50 µg/cm$^2$. The thickness of the various targets was carefully chosen in order to obtain an energy resolution which allows to distinguish the transition to the residual nucleus ground state from its first excited state. Indeed, the selected thickness of $^{116}$Cd is much higher than that of $^{76}$Ge and $^{130}$Te, because the first excited state in $^{116}$Sn case is at 1.293 MeV, to be compared to 0.559 MeV in $^{76}$Se and 0.536 MeV in $^{130}$Xe. The MAGNEX spectrometer was placed at forward angles including zero degrees in the full acceptance mode (50 msr). Despite the experimental limitations, we were able to measure energy spectra and absolute cross sections for the DCE reaction channel. Moreover, we measured also other reaction channels: one- and two-proton transfer, one- and two-neutron transfer and Single Charge Exchange, in order to estimate the role of the sequential multi-nucleon transfer routes on the diagonal DCE process.
### 3. Conclusions and outlook

Pioneering experiments on ($^{18}$O,$^{18}$Ne) and ($^{20}$Ne,$^{20}$O) DCE performed at INFN-LNS Laboratory in Catania have shown that accurate cross sections measurements at very forward angles can be done. The main activity characterizing the NUMEN project is the measurement of DCE absolute cross sections, with the related processes, and the extraction of relevant NMEs. The NUMEN “Holy Grail” is to find a connection between the NMEs extracted from DCE reactions and those characterizing $0v\beta\beta$ decay, at least in the nuclei in which this process is energetically allowed. NUMEN is a big challenge both for nuclear technology and nuclear theory. Moreover it promotes an important upgrade of the experimental facilities and the development of the different theoretical aspects, connected with the nuclear structure and reaction mechanisms, involved in heavy ions induced in DCE reactions. High intensity beams are the new frontier for these challenging studies. NUMEN indicates a possible growth prospect of heavy-ion physics in synergy with neutrino physics, aims at giving an innovative contribution in one of the most promising fields of fundamental physics.

### References

[1] J. D. Vergados et al., Reports on Progress in Physics 75, 106301 (2012).

[2] P. Vogel, Jour. of Phys. G 39, 124002 (2012).

[3] J. Barea, J. Kotila, F. Iachello, Phys. Rev. Lett. 109, 042501 (2012).

[4] S. Dell'Oro et al., Advances in High Energy Physics 2016, 216259 (2016).

[5] F. Cappuzzello et al., Eur. Phys. J. A 54, 72 (2018).

[6] C. Agodi et al., Nucl. Part. Phys. Proc. 265, 28 (2015).

[7] F. Cappuzzello et al., Eur. Phys. J. A 52, 167 (2015).

[8] F. Cappuzzello et al., Nature Communications 6, 6743 (2015).

[9] D. Carbone et al., Phys. Rev. C 95, 034603 (2017).

[10] J. R. B. Oliveira et al., J. Phys. G 40, 105101 (2013).

[11] M. Cavallaro et al., Phys. Rev. C 93, 064323 (2016).

[12] M. Cavallaro et al., Nucl. Instr. and Meth. A 700, 65 (2013).

[13] F. Cappuzzello et al., Eur. Phys. J. A 51, 145 (2015).

[14] L. Calabretta et al., Modern Physics Letters A 32, 17 (2017).

[15] M. Cortesi et al., Review of Scientific Instruments 88, 013303 (2017).

[16] D. Lo Presti et al., J. Phys. Conf. Ser. 18, 012034 (2018).

[17] S. Tudisco et al., Sensors 18, 2289 (2018).

[18] A. Muoio et al., EPJ Web of Conferences 117, 10006 (2016).

[19] D. Carbone et al., Results in Physics 6, 863-865 (2016).

[20] J. R. B. Oliveira et al., J. Phys. Conf. Ser. 18, 012040 (2018).

[21] F. Pinna et al., J. Phys. Conf. Ser. 1056, 012046 (2018).

[22] F. Iazzi et al., WIT Transactions on Engineering Science 116, 206 (2017).

[23] S. Calabrese et al., Acta Phys. Pol. B 49, 275 (2018).

[24] H. Lenske et al., Phys. Rev. C 98, 044620 (2018).

[25] E. Santopinto et al., Phys. Rev. C 98, 061601(R) (2018).

[26] J. Bellone et al., J. Phys. Conf. Ser. 1056, 012004 (2018).
### 3. Conclusions and outlook

Pioneering experiments on ($^{18}$O,$^{18}$Ne) and ($^{20}$Ne,$^{20}$O) DCE performed at INFN-LNS Laboratory in Catania have shown that accurate cross sections measurements at very forward angles can be done. The main activity characterizing the NUMEN project is the measurement of DCE absolute cross sections, with the related processes, and the extraction of relevant NMEs. The NUMEN “Holy Grail” is to find a connection between the NMEs extracted from DCE reactions and those characterizing $0v\beta\beta$ decay, at least in the nuclei in which this process is energetically allowed. NUMEN is a big challenge both for nuclear technology and nuclear theory. Moreover it promotes an important upgrade of the experimental facilities and the development of the different theoretical aspects, connected with the nuclear structure and reaction mechanisms, involved in heavy ions induced in DCE reactions. High intensity beams are the new frontier for these challenging studies. NUMEN indicates a possible growth prospect of heavy-ion physics in synergy with neutrino physics, aims at giving an innovative contribution in one of the most promising fields of fundamental physics.

### References

[1] J. D. Vergados et al., Reports on Progress in Physics 75, 106301 (2012).

[2] P. Vogel, Jour. of Phys. G 39, 124002 (2012).

[3] J. Barea, J. Kotila, F. Iachello, Phys. Rev. Lett. 109, 042501 (2012).

[4] S. Dell'Oro et al., Advances in High Energy Physics 2016, 216259 (2016).

[5] F. Cappuzzello et al., Eur. Phys. J. A 54, 72 (2018).

[6] C. Agodi et al., Nucl. Part. Phys. Proc. 265, 28 (2015).

[7] F. Cappuzzello et al., Eur. Phys. J. A 52, 167 (2015).

[8] F. Cappuzzello et al., Nature Communications 6, 6743 (2015).

[9] D. Carbone et al., Phys. Rev. C 95, 034603 (2017).

[10] J. R. B. Oliveira et al., J. Phys. G 40, 105101 (2013).

[11] M. Cavallaro et al., Phys. Rev. C 93, 064323 (2016).

[12] M. Cavallaro et al., Nucl. Instr. and Meth. A 700, 65 (2013).

[13] F. Cappuzzello et al., Eur. Phys. J. A 51, 145 (2015).

[14] L. Calabretta et al., Modern Physics Letters A 32, 17 (2017).

[15] M. Cortesi et al., Review of Scientific Instruments 88, 013303 (2017).

[16] D. Lo Presti et al., J. Phys. Conf. Ser. 18, 012034 (2018).

[17] S. Tudisco et al., Sensors 18, 2289 (2018).

[18] A. Muoio et al., EPJ Web of Conferences 117, 10006 (2016).

[19] D. Carbone et al., Results in Physics 6, 863-865 (2016).

[20] J. R. B. Oliveira et al., J. Phys. Conf. Ser. 18, 012040 (2018).

[21] F. Pinna et al., J. Phys. Conf. Ser. 1056, 012046 (2018).

[22] F. Iazzi et al., WIT Transactions on Engineering Science 116, 206 (2017).

[23] S. Calabrese et al., Acta Phys. Pol. B 49, 275 (2018).

[24] H. Lenske et al., Phys. Rev. C 98, 044620 (2018).

[25] E. Santopinto et al., Phys. Rev. C 98, 061601(R) (2018).

[26] J. Bellone et al., J. Phys. Conf. Ser. 1056, 012004 (2018).