# Nuclear physics midterm plan at Legnaro National Laboratories (LNL)

M Ballan, S Bottoni, M Caamaño, A Caciolli, M Campostrini, M Cicerchia, F.C.L Crespi, S Cristallo, D Dell'Aquila, R Depalo, et al.

► To cite this version:

M Ballan, S Bottoni, M Caamaño, A Caciolli, M Campostrini, et al. Nuclear physics midterm plan at Legnaro National Laboratories (LNL). The European Physical Journal Plus, 2023, 138 (8), pp.709. 10.1140/epjp/s13360-023-04249-x. hal-04185215

HAL Id: hal-04185215

https://hal.science/hal-04185215v1

Submitted on 20 Oct 2023

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Nuclear physics midterm plan at Legnaro National Laboratories (LNL)

M. Ballan<fnref n="1" />, S. Bottoni<fnref n="2" />,<fnref n="3" />, M. Caamaño<fnref n="4" />, A. Caciolli<fnref n="5" />,<fnref n="6" />, M. Campostrini<fnref n="1" />, M. Cicerchia<fnref n="1" />, F. C. L. Crespi<fnref n="2" />,<fnref n="3" />, S. Cristallo<fnref n="7" />,<fnref n="8" />,
D. Dell'Aquila<fnref n="9" />,<fnref n="10" />, R. Depalo<fnref n="2" />,<fnref n="3" />, F. Fioretto<fnref n="1" />, F. Galtarossa<fnref n="1" />,<fnref n="5" />, L. R. Gasques<fnref n="11" />, A. Gottardo<fnref n="1" />, F. Gramegna<fnref n="1" />,
F. Gulminelli<fnref n="12" />, T. Kurtukian-Nieto<fnref n="13" />, M. La Cognata<fnref n="10" />, S. M. Lenzi<fnref n="5" />,<fnref n="6" />, T. Marchi<fnref n="1" />, K. Mazurek<fnref n="14" />, D. Mengoni<fnref n="5" />,<fnref n="6" />,α ID,
L. Mou<fnref n="1" />,<fnref n="15" />, R. Nania<fnref n="16" />, G. Pupillo<fnref n="1" />, J. J. Valiente-Dobón<fnref n="1" />,ᵇ, I. Zanon<fnref n="1" />,<fnref n="15" />, L. Acosta<fnref n="17" />, M. A. G. Alvarez<fnref n="18" />, A. Andrighetto<fnref n="1" />,
A. Arazi<fnref n="19" />, A. Arzenton<fnref n="1" />,<fnref n="20" />, M. Assié<fnref n="21" />, M. Bagatin<fnref n="5" />, F. Barbaro<fnref n="6" />,<fnref n="22" />, C. Barbieri<fnref n="2" />,<fnref n="3" />, S. Barlini<fnref n="23" />,<fnref n="24" />, L. Basiricò<fnref n="25" />,
G. Battistoni<fnref n="3" />, D. Beaumel<fnref n="20" />, M. A. Bentley<fnref n="26" />, G. Benzoni<fnref n="3" />, S. Bertoldo<fnref n="1" />, C. Bertulani<fnref n="27" />, A. Bonasera<fnref n="10" />,<fnref n="28" />, A. Camaiani<fnref n="29" />,
L. Canton<fnref n="6" />, V. Capirossi<fnref n="30" />, M. P. Carante<fnref n="22" />,<fnref n="31" />, C. Carraro<fnref n="1" />, S. M. Carturan<fnref n="1" />,<fnref n="5" />, G. Casini<fnref n="23" />, F. Cavanna<fnref n="32" />, L. Centofante<fnref n="1" />,
E. R. Chávez<fnref n="17" />, A. Chbihi<fnref n="33" />, M. Ciemała<fnref n="14" />, S. Cisternino<fnref n="1" />,<fnref n="3" />,<fnref n="4" />, A. Colombi<fnref n="22" />,<fnref n="31" />, M. Colucci<fnref n="2" />,<fnref n="3" />, A. Compagnucci³⁵,
S. Corradetti<fnref n="1" />, L. Corradi<fnref n="1" />, G. D'Agata<fnref n="10" />,³⁶, G. de Angelis<fnref n="1" />, L. De Dominicis<fnref n="1" />,<fnref n="5" />, D. De Salvador<fnref n="5" />, E. DeFilippo³⁷,
M. Del Fabbro<fnref n="6" />,<fnref n="15" />, A. Di Nitto³⁸,³⁹, S. Ditalia Tchernij⁴⁰, A. Donzella<fnref n="31" />,⁴¹, T. Duguet<fnref n="29" />,⁴², J. Esposito<fnref n="1" />, F. Favela<fnref n="17" />,
J. P. Fernández-García<fnref n="18" />, F. Flavigny⁴³, A. Fontana<fnref n="31" />, B. Fornal<fnref n="14" />, J. Forneris⁴⁰, B. Fraboni<fnref n="25" />, J. Frankland<fnref n="33" />,
E. Gamba<fnref n="2" />,<fnref n="3" />, E. Geraci³⁶,³⁷, S. Gerardin<fnref n="5" />, S. A. Giuliani⁴⁴, B. Gnoffo³⁶,³⁷, F. Groppi<fnref n="2" />,<fnref n="3" />, D. Gruyer⁴², F. Haddad⁴⁵,⁴⁶,
J. Isaak⁴⁷, M. Kmiecik<fnref n="14" />, A. Koning⁴⁸, L. Lamia<fnref n="10" />,³⁶, N. Le Neindre<fnref n="33" />, S. Leoni<fnref n="2" />,<fnref n="3" />, A. Lépine-Szily<fnref n="11" />, G. Lilli<fnref n="1" />,
I. Lombardo³⁶,³⁷, M. Loriggiola<fnref n="1" />, L. Loriggiola<fnref n="1" />, M. Lunardon<fnref n="5" />,<fnref n="6" />, G. Maggioni<fnref n="1" />,<fnref n="5" />, A. Maj<fnref n="14" />, S. Manenti<fnref n="2" />,<fnref n="3" />,
M. Manzolaro<fnref n="1" />, L. E. Marcucci⁴⁹,⁵⁰, D. J. Marín-Lámbarri<fnref n="17" />, E. Mariotti<fnref n="20" />, G. Martin Hernandez⁵¹, C. Massimi<fnref n="16" />,<fnref n="25" />,
P. Mastinu<fnref n="1" />, M. Mazzocco<fnref n="5" />,<fnref n="6" />, A. Mazzolari⁵², T. Mijatović⁵³, T. Mishenina⁵⁴, K. Mizuyama⁵⁵, A. Monetti<fnref n="1" />,
G. Montagnoli<fnref n="5" />,<fnref n="6" />, L. Morselli<fnref n="1" />,<fnref n="15" />, L. Moschini⁵⁶, E. Musacchio Gonzalez<fnref n="1" />, A. Nannini<fnref n="23" />, Y. F. Niu⁵⁷, S. Ota⁵⁸,
A. Paccagnella⁵⁹, S. Palmerini<fnref n="8" />,⁶⁰, L. Pellegri⁶¹, A. Perego⁶², S. Piantelli<fnref n="23" />, D. Piatti<fnref n="5" />,<fnref n="6" />, F. Picollo⁴⁰, M. Pignatari⁶³,⁶⁴,
F. Pinna<fnref n="30" />, S. Pirrone³⁷, R. G. Pizzone<fnref n="10" />, M. Poletti<fnref n="2" />,<fnref n="3" />, G. Politi³⁶,³⁷, L. Popescu⁶⁵, G. Prete<fnref n="1" />, A. Quaranta⁶⁶,⁶⁷,
R. Raabe<fnref n="29" />, J. P. Ramos⁶⁵, W. Raniero<fnref n="1" />, G. G. Rapisarda<fnref n="10" />,³⁶, F. Recchia<fnref n="5" />,<fnref n="6" />, V. Rigato<fnref n="1" />, X. Roca Maza<fnref n="2" />,<fnref n="3" />, M. Rocchini<fnref n="23" />,
T. Rodriguez⁴⁴, C. Roncolato<fnref n="1" />, D. Rudolph⁶⁸, P. Russotto<fnref n="10" />, Á. M. Sánchez-Benítez⁶⁹, D. Savran⁷⁰, D. Scarpa<fnref n="1" />,
M. Scheck⁷¹, K. Sekizawa⁷²,⁷³, M. L. Sergi<fnref n="10" />,³⁶, F. Sgarbossa<fnref n="1" />,<fnref n="5" />, L. Silvestrin<fnref n="5" />,<fnref n="6" />, O. Singh Khwairakpam<fnref n="1" />,<fnref n="20" />,
J. Skowronski<fnref n="5" />,<fnref n="6" />, V. Somà⁴², R. Spartà<fnref n="10" />, M. Spieker⁷⁴, A. M. Stefanini<fnref n="1" />, H. Steiger⁷⁵,⁷⁶, L. Stevanato<fnref n="6" />, M. R. Stock⁷⁶,
E. Vardaci³⁸,³⁹, D. Verney<fnref n="21" />, D. Vescovi<fnref n="7" />,<fnref n="8" />,⁷⁷, E. Vittone⁴⁰, V. Werner⁴⁷, C. Wheldon⁷⁸, O. Wieland<fnref n="3" />, K. Wimmer⁷⁰,
J. Wyss<fnref n="6" />,⁷⁹, L. Zago<fnref n="1" />,<fnref n="5" />, A. Zenoni<fnref n="31" />,⁴¹

<footnote n="1">¹ Laboratori Nazionali di Legnaro, Istituto Nazionale di Fisica Nucleare, Viale dell'Università 2, 35020 Legnaro, Italy</footnote>

<footnote n="2">² Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milan, Italy</footnote>

<footnote n="3">³ Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy</footnote>

<footnote n="4">⁴ IGFAE, Universidade de Santiago de Compostela, Santiago de Compostela, Spain</footnote>

<footnote n="5">⁵ Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via Marzolo 8, 35131 Padua, Italy</footnote>

<footnote n="6">⁶ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padua, Italy</footnote>

<footnote n="7">⁷ INAF - Osservatorio Astronomico d'Abruzzo, Via Mentore Maggini snc, Loc. Collurania, 64100 Teramo, Italy</footnote>

<footnote n="8">⁸ Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via Alessandro Pascoli, 06123 Perugia, Italy</footnote>

<footnote n="9">⁹ Dipartimento di Fisica "Ettore Pancini", Università degli Studi di Napoli "Federico II", Naples, Italy</footnote>

<footnote n="10">¹⁰ Laboratori Nazionali del Sud, Instituto Nazionale di Fisica Nucleare, Via S. Sofia 62, 95123 Catania, Italy</footnote>

<footnote n="11">¹¹ Universidade de Sao Paulo, Instituto de Fisica, Rua do Matao, 1371, Sao Paulo 05508-090, Brazil</footnote>

<footnote n="12">¹² LPC (IN2P3-CNRS/Ensicaen et Université), 14076 Caen Cédex, France</footnote>

<footnote n="13">¹³ CNRS/IN2P3 Université de Bordeaux LP2IB (CENBG), 19 chemin du Solarium, 33170 Gradignan, France</footnote>

<footnote n="14">¹⁴ Institute of Nuclear Physics Polish Academy of Sciences, 31342 Kraków, Poland</footnote>

<footnote n="15">¹⁵ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Ferrara, Italy</footnote>

<footnote n="16">¹⁶ Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Bologna, Italy</footnote>

<footnote n="17">¹⁷ Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México City, Mexico</footnote>

<footnote n="18">¹⁸ Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, Apartado 1065, 41080 Seville, Spain</footnote>

<footnote n="19">¹⁹ Laboratorio TANDAR, Comisión Nacional de Energía Atómica, Avenida General Paz 1499, BKNA1650 San Martín, Argentina</footnote>

<footnote n="20">²⁰ Dipartimento di Scienze Fisiche, della Terra e dell'Ambiente, Università di Siena, Siena, Italy</footnote>

<footnote n="21">²¹ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France</footnote>

<footnote n="22">²² Dipartimento di Fisica, Università di Pavia, Pavia, Italy</footnote>

<footnote n="23">²³ Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Florence, Italy</footnote>

<footnote n="24">²⁴ Physics and Astronomy Department, University of Firenze, Florence, Italy</footnote>

<footnote n="25">²⁵ Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy</footnote>

<footnote n="26">²⁶ School of Physics, Engineering and Technology, University of York, Heslington, York YO105DD, UK</footnote>

<footnote n="27">²⁷ Department of Physics and Astronomy, Texas A&M University, Commerce, TX, USA</footnote>

<footnote n="28">²⁸ Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA</footnote>

<footnote n="29">²⁹ Instituut voor Kern- en Stralingsfysica, K.U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium</footnote>

<footnote n="30">³⁰ Department of Applied Science and Technology, Politecnico di Torino, Turin, Italy</footnote>

<footnote n="31">³¹ Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy</footnote>

<footnote n="32">³² Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P.Giuria 1, 10125 Turin, Italy</footnote>

<footnote n="33">³³ Grand Accélérateur National d'Ions Lourds (GANIL), UPR 3266, CEA-DRF/CNRS-IN2P3, Boulevard Henri Becquerel, 14076 Caen Cedex, France</footnote>
Received: 1 February 2023 / Accepted: 2 July 2023

© The Author(s) 2023

**Abstract** The next years will see the completion of the radioactive ion beam facility SPES (Selective Production of Exotic Species) and the upgrade of the accelerators complex at Istituto Nazionale di Fisica Nucleare – Legnaro National Laboratories (LNL) opening up new possibilities in the fields of nuclear structure, nuclear dynamics, nuclear astrophysics, and applications. The nuclear physics community has organised a workshop to discuss the new physics opportunities that will be possible in the near future by employing state-of-the-art detection systems. A detailed discussion of the outcome from the workshop is presented in this report.

<footnote n="34">³⁴ Dipartimento di Ingegneria Industriale, Università di Padova, Padua, Italy</footnote>

<footnote n="35">³⁵ Gran Sasso Science Institute, L'Aquila, Italy</footnote>

<footnote n="36">³⁶ Dipartimento di Fisica e Astronomia "Ettore Majorana", Università degli Studi di Catania, Via S. Sofia 64, 95123 Catania, Italy</footnote>

<footnote n="37">³⁷ Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 62, 95123 Catania, Italy</footnote>

<footnote n="38">³⁸ Physics Department, University of Naples, Naples, Italy</footnote>

<footnote n="39">³⁹ Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Naples, Italy</footnote>

<footnote n="40">⁴⁰ Dipartimento di Fisica, Università di Torino, Turin, Italy</footnote>

<footnote n="41">⁴¹ Dipartimento di Ingegneria meccanica e industriale, Università degli Studi di Brescia, Brescia, Italy</footnote>

<footnote n="42">⁴² CEA, Saclay, France</footnote>

<footnote n="43">⁴³ Normandie Université ENSICAEN, UNICAEN, CNRS/IN2P3, Caen, France</footnote>

<footnote n="44">⁴⁴ Departamento de Física Teórica, Universidad Autonoma de Madrid (UAM), Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain</footnote>

<footnote n="45">⁴⁵ Laboratoire SUBATECH, CNRS/IN2P3, IMT Atlantique, Nantes Université, Nantes, France</footnote>

<footnote n="46">⁴⁶ GIP ARRONAX, Saint Herblain, Nantes, France</footnote>

<footnote n="47">⁴⁷ Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany</footnote>

<footnote n="48">⁴⁸ International Atomic Energy Agency (IAEA), Wien, Austria</footnote>

<footnote n="49">⁴⁹ Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo, 3, 56127 Pisa, Italy</footnote>

<footnote n="50">⁵⁰ Dipartimento di Fisica, Università degli Studi di Pisa, Largo B. Pontecorvo, 3, 56127 Pisa, Italy</footnote>

<footnote n="51">⁵¹ Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear, Havana, Cuba</footnote>

<footnote n="52">⁵² Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Ferrara, Italy</footnote>

<footnote n="53">⁵³ Ruder Bošković Institute, Zagreb, Croatia</footnote>

<footnote n="54">⁵⁴ Astronomical Observatory, Odessa National University, 1v, Marazliyivska st, Odessa 65014, Ukraine</footnote>

<footnote n="55">⁵⁵ Duy Tan University, Da Nang, Vietnam</footnote>

<footnote n="56">⁵⁶ Department of Physics, University of Surrey, Stag Hill, Guildford GU2 7XH, UK</footnote>

<footnote n="57">⁵⁷ Lanzhou University, Lanzhou, China</footnote>

<footnote n="58">⁵⁸ RCNP Osaka University, Osaka, Japan</footnote>

<footnote n="59">⁵⁹ Dipartimento di Ingegneria dell' Informazione, Università di Padova, Padua, Italy</footnote>

<footnote n="60">⁶⁰ Dipartimento di Fisica e Geologia, Università degli Studi di Perugia, Via Alessandro Pascoli, 06123 Perugia, Italy</footnote>

<footnote n="61">⁶¹ WITS & iTL South Africa, Cape Town, South Africa</footnote>

<footnote n="62">⁶² Dipartimento di Fisica, Università degli Studi di Trento, Via Sommarive, 14, 38123 Povo, Italy</footnote>

<footnote n="63">⁶³ Konkoly Observatory, Konkoly-Thege Miklós út 13-17, Budapest 1121, Hungary</footnote>

<footnote n="64">⁶⁴ Hull University, Hull HU6 7RX, UK</footnote>

<footnote n="65">⁶⁵ Belgian Nuclear Research Centre SCK CEN, Boeretang 200, 2400 Mol, Belgium</footnote>

<footnote n="66">⁶⁶ Dipartimento di Ingegneria Industriale, Università di Trento, Trento, Italy</footnote>

<footnote n="67">⁶⁷ INFN, Trento Institute for Fundamental Physics and Application (TIFPA), Trento, Italy</footnote>

<footnote n="68">⁶⁸ Department of Physics, Lund University, 22100 Lund, Sweden</footnote>

<footnote n="69">⁶⁹ Centro de Estudios Avanzados en Física Matemática y Computación, Universidad de Huelva, Calle Dr. Cantero Cuadrado, 6, 21004 Huelva, Spain</footnote>

<footnote n="70">⁷⁰ GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany</footnote>

<footnote n="71">⁷¹ University of the West of Scotland, Paisley, UK</footnote>

<footnote n="72">⁷² Department of Physics, School of Science, Tokyo Institute of Technology, Tokyo 152-8551, Japan</footnote>

<footnote n="73">⁷³ Nuclear Physics Division, Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8577, Japan</footnote>

<footnote n="74">⁷⁴ University of Florida State, Tallahassee, USA</footnote>

<footnote n="75">⁷⁵ Johannes Gutenberg-Universität Mainz, Mainz, Germany</footnote>

<footnote n="76">⁷⁶ Technische Universität München, Munich, Germany</footnote>

<footnote n="77">⁷⁷ Institute for Applied Physics, Goethe University, 60438 Frankfurt, Germany</footnote>

<footnote n="78">⁷⁸ University of Birmingham, Birmingham, UK</footnote>

<footnote n="79">⁷⁹ Dipartimento di Ingegneria Civile e Meccanica, Università degli Studi di Cassino e del Lazio Meridionale, Cassino, Frosinone, Italy</footnote>

<footnote>ª e-mail: daniele.mengoni@pd.infn.it (corresponding author)</footnote>

<footnote>ᵇ e-mail: javier.valiente@lnl.infn.it (corresponding author)</footnote>
# 1 Executive summary

The Legnaro National Laboratories (LNL) of the Istituto Nazionale di Fisica Nucleare (INFN) are an user-oriented large-scale facility mainly dedicated to research programs in nuclear physics and nuclear astrophysics, and to high-level technology developments relevant to several disciplines [1]. The LNL accelerator complex consists in two smaller electrostatic accelerators (the 2 MV AN2000 and the 7 MV CN) and the Tandem-ALPI-PIAVE complex (TAP), with a 15 MV Tandem XTU and the superconducting RFQ PIAVE [2], equipped with an ECR source, acting as injectors of the superconducting Linac ALPI [3]. In addition, the SPES (Selective Production of Exotic Species) project will provide second-generation ISOL (Isotope Separation On-Line) beams. The SPES project is based on a dual-exit cyclotron B70 providing proton beams with energies ranging between 35 MeV and 70 MeV and a maximum beam intensity of 0.75 mA. This is the primary accelerator of the ISOL system, based on a UCx target, for the production of neutron-rich unstable ion beams. The cyclotron will be also used for applied physics activities. The available facilities at LNL together with the state-of-the-art instrumentation are discussed in Sect. 2. The SPES facility will provide ion beams that are complementary to the fragmentation beams which will be produced by FraISe (FRAgment Ion Separator) [4] at LNS. These two main laboratories of INFN devoted to nuclear physics are, and will be even more in the near future, attractive poles for worldwide users. The SPES facility will operate in a very competitive international environment with other facilities such as: HIE-ISOLDE, GANIL-SPIRAL, TRIUMF, etc. In this manuscript, many cases where SPES can coherently contribute to the the international endeavour will be presented.

The Nuclear Physics Mid Term Plan in Italy (https://web.infn.it/nucphys-plan-italy/) made possible to trigger and coordinate new ideas from the whole international community, in particular from the new generation of nuclear physics researchers that will be the leading forces in the exploitation of the new facilities. The LNL session of the workshop (https://agenda.infn.it/event/28738/) comprised four working groups on Nuclear Astrophysics, Nuclear Structure, Nuclear Dynamics and Applications, involving experimental and theoretical physicists.

This initiative follows the previous INFN Nuclear Physics Division joint initiatives on nuclear astrophysics [5] and on particle identification [6].

## 1.1 Nuclear astrophysics

A large variety of opportunities to be explored at LNL in the future have been highlighted. Two big topics have been discussed, the nucleosynthesis up to the iron peak (Sect. 3.1) and the nucleosynthesis of trans-iron elements (Sect. 3.2). The variety of accelerator facilities, innovative targets and state-of-the-art detection systems will allow the community to measure nuclear cross sections of astrophysical interest using both direct and indirect techniques. This will open a window on a wide range of astrophysical scenarios, including Big Bang Nucleosynthesis, quiescent stellar burning and explosive stellar burning. Radioactive beams from SPES will be used to investigate the properties of unstable nuclei and study nuclear reactions which are essential to explain the presence of radioactive elements in our Galaxy, as well as the synthesis of heavy elements through the s-, i- and r- processes.

## 1.2 Nuclear structure

An ample range of open problems and challenges in nuclear structure and astrophysical processes have been highlighted as explorable at LNL in the near and medium future using stable and radioactive beams from SPES. The interest of the community spans from light stable and near stable nuclei (Sect. 4.2) to neutron-rich ISOL beams from SPES to tackle subjects such as 3-body forces, mirror-symmetry breaking (Sect. 4.3), shell evolution (Sect. 4.4) and collective and resonant states (Sect. 4.5). The working group has also encouraged theoretical discussions on models that, by solving the many-body problem using either recent ab-initio theories, interacting shell model approaches or energy density functional theories (Sect. 4.1), could stimulate future experimental initiatives.

## 1.3 Nuclear dynamics

The attention was put on the several processes that drive the evolution of a nuclear reaction between heavy nuclei, considering its interplay with the structure. In fusion reactions, deviations from a purely statistical model in the evaporation channel have been observed. Their explanation require a detailed investigation of competing mechanisms (e.g. out-of-equilibrium emissions) and a better understanding of the role of nuclear clusters (Sect. 5.1). The study of more peripheral collisions allows to constrain shell model approaches and it is a powerful indirect method to probe reactions relevant in astrophysics. Moreover, multinucleon transfer processes close to the Coulomb barrier can be used to investigate nucleon-nucleon correlations and the population of neutron-rich heavy nuclei (Sect. 5.2). The upcoming availability of $^{238}$U beams at energies around the Coulomb barrier opens up the possibility of using transfer and inelastic reactions to populate and study a wide variety of fissioning systems along the nuclear chart. At lower energies, sub-barrier fusion allows to probe the quantum behaviour of nuclear systems (Sect. 5.3).
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Aereal view of the Laboratori Nazionali di Legnaro</figcaption></figure>

## 1.4 Nuclear physics applications

A wide range of fields were covered, ranging from medicine to material science, from nuclear waste management up to targets and detector development and characterization, radiation damage, etc. Thanks to the SPES facility, LNL will be a unique center in Europe for the production of novel medical radionuclides, able to exploit both the direct activation method (Sect. 6.1) with the LARAMED project and the ISOL-technique (Sect. 6.2) with the ISOLPHARM project. Considering the SPES cyclotron and the future beamlines, the refurbished XTU-Tandem and the upgrades at the CN, LNL will be able to offer a suite of neutron beams (En ≥ thermal) capable of serving a worldwide community, spread over a broad range of physics subjects, from basic to applied research (Sect. 6.1). The development, characterization and modification of material for nuclear physics applications have a consolidated background at LNL and a bright future, that range from micro beam analysis to detector development (Sect. 6.3).

For each working group, a dedicated chapter will describe the outcome of the discussions among the participants. The introduction of each chapter will contain a schematic view and a table with the main measurements and their tentative time-sequence (Phase A at the start of operations, which include the activities that can be performed as soon as the facilities will be ready, Phase B activities that can be performed with some minor upgrades, Phase C a longer Research and Development work is requested).

## 2 Introduction

The Legnaro National Laboratoires (LNL) [1] of the Istituto Nazionale di Fisica Nucleare (INFN) are a user-oriented large-scale facility mainly dedicated to research programs in nuclear physics and nuclear astrophysics, and to high-level technology developments relevant to several disciplines (accelerator science, innovative detectors, material science and applications of nuclear techniques). Currently, nuclear physics and astrophysics experiments mainly benefit from the high-quality ion beams delivered by the Tandem-ALPI-PIAVE complex (TAP) which consists of the 15 MV Tandem XTU and the superconducting RFQ PIAVE [2], equipped with a ECR source, acting as injectors of the superconducting Linac ALPI [3]. In particular, ion beams from hydrogen to lead are currently provided with energies ranging from few to 20 MeV/u and intensities up to ~ 20 pA. The foreseen upgrade of ALPI cavities in 2023 will further increase the final energy. The complete list of the available ion beams, maximum energy and intensity can be found at: https://www.lnl.infn.it/wp-content/uploads/Fasci_TAP.pdf. On the basis of new requests triggered by the User Community, authorizations for the acceleration of $^{238}$U beam and the use of $^{232}$Th and $^{238}$U radioactive targets have been submitted to the regulatory authority responsible for nuclear safety and radiation protection. The $^{238}$U beam will be delivered by the PIAVE-ALPI complex at an energy of 7.2 MeV/u, allowing to carry out experiments in inverse kinematic addressed to both the study of nuclear structure of exotic neutron-rich fission fragments and a better understanding of the fission process.

The most important initiative of LNL is the SPES (Selective Production of Exotic Species) project aiming at the construction and operation of a second-generation ISOL (Isotope Separation On-Line) facility, on which the mid- and long-term strategy of the laboratory is centred. An aerial view of the LNL can be seen in Fig. 1.

The SPES facility [7] will provide both low-energy (about 40 keV) and re-accelerated radioactive ion beams (10 AMeV for masses around A = 130) to carry out forefront research in nuclear physics and nuclear astrophysics. The facility, currently under construction, is based on a dual-exit cyclotron B70 providing proton beams with energies ranging between 35 MeV and 70 MeV and a maximum beam intensity of 0.75 mA. The cyclotron acts as driver accelerator for the ISOL system based on a UCx target
able to sustain a power of 10 kW. The fission mechanism induced by protons (40 MeV, 200 µA) inside the UCx target produces more than $10^{13}$ fissions/s, allowing the production of neutron-rich unstable ion beams with intensities one order of magnitude higher than in existing facilities. The second exit of the cyclotron will be used for applied physics activities such as the development and the production of innovative radionuclides for medicine, and neutron sources for material science study. SPES is included in the NuPECC Road map (https://www.nupecc.org/?display=front), together with HIE-ISOLDE at CERN (Switzerland) and SPIRAL2 at GANIL (France).

Depending on the needed efficiency and selectivity, different methods will be used for the extraction and selection of the fission products. In particular, three kinds of sources have been developed at SPES: the surface ionization source (SIS), the plasma ion source (PIS) and the Laser Ionization Source (LIS). The latter provides the most selective ionization process with inherent suppression of unwanted isobaric contaminations at the ion source. In addition, a High-Resolution Mass Separator (HRMS), with a resolving power $R \sim 1/20000$, will allow to reach a degree of purity of the beam nowadays not available.

The primary accelerator of SPES has already been installed and commissioned. First exotic beams re-accelerated with the Linac ALPI are expected to be available in 2026, allowing to perform experiments initially with Medium-Resolution Mass Separator (MRMS), and, subsequently, with full performance using the High-Resolution Mass Separator (HRMS). The schematic layouts of the SPES facility and the TAP complex are shown in Fig. 2. A complete list of the SPES beams and the foreseen intensities is available at the link https://web.infn.it/spes/index.php/characteristics/spes-beams-7037/spesbeamstable.

A schedule has been planned according to the main requests from the users, on the basis of the Letters of Intent (LOI) presented during the Third International SPES Workshop [8], and to the best compromise for the first operation of the SPES Target-Ion-Source (TIS) system.

For a safer commissioning of the ISOL system, at the beginning $^{26}$Al and $^{26}$Si beams will be produced with a SiC target. After these first experimental tests, a selection of beams produced with a reduced current (20 µA) on the UCx target, will be commissioned and provided, according to the feasibility and the user requests, also in terms of purity, for experiments to be performed with and without re-acceleration. In particular, the re-accelerated $^{132}$Sn beam represents a benchmark for the nuclear physics community being requested by a large number of LoIs and involving all experimental setups installed at LNL and the itinerant ones such as AGATA [9], NEDA [10], PARIS [11] and FAZIA [12].

The current main research programs for nuclear physics and astrophysics concern studies on:

* Structure of neutron-rich nuclei populated by binary reactions

* Shell and shape evolution in different mass regions

* Nuclear structure at high spins, neutron-deficient nuclei and superdeformation

* Fusion and grazing collisions around and below the Coulomb barrier

* Fission and quasi-fission dynamics with heavy-ion beams

* Nuclear structure at high excitation energy (giant resonances)

* Nuclear reactions of astrophysical interest induced by light ions and neutrons

* Clustering processes in light nuclei

The forthcoming operation of the SPES facility will allow to extend those research line to unexplored regions of the nuclide chart.

## 2.1 Resident instrumentation for nuclear physics

Nuclear structure and reaction dynamics studies at bombarding energies above as well as well below the Coulomb barrier are based on dedicated instrumentation for $\gamma$-rays, light particles and complex fragments. Some of the techniques used in these dedicated instrumentation are discussed in Ref. [6].

Major experimental instrumentation resident at Tandem-ALPI-PIAVE accelerator complex consists of:

* PRISMA [13]: a large acceptance magnetic spectrometer devoted to the study of quasi-elastic processes, nucleon-nucleon correlations, and population of neutron-rich nuclei in heavy-ion collisions. It is based on the trajectory reconstruction [14] of the ions travelling through the magnetic elements (a quadrupole singlet magnet followed by a dipole magnet) via the information provided by position-sensitive detectors at the entrance [15] and the focal plane [16] of the spectrometer. Thanks to its high-performance in terms of cross section sensitivity and resolving power of experimental observables (such as nuclear charge, mass and Q-values), PRISMA was successfully used, during the 20 years of operation at LNL, for specific experimental campaigns in conjunction with several $\gamma$-ray arrays, such as CLARA [17] and AGATA Demonstrator [18]. Currently, PRISMA is being coupled to the $\gamma$-ray spectrometer AGATA in the $1\pi$ configuration for a first experimental campaign with stable ion beams. Several upgrades, aiming at improving the charge resolution and the efficiency for light ions, are under development in view of the exotic beams of SPES.

* GALILEO [19]: a $\gamma$-ray spectrometer composed of 25 Compton-suppressed tapered HPGe detectors at 90° and forward angles, and 10 triple clusters Ge detectors, mounted at backward angles. This compact array allows for high detection efficiency and energy resolution. The spectrometer is equipped with digital electronics with high-rate capabilities. It can be used together with several complementary detectors for light particles and fragments [20–22], LaBr$_3$(Ce) for the detection of high-energy $\gamma$-rays, and a plunger device for lifetime measurements. GALILEO is a competitive device for $\gamma$-ray spectroscopy fully dedicated to the SPES radioactive nuclear beams.
<figure><img src="image_3.png" /><figcaption>Fig. 2 Layouts of the SPES facility and the TAP complex</figcaption></figure>

<figure><img src="image_4.png" /></figure>
* GARFIELD [23]: a large solid angle multi-detector array devoted to studies of both direct, clustering and fusion-evaporation processes in the light-ion region and fusion-evaporation and fusion-fission reactions in the medium-mass region. The apparatus consists of two large volume gas detectors employing micro-strip gas chambers (MSGC) as ΔE stage, followed by CsI(Tl) scintillators as residual energy detectors. This allows to achieve low identification thresholds (0.8–1 AMeV) using the ΔE-E technique. The detector is also equipped with a Ring Counter, an annular three-stage telescope array (Ionization chamber-Si-CsI) at forward angles, and full digital electronics. An upgrade of the GARFIELD electronics is in progress in view of the first exotic beams of SPES.

* ATS (Active Target for SPES): an active target to study elastic and inelastic scattering, and few nucleons transfer reactions with low-intensity and low-energy exotic beams delivered by SPES. It is based on the design of the ACTAR TPC project [24] and makes use of the Micromegas technology in the amplification region and can be equipped with ancillary detectors such as Si-Si or Si-CsI(Tl) telescopes for escaping particles, to have a better reconstruction of the reactions of interest, and LaBr₃ or HPGe for γ-particle coincidences. The OSCAR hodoscope [25], developed by the NUCLEX collaboration, is an example of a complementary detector for the ATS. It is a modular detector made by two detection stages (SSSSD and silicon pads) allowing to identify low energy (about 1 AMeV) particles. It can be used standalone or as an ancillary detector.

* PISOLO [26]: a set-up composed of an electrostatic deflector followed by a time-of-flight spectrometer (two micro-channel plate detectors in transmission configuration followed by a transverse-field ionization chamber and a large area Si detector) used for fusion cross section measurements around and below the Coulomb barrier. A fast multi-electrode ionization chamber has been designed to be used with re-accelerated SPES beams. Preliminary in-beam tests proved that the detector can be operated at rates of the order of 100 kHz.

* EXOTIC [27]: a facility devoted to the in-flight production of low-energy light exotic beams (such as $ ^7$Be, $ ^8$B, $ ^{17}$F, $ ^{15}$O, $ ^8$Li, $ ^{10}$C and $ ^{11}$C with intensities ranging from $10^3$ to $10^6$ pps) by inverse kinematics reactions. It is composed of: (i) a production gas target ($H_2$, $D_2$, $ ^3$He and $ ^4$He); (ii) a beam selection and transport system (a quadrupole triplet, a 30° bending magnet, a Wien filter and a second quadrupole triplet before the reaction chamber). EXOTIC is equipped with a detection system for reaction mechanism studies consisting of a radioactive ion beam (RIB) tracking system, based on position-sensitive Parallel Plate Avalanche Counters, and the charged-particle array EXPADES [28]. A Technical Design Report, concerning the coupling of EXOTIC to AGATA for nuclear structure studies with light radioactive beams, has been finalized in view of a future experimental campaign.

## 2.2 Itinerant instrumentation for nuclear physics

Existing collaborations between different European Research infrastructures allows at present and in the forthcoming years to share dedicated detection systems and electronics, designed and constructed to be used at RIB facilities under construction, among which SPES. Major itinerant European detectors which expressed the intent to perform experimental campaigns at LNL with stable and radioactive ion beams are the following:

* **AGATA [9]:** a γ-ray spectrometer based on the principle of γ-ray tracking through segmented high-purity germanium crystals, advanced digital electronics, and pulse-shape analysis [29]. It is the result of a combined effort of many different countries and institutions aimed at providing a new generation γ-ray array optimized for the new research challenges. The high energy resolution, coupled to the unprecedented position resolution, makes AGATA the best suitable array to study weak transitions or reactions involving large Doppler displacements. It is one of the major instruments foreseen to be used with re-accelerated RIBs of SPES allowing to access information on very exotic nuclei involved in the processes which govern the element formation in the universe. The spectrometer will be equipped with several complementary detectors for light particles and fragments, high-energy γ-rays (LaBr$_3$:Ce), and a plunger device [30], among which:

- **NEDA [10]:** a Neutron Detector Array with a large efficiency and a good neutron-gamma discrimination, for nuclear structure studies with stable and radioactive ion beams. It allows the selection of neutron decay channels in nuclear reactions, providing multiplicity and energy information. NEDA turned out to be a very efficient set-up for the study of neutron-deficient nuclei, populated through fusion-evaporation reactions, and a well-suited device for the investigation of exotic nuclei populated with transfer reactions, where the emitted particle is a neutron. NEDA is equipped with full digital electronics and will be coupled to AGATA to perform measurements both with stable and radioactive ion beams.

- **DANTE [31]:** a heavy-ion position-sensitive array, based on Micro-channel Plates (MCP) detectors of the CORSET type, suited to be installed in small reaction chamber like those used by γ-ray arrays. The main features are good position and timing resolutions, of the order of a few mm and hundred ps, respectively. DANTE allows to perform γ-γ coincidences, for the events outside the acceptance of PRISMA. The Doppler correction is performed using the position given by DANTE detectors and a velocity estimated by using the binary kinematics of the reaction leading to the product of interest.

- **SPIDER [20]:** a modular array of segmented Si detectors for low-energy Coulomb-excitation experiments, to be used as an ancillary device for modern γ-ray spectrometers such as GALILEO and AGATA. Every module has a trapezoidal shape and is segmented on the junction side into eight annular strips. Each detector (300 μm thick) covers one-eighth of $2\pi$ in the azimuthal angle. It is possible to arrange SPIDER into different configurations, allowing for the array to be adapted to scattering chambers of different dimensions.
- EUCLIDES [21]: a light charged particle array made up of 40 Si telescopes ΔE-E (130 µm and ~1000 µm thick). In such configuration EUCLIDES can be inserted in the reaction chamber of γ-ray arrays. The EUCLIDES electronics is fully digital and it is synchronized by a distributed clock delivered by the GTS (Global Trigger and Synchronization) system, which enables the time synchronization between the γ-ray array spectrometer and all other ancillary detectors.

* GRIT [32]: a charged particle detector array consists in a new type of compact, high granularity, ~$4\pi$ acceptance Si array, with a new electronics read-out, allowing integration inside the AGATA array, as well as with the PARIS scintillator array. It is composed of a conical-shaped set of 8 trapezoidal telescopes in both the forward and backward hemisphere with respect to the beam direction, assembled together with a ring of squared-shape silicon telescopes around 90°. The first layer, made of small-pitch DSSD for position measurement, is also meant to perform Pulse Shape Discrimination (PSD) of low energy particles. The second layer is dedicated to residual energy measurements. Very forward/backward angles will be covered by annular type detectors. It will be used at LNL in conjunction with AGATA or FAZIA in experiments with RIBs, with the possibility to couple it also to cryogenic targets. Partial implementations of GRIT, such as the MUGAST [33] and TRACE [34] arrays, will also be available at LNL.

* PARIS [11]: a novel large solid angle γ-ray calorimeter for high-energy photons and medium-resolution γ-ray detection, to be used for the study of Giant Dipole Resonances, near barrier resonances, Pigmy Dipole Resonances and shell structure of light-mass nuclei. The device is composed of phoswich detectors: LaBr₃:Ce or CeBr₃ scintillators for the inner volume (high efficiency, excellent time resolution and relatively good energy resolution in a large energy range) and NaI(Tl) scintillators for the outer shell. The array can be used standalone or in different configurations (spherical or cubic) when coupled with other detection systems, like HPGe arrays (e.g., AGATA, GALILEO), particle detectors (e.g., MUGAST, NEDA, FAZIA, ATS) or heavy-ion magnetic spectrometers (e.g., PRISMA). It is planned to be used at LNL in experiments with both intense stable and radioactive ion beams.

* FAZIA [12]: a multi-detector array for charged particles and complex fragments, mainly devoted to the study of the thermodynamics and the dynamics of the exotic nuclei, to explore the isospin degrees of freedom of the nuclear matter. It is a modular detection system with high granularity and very good energy resolution, with A and Z identification capability and low-energy thresholds. A module of FAZIA consists of 16 three-stage telescopes Si-Si-CsI(Tl). It uses up-to-date techniques concerning detection, signal processing and data flow, with full digital electronics. It is foreseen to be used, coupled to GARFIELD or PARIS, in experiments with both intense stable and radioactive ion beams at LNL.

* CTADIR (Cryogenic TAget for DIrect Reactions) [35]: a cryogenic $^{3,4}$He target developed by INFN LNL, financed by the PRIN2017 call for funding. The He gas will be kept at a pressure of 1 atm and a temperature of 8K, reaching a thicknesses of around $4 \times 10^{20}$ atoms/cm$^2$. The cryogenic source of the CTADIR target is a Gifford-McMahon device, with a cooling power of 2 W at 4 K. A cold finger connects the second stage of the device to the target itself. This is made of a cylindrical aluminium body to minimize γ-ray absorption, with a diameter of about 6 cm. The gas chamber has a thickness of 4 mm, a diameter of 1 cm, and it is closed by 2 µm-thick Havar windows. The target is foreseen to be used during campaign of measurements using GRIT coupled to AGATA and other arrays to perform direct reactions like the proton transfer ($^{3}$He, d), the neutron transfer ($^{4}$He, $^{3}$He) or inelastic ($^{4}$He, $^{4}$He') scattering.

* SUGAR (SUPersonic GAs Jet TaRget) [36]: a device developed by Instituto de Física, UNAM (IF-UNAM), Mexico, to produce gas-jet targets for nuclear reactions studies, where the purity and thickness of targets are crucial. Pure targets in gas state may be produced with SUGAR, reaching thicknesses around $1 \times 10^{18}$ particles/cm$^2$. SUGAR is essentially composed of three main parts: a differential vacuum system, a jet chamber, and a pumping jet system. The differential pumping system prevents the need of entrance windows making SUGAR an ideal instrument for nuclear astrophysics experiments where an accurate knowledge of the beam energy is paramount. A campaign of measurements using SUGAR coupled to AGATA and NEDA arrays is planned, searching the simultaneous detection of charge particles, γ rays and neutrons from reactions involving pure gas targets.

## 2.3 New instrumentation for nuclear physics

It is worthwhile to mention that, according to the present time schedule, the first nuclear physics experiments at SPES will be performed by using low-energy RIBs. Major instrumentation is being developed at INFN for this as follows:

* A Tape Station (b-DS, Beta-decay station) equipped with plastic detectors at the implantation point for the identification of the emitted electron/positron and HPGe detectors (coaxial Ge detectors or Triple clusters of the GALILEO γ-ray spectrometer) to define the de-excitation scheme following the parent's decay. The b-DS station will allow to study decay processes in a large range of lifetimes (few tens of ms up to hours) and is planned to be flexible in order to host detectors for lifetime measurements and high-energy gamma rays (LaBr₃:Ce scintillators), conversion electrons (Si(Li) detectors), beta-delayed neutrons (NEDA detectors).

* SLICES [37]: an off-line decay chamber coupled to the tape station will be used as a second measuring point hosting an electron spectrometer. The main components of SLICES are a magnetic transport system and a segmented, large-area lithium-drifted silicon Si(Li) detector. The magnetic lens, made of a set of permanent NdFeB N52 magnets, guides the electrons around a central photon shield towards the Si(Li) detector.
## 2.4 Instrumentation for applied physics

Applied and interdisciplinary projects make use of beams delivered by the TAP complex as well as the CN and AN2000 Van de Graaf accelerators. The main activities related to nuclear physics and SPES applications concern: the characterization of targets for precision cross section measurements; elemental microanalysis of targets for radionuclide production; in-beam tests and characterization of detectors; radiation damage of materials and devices. Available major experimental instrumentation for interdisciplinary and biomedical physics are the following:

* SIRAD: an irradiation facility, located at the TAP complex, for radiation damage studies equipped with a general-purpose irradiation chamber and an ion electron microscope.

* STARTRACK: detector for the measurement of the ionization-cluster-size distributions produced by protons and carbon ions in gas-filled cylindrical volumes. It uses stable beams from the TAP complex.

* BELINA: neutron time-of-flight system at CN, used both for the study of nuclear reactions of astrophysical interest and interdisciplinary activities.

* TOTAL-IBA: a facility to perform Ion Beam Analysis at CN comprising simultaneous PIXE, PIGE, prompt NRA and elastic back-scattering.

* Scattering chambers dedicated to Ion Beam Analysis with Rutherford and not-Rutherford Backscattering, Elastic Recoil Detection Analysis, prompt Nuclear Reaction Analysis, RBS-Channeling, in combination with Ion Beam Induced Luminescence (IBIL) and PIXE at AN2000.

* MICRO-BEAM: beamline equipped with the instrumentation for micro-PIXE analysis with a dedicated HPGe detector. Proton beams with typical size of 2–3 micrometers can be used at rated current of 500 pA. The beam line is also used for rarefied beam (10²–10³ protons/s) irradiation of detectors and IBIL and Ion Beam Induced Charge (IBIC) recording.

* LOW ENERGY IRRADIATION: a facility to irradiate with low energy protons (0.4–2.2 MeV) large area (up to 20 cm x 20 cm) spacecraft optical and optoelectronic materials and components. Also usable at CN accelerator for higher energy irradiation.

## 2.5 Infrastructures for applied physics

The forthcoming operation of SPES will allow to study and develop innovative radionuclides for medicine within the LARMED (LAboratory for RAdioisotopes of MEDical interest) and ISOLPHARM projects, and to develop a neutron and proton irradiation facility (NEPIR) in the 20–70 MeV energy range, see Sect. 6.

The proposed fast neutron and proton irradiation facility NEPIR [38] will be constructed in phases: a first -minimal but effective- configuration, NEPIR-0, and a final configuration, NEPIR-1. With this project, LNL and Italy will have, for the first time, high-level neutron beams. For this reason, the NEPIR facility is part of the CANS [39] and the ELENA associations [40].

The NEPIR-0 is almost completely funded by the Italian Ministry for University Research (MUR), within the Italian SPARE (Space Radiation Shielding) project that deals with health risks due to cosmic radiation. In this phase the neutron source is a relatively simple, thick, low power (100 W) beryllium target located inside the conduit between the cyclotron hall and experimental hall of the SPES building [41]. The 3 m thick wall of the cyclotron cave provides shielding and the conduit acts as a collimator for the neutron beam directed to the neutron’s experimental area. The expected neutron beam has a continuum spectrum with a different cut-off according to different proton energies. In this phase, a low proton current will be used (~ 1 μA) to reduce the radiation protection problems. The phase-0 facility will be open to academic and industrial users, to test microelectronic components and devices, for neutron detector characterization, and neutron shielding materials for space missions, in partnership with ASI.

In the final NEPIR-1 phase [42], the facility will be significantly extended: a dedicated bunker will be constructed, the proton beam current will be raised to ~ 10 μA, and two neutron production targets will be used to generate high-flux neutron beams for different applications:

* thin (few mm) lithium and beryllium targets to produce Quasi Mono-energetic Neutron (QMN) beams [43] with a controllable energy peak in the 20–70 MeV energy range;

* Atmospheric Neutron Emulator (ANEM) system, a rotating composite target made of a beryllium sector and a tungsten disk, to produce an intense beam of fast neutrons with an atmospheric-like energy distribution in the 1–70 MeV energy range.

An independent, low intensity direct proton beam line is also foreseen.

## 3 Nuclear astrophysics

Nuclear astrophysics is an interdisciplinary field, characterized by a strong interplay of nuclear physics, astronomy and stellar modelling. The ambitious goal of nuclear astrophysics is to understand where and how all elements in the Universe are formed, and how nuclear reactions influence stellar evolution.

It is currently widely acknowledged that the first nucleosynthesis event happened a few minutes after the Big Bang [44]. Such event, called Big Bang Nucleosynthesis, left the Universe made of hydrogen, helium and traces of lithium. The vast majority of
<figure><img src="image_5.png" /><figcaption>Fig. 3 Summary of nuclear astrophysics activities that could be performed at LNL in the next future, sorted according to the time phase</figcaption></figure>

the other elements was produced (and is still being produced) in stars, through a complex network of nuclear reactions. Nuclear reactions are also a major source of energy for stars, and hence have a strong influence on stellar evolution. Nowadays, astronomical observations and analyses of meteorites provide very precise measurements of the abundances of the elements, and in many cases even isotopic abundances. On the other hand, stellar models aim at reproducing the observed abundances, exploiting increasingly high computational power to develop more and more realistic simulations. Stellar models rely on a number of parameters, including the cross sections of all nuclear processes involved in a given astrophysical scenario.

Italian nuclear astrophysics groups and laboratories have contributed significantly to the field for many years [5]. In the near future Legnaro National Laboratories will offer a variety of accelerator facilities and state-of-the-art detection systems, opening the possibility to explore a wide range of astrophysical processes. Figure 3 and Table 1 provide a snapshot of possible activities which could take place at LNL over the next years. Such activities entail the use of a number of different, and sometimes complementary, experimental techniques. Moreover, many nuclear astrophysics cases will benefit from advances in our knowledge of nuclear structure and nuclear reaction dynamics, as detailed in Sects. 4 and 5. Therefore, it is crucial to keep an active communication between the different groups.

The discussion on possible projects was carried out within heterogeneous working groups, each tackling a different topic: Nucleosynthesis up to the iron peak (WG1), nucleosynthesis of trans-iron elements (WG2) and nuclear astrophysics theory (WG3). A more detailed description of future possibilities at LNL is discussed in the next sections.

## 3.1 Nucleosynthesis up to the iron peak

In this section, we focus on all astrophysical environments contributing to the production of the elements up to the iron peak, starting from Big Bang Nucleosynthesis and proceeding through increasingly more advanced stellar burning phases.

### 3.1.1 Constraining big bang nucleosynthesis

Primordial abundances of light elements, produced during the so-called Big Bang Nucleosynthesis (BBN), can be used to probe the physics of the Universe a few minutes after its birth (for reviews see [44, 45]). The theoretical description of BBN is based on the standard cosmological model and predicts the abundances of primordial nuclides, as a function of the density of ordinary matter, or baryon density. Therefore, a comparison between the observed primordial abundances and those predicted by the BBN can be used to constrain this fundamental quantity. BBN probes the Universe during the first ≈10 min, in an epoch when observable quantities of $^2$H, $^{3,4}$He and $^7$Li were produced. At that epoch, the temperature and the density were large enough for nuclear reactions to take place. Considering the limited number of isotopes involved in the BBN, the network of active nuclear reactions is relatively small (less than 15 reactions), but not yet known to the level of precision required by modern cosmology.
<table><caption>**Table 1** Summary of key nuclear astrophysics topics and reactions that could be addressed at LNL in the next years. The activities are sorted according to the working group discussing the proposal and the time phase</caption><thead><tr><th>Tag</th><th>Description</th><th>Reaction</th><th>Phase</th></tr></thead><tbody><tr><td>LNL-NA-LE-a0</td><td>The bottleneck of the CNO cycle: <sup>14</sup>N(p, γ)<sup>15</sup>O</td><td><sup>16</sup>O(<sup>3</sup>He,<sup>4</sup>He)<sup>15</sup>O</td><td>A</td></tr><tr><td>LNL-NA-LE-a1</td><td>3α process and the Hoyle state</td><td><sup>14</sup>N(d,α)<sup>12</sup>C</td><td>A</td></tr><tr><td>LNL-NA-LE-a2</td><td><sup>24</sup>Mg excited states and their role in carbon fusion</td><td><sup>20</sup>Ne(α,α')<sup>20</sup>Ne</td><td>A</td></tr><tr><td>LNL-NA-LE-b0</td><td>Astrophysics with radioactive elements: the <sup>26</sup>Al case</td><td><sup>26</sup>Al<sup>m</sup>(n,p)<sup>26</sup>Mg</td><td>B</td></tr><tr><td>LNL-NA-LE-b1</td><td>Astrophysics with radioactive elements: the <sup>26</sup>Al case</td><td><sup>26</sup>Al<sup>m</sup>(n,α)<sup>23</sup>Na</td><td>B</td></tr><tr><td>LNL-NA-LE-b2</td><td>Astrophysics with radioactive elements: the <sup>26</sup>Al case</td><td><sup>26</sup>Al<sup>m</sup>(p,γ)<sup>27</sup>Si</td><td>B</td></tr><tr><td>LNL-NA-LE-b3</td><td>Constraining Big Bang Nucleosynthesis: Primordial deuterium abundance</td><td><sup>2</sup>H(p,γ)<sup>3</sup>He</td><td>B</td></tr><tr><td>LNL-NA-LE-b4</td><td>3α process and the Hoyle state</td><td><sup>4</sup>He(<sup>12</sup>C,<sup>12</sup>C*)<sup>4</sup>He</td><td>B</td></tr><tr><td>LNL-NA-LE-c0</td><td>Constraining Big Bang Nucleosynthesis: Primordial deuterium abundance</td><td>d+d</td><td>C</td></tr><tr><td>LNL-NA-LE-c1</td><td>Constraining Big Bang Nucleosynthesis: Primordial <sup>7</sup>Li abundance</td><td><sup>7</sup>Be(d,α)<sup>5</sup>Li</td><td>C</td></tr><tr><td>LNL-NA-LE-c2</td><td>Hydrogen burning in explosive scenarios: the <sup>13</sup>N(p,γ)<sup>14</sup>O case</td><td><sup>13</sup>N(d,n)<sup>14</sup>O</td><td>C</td></tr><tr><td>LNL-NA-LE-c3</td><td>Oxygen burning: the <sup>16</sup>O+<sup>16</sup>O reaction</td><td><sup>16</sup>O+<sup>16</sup>O</td><td>C</td></tr><tr><td>LNL-NA-HE-a0</td><td>Measurement of key nuclear decay properties</td><td></td><td>A</td></tr><tr><td>LNL-NA-HE-a1</td><td>Neutron activation measurements on key isotopes</td><td></td><td>A+B</td></tr><tr><td>LNL-NA-HE-b0</td><td>Abundances of the elements at the first r-process peak: (α,n) reactions</td><td></td><td>B</td></tr><tr><td>LNL-NA-HE-b1</td><td>Neutron capture cross sections s-process: surrogate method with batch mode beams</td><td></td><td>B</td></tr><tr><td>LNL-NA-HE-b2</td><td>Neutron capture cross sections for i- and r-process: Surrogate Reaction Method</td><td></td><td>B+C</td></tr><tr><td>LNL-NA-HE-c0</td><td>Formation of the seed nucleus <sup>12</sup>C for the r-process</td><td><sup>9</sup>Be(α,n)<sup>12</sup>C</td><td>C</td></tr><tr><td>LNL-NA-HE-c1</td><td>Formation of the seed nucleus <sup>12</sup>C for the r-process</td><td><sup>4</sup>He(n,n,γ)<sup>6</sup>He</td><td>C</td></tr><tr><td>LNL-NA-TH-a0</td><td>Sensitivity study</td><td></td><td>A+B</td></tr><tr><td>LNL-NA-TH-b0</td><td>Impact of new results on stellar evolution and nucleosynthesis</td><td></td><td>B+C</td></tr></tbody></table>

## Primordial deuterium abundance

The observed primordial abundances are usually provided by spectroscopic observations of ancient astrophysical objects. The value of deuterium abundance relative to hydrogen has now reached percent accuracy, $D/H = (2.527 \pm 0.030) \times 10^{-5}$ at 68% confidence level [46]. Moreover, this precision is expected to increase by nearly an order of magnitude using new 30 m-class telescopes [47]. The reactions involved in the synthesis of deuterium are: production via the well known p(n,γ)d process and destruction via the $d(d,n)^3$He $d(d,p)^3$H and $d(p,γ)^3$He reactions. At present, several groups [48–51] have calculated the primordial deuterium abundance, obtaining different results depending on the adopted rate for deuterium burning reactions. As a consequence, cosmological predictions are also in disagreement.

A very recent breakthrough in BBN has been the new underground measurement of the $d(p,γ)^3$He reaction by the LUNA Collaboration [52] at the Gran Sasso National Laboratory in Italy, providing a reaction rate with unprecedented precision [53]. After the LUNA measurement, all most recent BBN analyses [48–50] agree that the largest contribution to the error on primordial deuterium from theoretical predictions comes from the uncertainty on two destruction process rates: $d(d,n)^3$He and $d(d,p)^3$H.

As a matter of fact, the study of the $d(d,n)^3$He, $d(d,p)^3$H and $d(p,γ)^3$He reactions with percent-level accuracy is extremely challenging. The measurement of the first two is crucial to match the precision of astronomical observation on the primordial deuterium abundance. The $d(p,γ)^3$He reaction is now well known at energies up to 400 keV, but in the energy range 400–800 keV there are still extrapolations in disagreement with each other [53, 54]. At LNL there are two accelerators potentially able to provide deuterium beam: the AN2000 and CN. The first one can reach the BBN relevant energies. The measurement can be performed delivering the deuterium beam to different types of solid deuterium targets, such as ZrD$_2$ or CD$_2$, both under development at LNL. The charged particles emitted by both reactions can be detected by an array of silicon detectors placed in close geometry at different angles to measure not only the total cross section, but also the angular distribution. To study the $d(p,γ)^3$He reaction, two CeBr$_3$ detectors can be used. In this way it will be possible to measure all three deuterium-destruction channels in a broad energy range, and possibly with a very high accuracy and precision.
### Primordial $^7\text{Li}$ abundance

While predicted and observed deuterium and helium abundances are overall in good agreement, the $^7\text{Li}$-problem still remains largely debated in the scientific community because of the factor ~2–3 discrepancy between the theoretical BBN abundances and the observed ones in halo stars [55]. Primordial $^7\text{Li}$ is mostly produced by the decay of radioactive $^7\text{Be}$. From a purely nuclear point of view, several studies have been proposed in the last years in order to achieve a better understanding of the processes affecting the production and destruction of $^7\text{Be}$ and $^7\text{Li}$ (see, e.g., [56–58]). In this view, the Trojan Horse Method (THM) [59] has been recently exploited to study the $^7\text{Be}+\text{n}$ induced reactions, opening the new frontier of applying THM to reactions involving unstable nuclei and neutrons. Recent works [60–62] lead to a mitigation of the cosmological $^7\text{Li}$-problem, reducing the theoretical BBN abundances by ~10%. Measurements have also been carried out at the 7 MV CN accelerator, indicating that the $^7\text{Be}(n,p)^7\text{Li}$ reaction cross section is not large enough to guarantee a higher $^7\text{Be}$ burning rate during Big Bang Nucleosynthesis [63]. In order to further study the impact of nuclear reactions involving the unstable $^7\text{Be}$ isotope, a further channel to be investigated is the $^7\text{Be}(d,\alpha)^5\text{Li}$: a recent debate in the scientific community [64, 65] has been triggered by the direct measurements of Rijal et al., in 2019 [66]. A THM experiment could reach BBN energies, where resonant states of the intermediate $^9\text{B}$ nucleus could play an important role. For this purpose, THM could be applied to the quasi-free $^6\text{Li}(^7\text{Be},\alpha)^5\text{Li}$ $^4\text{He}$ break-up reaction by using a $^7\text{Be}$ beam impinging on a $^6\text{LiF}$ target, evaporated on a C backing. Indeed, $^6\text{Li}$ represents a suitable TH-nucleus because of its $\alpha+d$ structure, its relative low binding energy (~1.47 MeV), and its well known momentum distribution for the $\alpha$-d intercluster motion occurring in s-wave [59]. Moreover, the same approach could be also used to investigate the $^7\text{Be}(d,p)^8\text{Be}$ reaction, representing a further deuteron-induced destruction channel for $^7\text{Be}$ in primordial nucleosynthesis. This future experiments can be performed at the EXOTIC facility at LNL, with a detection system similar to the one used in [60], derived from the EXPADES detection setup [67].

### 3.1.2 Stellar hydrogen burning

H-burning is the nuclear engine which allows stars to shine for billions of years, balancing gravitational contraction. For stars belonging to the Upper Main Sequence (M> 1.5 $M_\odot$), the dominating process is the CNO cycle. The latter requires the presence of catalysts (carbon, nitrogen and oxygen isotopes), which allow the conversion of H into He. Although our understanding of stellar hydrogen burning has greatly improved in the last century, there are still open questions that could be addressed at LNL in the upcoming years.

#### The bottleneck of the CNO cycle: $^{14}\text{N}(p, \gamma)^{15}\text{O}$ reaction

The $^{14}\text{N}(p, \gamma)^{15}\text{O}$ is the slowest reaction in the CNO cycle. Hence, it regulates the rate of energy generation and impacts several areas of stellar structure and evolution. Its reaction rate at astrophysical energies is highly affected by a sub-threshold resonance located at $E_{cm} = -504$ keV, corresponding to the $E_x = 6.793$ MeV state in $^{15}\text{O}$. The sub-threshold resonance greatly affects the cross section of the ground state transition at the typical energies of solar hydrogen burning (~30 keV), where no direct cross section measurements are available. A precise extrapolation at solar energies is necessary to solve the so called solar composition problem [68], and to explain the observed flux of CNO neutrinos [69].

One of the methods to constrain the contribution of the sub-threshold resonance is the measurement of the lifetime of the corresponding excited state. The values for this lifetime, reported in literature, range from 0.6 fs [70] to 1.6 fs [71]. Other studies have reported only upper limits, which agree with a lifetime of the order of 1 fs [72, 73]. A promising technique to measure such a short lifetime is the Doppler Shift Attenuation Method (DSAM), applicable when $\gamma$ emission occurs while the nucleus is slowing down inside the target.

Nevertheless, the expected lifetime of the 6.793 MeV state lies at the edge of DSAM sensibility. The AGATA array makes it possible to track the detected $\gamma$-rays, and thus to derive their direction of emission, with unprecedented resolution. Using the $^3\text{He}(^{16}\text{O},^{15}\text{O})^4\text{He}$ reaction to populate the 6.793 MeV state and coupling AGATA to the SPIDER silicon detector array, it is possible to derive the energy and direction of the $^{15}\text{O}$ particles and thus to reconstruct the real energy of the photon, pushing the sensitivity of the DSAM method to extremely short lifetimes. Preliminary simulations show that, thanks to the high angular resolution of the AGATA detector, the lifetime of the 6.793 MeV state can be determined at LNL with the precision required by R-Matrix models.

#### Hydrogen burning in explosive scenarios: the $^{13}\text{N}(p, \gamma)^{14}\text{O}$ case

The hot-CNO cycle heavily affects the nucleosynthesis in classical novae explosions. In this framework, several reactions induced by radioactive ions become important and their reaction rates provide necessary nuclear inputs for novae modeling, as well as novae nucleosynthesis [74]. The $^{13}\text{N}(p, \gamma)^{14}\text{O}$ reaction can be studied at LNL in the energy range of astrophysical interest by means of the Asymptotic Normalization Coefficients (ANCs) indirect method, explained in more details in Sect. 5.2.4, applied to the $^{13}\text{N}(d,n)^{14}\text{O}$ reaction in inverse kinematics, at a $^{13}\text{N}$ beam energy of 50 MeV. Simultaneously, the d + $^{13}\text{N}$ elastic scattering could also be studied in a proper angular range with expected statistical uncertainties around 10–15%. The experiment will be performed with an array of silicon detectors, allowing the required angular resolution, or with standard PSD, as performed in recent ANC applications [75, 76]. The experimental differential cross sections will be analyzed in order to compute the optical model parameters for the d + $^{13}\text{N}$ elastic scattering and the ANC for the reaction $^{13}\text{N}(d,n)^{14}\text{O}$. It will be then possible to extract the ANC for the $^{13}\text{N}(p,\gamma)^{14}\text{O}$ reaction g.s. transition, and to obtain a more reliable estimate of its astrophysical S-factor at extremely low energies as well as its rate
within the novae temperature region. As a first step, we propose the development of a ¹³N Radioactive Ion Beam (RIB) by means of the facility EXOTIC [77]. The RIB production technique will employ the two-body charge-exchange reaction p(¹³C, ¹³N)n and the ¹³N secondary beam will be selected and purified using the double filter on magnetic rigidity and velocity provided by the facility EXOTIC.

### 3.1.3 Advanced stellar burning stages

After the long-lasting H-burning phase, stars experience further nuclear burning stages. Low-mass stars ($M<8 M_\odot$) are only able to trigger He-burning. The latter occurs through two key reactions: the 3α process and the ¹²C(α,γ)¹⁶O reaction. The interplay between these two reactions determines the final carbon and oxygen budget of the star. More massive stars, on the other hand, are able to trigger advanced burnings up to the formation of an iron-rich core. Two key processes, characterizing the C-burning and the O-burning phases, are the ¹²C+¹²C and the ¹⁶O+¹⁶O fusion reactions, respectively. Both reactions are characterized by an extremely low cross section at astrophysical energies and multiple exit channels, making their experimental measurement very difficult.

#### 3α process and the Hoyle state

Carbon is one of the fundamental elements for the existence of life on Earth, and it is most effectively produced in stars through the so-called 3α process, which occurs during helium burning. Helium burning proceeds predominantly through the formation of the unbound ⁸Be nucleus and the subsequent radiative capture of a ⁴He nucleus. The rate of the 3α process is enhanced by the so-called Hoyle state, i.e. the 7.654 MeV state in ¹²C.

The reaction rate of the 3α process depends crucially on the energy and radiative decay partial width $\Gamma_{rad}$ of the Hoyle state. An accurate knowledge of $\Gamma_{rad}$ is therefore crucial to describe the production rate of ¹²C. Literature data on the branching ratio for the radiative decay of the Hoyle state are conflicting [78, 79]. Recently, new measurements were performed at LNS for the γ decay of excited states of ¹²C [80]. For the first time the two-γ-decay cascade to the ground state from the 9.64 MeV level was directly observed. The same level was also studied at RCPN Osaka laboratory [81], finding a γ-decay yield larger than the previously accepted lower limit [82]. In addition, the γ decay of the Hoyle state was measured finding an exceedingly large decay width, suggesting the possible presence of an Efimov state near the Hoyle level [83]. The radiative branching ratio $\Gamma_{rad}/\Gamma$ of the Hoyle state in ¹²C can be measured at LNL exploiting high-sensitivity charged-particle spectroscopy techniques and the CN accelerator beams. The proposed experiment uses the ¹⁴N(d,α)¹²C reaction, at about 2.7 MeV incident energy, to populate the Hoyle state (7.654 MeV, 0+) in the residual ¹²C nucleus. The excitation energy and the emission direction of the residual nucleus are determined by measuring the light ejectile α, as done in a previous investigation [84]. A pair of detectors will be used, one placed at backward angles and one positioned at forward angles, allowing the study of coincidences between α particles and ¹²C.

The experiment will be designed in a way that measured coincidences will be directly related to the decay branching ratio without the need to model the detection efficiency. A first test performed in October 2021 at the CN accelerator highlighted some issues concerning the beam spot, beam intensity and beam positioning, which will hopefully be solved in view of future experiments.

In addition to the Hoyle state, new states belonging to the ground state rotational band have been recently observed for the first time [85, 86]. On the theoretical side, the Algebraic Cluster Model and the Semimicroscopic Algebraic Cluster Model [87] do predict such states, and others that haven't been observed yet. An experiment could be performed at LNL to detect and identify some of the predicted states that remain unobserved, and confirm the existence of a rotational band built on the Hoyle state. The ⁴He(¹²C, ¹²C*)⁴He break-up reaction is the best option to look for cluster-like states. The measurement will be performed using a ¹²C beam from the TAP complex and a windowless Helium target, SUGAR. Charged reaction products will be detected by a silicon detector array (approximately 1500 µm thick). AGATA will detect coincident γ-rays.

#### ²⁴Mg excited states and their role in carbon fusion

¹²C+¹²C fusion is responsible for the ignition of carbon burning in stars, and its cross section is a crucial parameter in modern astrophysics. The evolution and final fate of a star are closely related to the astrophysical reaction rate of the ¹²C+¹²C reaction. Indeed, only stars with mass higher than a critical value, $M_{up}$, can reach high-enough temperatures to ignite quiescent carbon burning. Those stars are believed to end their life as core-collapse supernovae, neutron stars or black holes. On the other hand, stars with mass lower than $M_{up}$ become electron-degenerate before reaching the temperature needed for the ignition of the ¹²C+¹²C reaction, and end their life as C-O white dwarfs. Recently, an indirect study using the Trojan Horse Method (THM) has been published in Nature [88]. The authors reported results for proton and alpha channels down to 800 keV in the center of mass. The authors have observed several resonances, corresponding to excited states of the ²⁴Mg at energies between 14 and 17 MeV. As a result, the astrophysical reaction rate of ¹²C+¹²C fusion is increased by one order of magnitude. The observed ²⁴Mg levels are known from the literature, but their characterization is still poor. Therefore, a detailed study of those excited states may provide valuable information for the reaction rate calculation (i.e. precise resonance energies, spin, parities and partial widths of the states). Such a study could be performed at LNL using the resonant scattering technique, which allows to access multiple resonant states in the “compound” nucleus by measuring an increased cross section with respect to the nuclear elastic scattering. The ²⁴Mg excited states relevant to carbon burning can be investigated through ²⁰Ne+α resonant scattering using the ACTAR active-target demonstrator. Exploiting the
TPC that constitutes also the target for the experiment, it will be possible to reconstruct the trajectories and energies of the reaction products, and to separate the elastic events, thanks to the improved energy resolution.

### Oxygen burning: the $^{16}$O+$^{16}$O reaction

In massive stars, during the oxygen burning phase, the nucleosynthesis depends not only on the $^{16}$O+$^{16}$O reaction rate, but also on the branching between proton-, neutron-, or α-decay channels of the compound nucleus. The oxygen fusion reaction produces compound nuclear states of $^{32}$S that may decay by any of these four channels: i) $^{31}$S+n (Q = 1.45 MeV); ii) $^{31}$P+p (Q = 7.68 MeV); iii) $^{30}$P+d (Q = 2.41 MeV); iv) $^{28}$Si+α (Q = 9.59 MeV) [89]. At present, these reactions have only been measured at energies that are much higher than those of astrophysical interest. The main reasons for this are limitations in detector efficiencies, background reduction, and reaction yields. Therefore, the cross section at astrophysical energies can only be derived through extrapolations of existing experimental data. Unfortunately, discrepancies exist both between literature data sets [90] and theoretical predictions at energies below 5 MeV [91]. These facts clearly show the need of new experimental studies on this reaction. In the next years, the $^{16}$O+$^{16}$O reaction could be studied using a gaseous target, like SUGAR, and detecting the light fragments in the exit channels. Although it is a challenge for the Tandem at LNL to accelerate $^{16}$O beam in the energy window from 4 up to 8 MeV, counting on the forefront detector systems AGATA, NEDA and GRIT to detect γ rays, neutrons and charged particles, respectively, it will be possible to study simultaneously different reaction channels with high energy and angular resolution, as well as high detection efficiency. Moreover, the use of particle-gamma coincidences would also allow to reduce the background.

When assessing the behavior of the $^{12}$C+$^{12}$C and $^{16}$O+$^{16}$O fusion cross sections at very low energies, a major unknown is the existence and the entity of the hindrance phenomenon, so far only observed in slightly heavier systems. In this respect, the collaboration with the reaction dynamics working group is key, since they will try to extend systematic studies of the hindrance phenomenon to increasingly lighter systems, as explained in Sect. 5.3.2.

### 3.1.4 Astrophysics with radioactive elements: the $^{26}$Al case

$^{26}$Al nucleosynthesis has recently been in the spotlight to understand the formation of the Solar System and assess the formation rate of neutron stars (which is a key parameter for Multimessenger Astronomy). Thanks to its powerful γ-emission, the observation of its radioactive decay is a direct evidence of the on-going nucleosynthesis in our Galaxy. Different $^{26}$Al sources have been suggested over the years, such as Asymptotic Giant Branch (AGB) stars, classical novae, Wolf-Rayet stars, core-collapse supernovae and cosmic ray radiation in protostellar nebulae. To ascertain the most likely nucleosynthesis scenario, the $^{26}$Al production and destruction mechanisms have to be investigated and the cross section of the reactions producing and destroying $^{26}$Al need to be measured with adequate precision (better than 20%). Unfortunately, at the moment, the rate of $^{26}$Al(n,p)$^{26}$Mg is trustworthy only for T < 3×10$^{8}$ K and for $^{26}$Al(n,α)$^{23}$Na, while the temperatures of interest are not covered at all by existing data. To this aim it is possible to study $^{26}$Al(n,p)$^{26}$Mg and $^{26}$Al(n,α)$^{23}$Na reactions via the THM, using $^{26}$Al$^{m}$ beam from SPES. It is worth noting that these measurements will be performed in synergy with LNS, where the same reactions on $^{26}$Al in the ground state will be measured. Proceeding with the $^{25}$Al nucleosynthesis, $^{26}$Al(n,γ)$^{27}$Al, $^{25}$Al(p,γ)$^{26}$Si and $^{26}$Al(p,γ)$^{27}$Si (this last one influential in convective core H-burning for T < 10$^{8}$ K) can be studied with the indirect ANC method using an array of silicon detectors placed at backward angles, both using g.s. and isomeric $^{26}$Al beams. Possible targets to study the neutron capture are d or $^{13}$C, while for the proton capture $^{3}$He or $^{10}$B could be used. For these THM and ANC measurements, SPES beams at energies of the order of 3–5 AMeV for $^{26}$Al are required, which can be easily obtained by the ALPI post-acceleration system.

## 3.2 Nucleosynthesis of trans-iron elements

Charged particle reactions in massive stars lead to the formation of iron-rich cores. The production of isotopes heavier than $^{56}$Fe through charged particles (as those described in previous sections) requires energy input, instead of releasing it. Moreover, the Coulomb repulsion increases with the atomic number of reactants. Therefore, elements heavier than iron cannot be produced via charged particle reactions. Such a problem is avoided if one of the reactant is a neutron. Observed stellar abundances can be roughly reproduced by postulating the existence of two main neutron capture processes: the slow neutron capture process (s process) and the rapid neutron capture process (r process). Their typical neutron fluxes are 10$^{7}$ neutrons/cm$^3$ and > 10$^{20}$ neutrons/cm$^3$, respectively. The s process always proceeds close to the β stability valley. Each time an unstable nucleus is created by a neutron capture on a stable one, it has time to decay to its stable isobar, before capturing another neutron.

In the case of the r-process, instead, isotopes very far from the β stability valley can be produced via a series of multiple neutron captures starting from a single stable isotope. Such a sequence proceeds until isotopes with very short lifetimes are created. Once the neutron flux comes to an end, those isotopes can decay to their relative stable isobars along the β stability valley. The stellar environments of interest are two: low mass stars during their Asymptotic Giant Branch phase, for the s process, and the evolution of single or binary massive stars, for the r process. In the last years, a third neutron capture process, the intermediate process (i-process; [92]) received particular attention, due to its capability to reproduce observational data that can be hardly matched by other n-capture processes.
### 3.2.1 The slow neutron capture process

The facilities at LNL will allow to determine neutron-capture rates and relevant nuclear properties of interest for the nucleosynthesis of heavy elements, applying a variety of experimental techniques, as described in more details in the following sections.

#### Neutron-capture cross sections for s-process: surrogate reaction method

Neutron capture reactions on unstable targets are of high interest for astrophysical models since the knowledge of their cross sections, combined with the experimental knowledge of $\beta$-decay rates and of isotopic abundances, allows probing the neutron flux and, therefore, the environmental conditions of s-process nucleosynthesis. At LNL, it will be possible to determine neutron-capture cross sections on a number of key radioactive isotopes using the Surrogate Reaction Method (SRM). This indirect technique is based on the use of a (d,p)$\gamma$ reaction as a surrogate for the (n,$\gamma$). The theory behind the SRM was recently developed by G. Potel and collaborators [93]. The method uses the fact that the neutron-induced reaction of interest proceeds through the formation of an intermediate compound nucleus (CN), which subsequently decays. In a surrogate-reaction experiment, a target-projectile pair is chosen to form a CN that has the same excitation energy and neutron and proton numbers as the one produced in the desired reaction.

At LNL, SRM experiments will be performed in inverse kinematics, delivering radioactive beams to a CD$_2$ target. Scattered light particles will be detected in a segmented Si array, while de-exciting $\gamma$-rays will be observed with a $\gamma$ detector array.

A notable example is the neutron capture cross section in $^{85}$Kr, competing with the $\beta$ decay of this unstable isotope with $T_{1/2} \approx 11$ year. Neutron capture on $^{84}$Kr leads to both the $^{85}$Kr ground state ($T_{1/2} = 10.7$ year) and the isomeric state at 350 keV ($T_{1/2} = 4.5$ s) [94]. Because of its comparably short half-life, 80% of the isomer undergoes $\beta$ decay to $^{85}$Rb, and the remaining 20% decays to the $^{85}$Kr g.s., whose half-life is long enough for the s-process flow to proceed further to $^{86}$Kr, and then to $^{87}$Rb, in competition with the $\beta$ decay to $^{85}$Rb. At low neutron density, the $\beta$-decay process dominates over the neutron capture and the s-process path runs from $^{84}$Kr to $^{85}$Rb to $^{86}$Sr. When the neutron density is larger than a few times $10 \text{ cm}^{-3}$ the neutron capture chain runs from $^{84}$Kr to $^{86}$Kr and on to $^{87}$Rb.

Therefore, the relative abundances of Rb, Sr, Y, and Zr observed in AGB stars depend on the peculiarities of the neutron flow near the magic neutron number $N = 50$, and can be used to estimate the physical condition of the inner stellar layers [95].

Both, direct and indirect measurements of $^{85}$Kr(n,$\gamma$) have been performed recently [96, 97], and a new experiment is ongoing at Argonne National Laboratories, but no conclusive results have yet been drawn. Future investigations at LNL could represent an important step forward in our knowledge of this branching point. Because radioactive $^{85}$Kr is abundantly available commercially, this measurement can be performed simply connecting a bottle of $^{85}$Kr directly to the ion source and accelerating it.

Another s-process branching point isotope, $^{79}$Se, is located in a region where two scenarios may contribute, massive stars (weak s-process component) and AGB stars (main s-process component). The knowledge of the neutron-capture cross section of $^{79}$Se provides a crucial test to assess the thermal conditions and, therefore, the role of the weak and main s-process components. The isotope $^{79}$Se could be produced using irradiations at a fast reactor. The material could then be inserted in the SPES ECRIS ion source for further acceleration.

#### Neutron activation measurements on key isotopes

In stars, the energy distribution of neutrons follows a Maxwell-Boltzmann distribution. Therefore, the quantity needed for the calculation of the stellar reaction rate of neutron-capture reactions is the Maxwellian-Averaged Cross-Section (MACS). For many isotopes, the calculated MACS uncertainties are higher than the requested accuracy, being 3–5% for the s-process. To have a precise measurement with a reliable uncertainty estimation, the neutron spectrum should follow as much as possible the Maxwell-Boltzmann neutron spectrum (MBNS). Discrepancies between the experimental spectrum and the real MBNS complicate the determination of the uncertainties. A solution was proposed in [98], where a method to obtain experimentally a MBNS at kT = 30 keV was proposed, using the $^{7}$Li(p,n)$^{7}$Be reaction. This method proposes to shape the neutron energy spectrum by shaping the projectile energy distribution in MBNS. Among different ways of shaping the proton beam, the easiest is to use a foil placed before the neutron-producing target: by choosing different materials of the shaper, beam energy, and integration angle, MBNS at different kT can be obtained. This method has been already validated at the CN accelerator, where a neutron beam line, called BELINA, has been developed. So far, a well-reproduced MBNS with 28 keV thermal temperature was measured.

In the next years, neutron beams with MBNS at different temperatures will be developed. This will open the possibility to perform activation measurements and determine the MACS at different kT. Since the MBNS at 28 keV was already measured, a first experiment to measure the MACS on two isotopes is planned. The proposal includes not only measuring the MACS on Au, as a reference measurement, but also measuring the MACS on Y and Zr as benchmark measurements. Then a long campaign of MACS measurement for s-process will start at BELINA. The results of the activation measurements will be directly compared with those obtained in the new NEAR station facility [99] at CERN (n_TOF collaboration; [100]). Once available, SPES RIBS can be implanted on a thin target, and the MACS measured at the BELINA beamline at CN. Because of the presence of both lines in situ, samples with very short lifetime can be measured.
### 3.2.2 The rapid neutron capture process

Determining the site (or sites) for the occurrence of the r-process is one of the main challenges for modern nuclear physics and astrophysics. The most natural candidates are explosive astrophysical scenarios, such as the collapse of a massive star or a merger of two neutron stars, or of a neutron star and a black hole. Obtaining a piece of direct observational evidence for one of these scenarios is a difficult task. However, following the detection of the kilonova A72017gfo as the electromagnetic counterpart of the gravitational-wave signal GW170817, it became clear that binary neutron-star mergers represent one of the main r-process sites in the Universe.

The high-temperature and density conditions of matter ejected from a binary neutron-star (BNS) merger allow neutron capture on heavy nuclei to proceed much faster than $\beta$ decay. Thus, during the r-process, highly unstable neutron-rich nuclei close to the neutron-drip line are produced. In this view, radioactive ion beam facilities like SPES will allow us to investigate the properties of unstable neutron-rich nuclei and perform more accurate astrophysical simulations to quantitatively predict elemental abundances and the electromagnetic radiation emitted from these environments.

#### Sensitivity studies to identify key nuclear properties

Among the most important and uncertain nuclear inputs, there are neutron-capture rates on unstable nuclei with short lifetimes. Their direct measurements are hardly feasible, so one can only rely on theoretical rates computed via the Hauser–Feshbach (HF) statistical approach. However, depending on the different choices for experimentally-unknown nuclear structure properties, optical potentials, level densities, and $\gamma$-ray strengths of nuclei located far from stability, large variations, by over three orders of magnitude, in the capture rates are predicted [101, 102].

The r-process is normally characterized by a huge amount of free neutrons. However, when the availability of free neutrons drastically reduces, the so-called freeze-out phase takes place. At that point, the equilibrium between neutron captures and photo-disintegrations is no longer maintained and a deep knowledge of neutron capture cross sections is needed to properly shape the final heavy element abundance distribution. Sensitivity studies on outflows from BNS mergers, adopting a typical factor of 100 for the n-capture rate uncertainty [103], have shown that those rates have a large global effect on the predicted r-process abundance distribution. These studies pointed out that major relevant neutron capture rates include those on Cu, Zn, Ga, Se, Br, In, Sn isotopes and neutron-rich closed-shell nuclei ($N = 126$) with low neutron binding energies. Nuclear properties measurements for these nuclei are therefore highly demanded (see Sect. 4) and future experiments performed at next-generation radioactive ion-beam facilities like SPES will better constrain r-process yields calculations of BNS mergers and their contribution to the production of heavy elements in Universe. Recently, r-process calculations were performed for a Neutron Star Merger (NSM) scenario by considering 5 trajectories chosen as representative of various conditions in initial electron fraction (Ye), entropy and expansion timescale [104]. Each set has been explored for the different NSM components. Figure 4 shows the various final patterns obtained by varying single ($n, \gamma$) rates (multiplied or divided by a factor of 100). This sensitivity study focused on those rates with the greatest impact on the final r-process abundance pattern, having also a good chance to be measured by future experimental campaigns at SPES. We refer to [104] for more details.

Another predominant role during the r-process nucleosynthesis is played by $\beta$ decays, which determine the speed at which heavy elements are synthesised, shaping the r-process abundances and, in the case of NSM, powering the electromagnetic transient known as kilonova [105, 106]. $\beta$-decay experimental campaigns, like the one planned at SPES, are thus crucial for a proper understanding of the r-process nucleosynthesis. Furthermore, these experimental efforts provide important feedback to nuclear models employed in network calculations and in the estimation of other observables. Finally, as revealed by previous campaigns at the RIB facilities, cross-checking previous measurements is vital to ensure the validity of experimental data employed in nuclear network calculations [105].

In order to assess the relevance of the planned $\beta$-decay experimental campaign at SPES in the context of the r-process, we carried out a sensitivity study exploring the impact of $\beta$ decays on r-process abundances. Starting from a baseline network calculation where $\beta$-decay half-lives ($t_\beta$) and $\beta$-delayed neutron-emission probabilities ($P_n$) were taken from the FRDM predictions [107], we varied the $t_\beta$ and $P_n$ of nuclei accessible at the SPES facility according to the predictions given by two other models: D3C* [108] and SkO' [109]. As for the astrophysical scenario, we employ four trajectories representative of different ejecta in NSM. The first two trajectories trace the baryonic wind produced by neutrino absorptions in NSM remnants [110] at different polar angles (along the polar axis, less neutron-rich, and at lower latitudes, more neutron-rich). The other two trajectories correspond to tidal dynamical ejecta in a 1.35–1.35 $M_\odot$ symmetric NSM system and shock-heated ejecta in a 1.4–1.2 $M_\odot$ asymmetric merger [111, 112].

Figure 5 shows the sensitivity of the final abundances when $\beta$-decay half-lives and $\beta$-delayed neutron emission probabilities of nuclei in the SPES region are varied. We find the largest differences around $95 \le A \le 115$ and above the second peak ($140 \le A \le 155$), where in some cases the variations on the predicted abundances are larger than 100%. These results suggest that future measurements of $\beta$-decay half-lives at the SPES facility around the neutron shell closures $N = 50$ and $N = 82$ could reduce the impact of nuclear uncertainties on network calculations estimating the production of lighter heavy elements and lanthanides in NSM, providing constraints regarding the existence of a light element primary process and the modelling of kilonova light curves.
<figure><img src="image_6.png" /><figcaption>**Fig. 4** Impact of n-captures rates uncertainties of nuclei in the SPES region on *r*-process abundances for three different trajectories. Final abundances as a function of mass number A are reported; bands represent variations obtained when different n-capture rates are employed. See [104] for further details and additional plots</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5** Impact of $\beta$-decay rates uncertainties of nuclei in the SPES region on *r*-process abundances for four different trajectories. Upper panel: final abundances as a function of mass number A. Bands represent variations obtained when different $\beta$-decay rates and $\beta$-delayed neutron probabilities are employed. Lower panel: relative difference of final abundances respect to the predicted FRDM baseline calculations</figcaption></figure>

Neutron capture cross sections for r-process: surrogate reaction method

As stressed in the previous section, any nuclear study aiming at extending the spectroscopic information, and providing the extraction of spectroscopic factors for n-rich unstable isotopes, is welcome. This is in particular true for the neutron-rich region around $^{132}$Sn. The evolution of the shell structure, especially in the vicinity of nuclei having a more stable configuration with respect to nearby isotopes (for instance nuclei with a magic number of protons or neutrons), but far-away from the valley of $\beta$ stability, is of paramount importance to investigate the nature of the nuclear mesoscopic system and the limit of nuclear existence. It is important to stress that the direct study of n-capture processes on nuclei far from the $\beta$ stability valley is extremely challenging. However, as for the s-process, the surrogate technique is a valid alternative method. A possible experimental campaign involves the measurement, via SRM, of the partial cross sections for the population of the final states of the residues formed in light-ion direct reactions in inverse kinematics, using SPES re-accelerated beams. A day-one experiment can be pursued on a plastic CD2 target or a thick cryo-target, as for example CTADIR [113]. The production rate of the secondary beams at the target position are expected to be of the order of ~ $10^{5} \div 8$ atoms/s, being the species of interest located only few nucleons away from the nearest stable nucleus. The expected yield, considering the lower and upper limits for the beam intensity, a target of 500 $\mu g/cm^2$ thickness, and an inclusive cross section of 10 mb for a typical direct reaction, will give from 0.01 to 10 ions/s of the final species. This will be reduced by the efficiency of the detection setup, which, for a direct reaction in inverse kinematics, consists in a $\gamma$ detector complemented by a silicon detector.
Therefore the use of new-generation detection system, like γ tracking array (AGATA [9]) and silicon detector with embedded PSA (TRACE/MUGAST/GRIT [22, 33, 114]), is strongly envisaged.

## Measurement of key nuclear decay properties

As previously stated, the knowledge of nuclear properties such as β-decay half-lives, as well as β-delayed neutron emission probabilities P<sub>n</sub>, are critical inputs that go into calculations of r-process nucleosynthesis. However, also the measurement of the decay schemes of neutron-rich nuclei is important because they provide γ-ray strengths, which are key inputs for neutron capture theoretical rates computed via the HF statistical approach. Decay schemes can be measured at SPES, by profiting of the isobar beam purification of the HRMS and the β-DS tape station surrounded by γ detectors. In addition E<sub>0</sub> and EC transitions will be also at reach by profiting of the SLICES MOS/Si(Li) linked to the β-DS tape station. P<sub>n</sub> values of the nuclei of interest, as well as neutron-gated γ-ray spectra, can be obtained by coupling the β-DS array to neutron detectors such as NEDA [10]. We would like to stress the importance of measuring nuclear properties not only for the nuclei with strong direct impact on the r process, namely around the closed shells 50, 82 and 126, but also for those with small impact, because they provide nuclear structure trends far away from stability, which can be important for building realistic nuclear models to be used in nucleosynthesis calculations.

## Abundances of the elements at the first r-process peak: (α,n) reactions

The first r-process peak has been overlooked in the past and most of the works concentrate on the second and third r-process peaks. An interesting case is the nucleosynthesis of Molybdenum (Mo, Z = 42) which is not yet fully understood. Galactic chemical evolution (GCE) simulations estimated that about 40% of the solar Mo is made by the s-process while the r-process contribution is uncertain (e.g., Ref. [115]). Mo is most likely characterized also by a contribution from different explosive nucleosynthesis processes in collapsing supernovae (CCSNe) that is not associated to the r-process (see below Sect. 3.2.3). Therefore, the study of Mo abundance observed in the Galactic disc is a challenging task for current GCE simulations [116]. In a high-temperature, high-entropy and relatively high-Ye astrophysical scenario, nuclear statistical equilibrium is achieved and is dominated by α particles and neutrons. A large neutron-to-seed ratio could be achieved at the time of the α freeze-out, without requiring a large neutron-to-proton ratio. This results in an enhancement of “α-elements” and an extension of the Fe group to higher masses up to A ≈ 90. Recent studies have shown the influence on the abundance patterns of different (α,n) reactions. During the α-freeze-out, (α,n) reactions gradually lead to the accumulation of certain elements, and are a source of additional neutrons during the collapse of the star’s core. Recent sensitivity studies include the neutrino-driven winds scenario [117], as well as the magneto-hydrodynamically driven supernovae [118] scenario. These studies have shown that (α,n) reactions most influence the nucleosynthesis while the reaction flow reaches the zone of Z = 26–45. Major relevant (α,n) rates include those on Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y, and Zr. These elements will be available at SPES as post-accelerated beams, so that we can study (α,n) reactions in inverse kinematics on a <sup>4</sup>He gas jet target, like SUGAR, and detecting neutrons with NEDA.

## Formation of the seed nucleus <sup>12</sup>C, for the r-process

The occurrence of the r-process in NSMs has been recently confirmed [119, 120]. In this context, two potential paths to the formation of the seed nucleus <sup>12</sup>C, for the r-process, to reach elements with mass number A = 50–80 are: (a) α(αn,γ)<sup>9</sup>Be(α,n)<sup>12</sup>C; (b) α(nn,γ)<sup>6</sup>He(α,n)<sup>9</sup>Be(α,n)<sup>12</sup>C. The relative weight of these two paths depends upon the reaction rates of all reactions involved, some of which are currently unexplored experimentally. In a neutron-rich environment, the formation of <sup>12</sup>C through the reaction <sup>9</sup>Be(α,n)<sup>12</sup>C can compete with the triple-α reaction and even dominate. Therefore, we propose to study <sup>9</sup>Be(α,n)<sup>12</sup>C reaction, in inverse kinematic with a <sup>4</sup>He gas target like SUGAR or CTADIR and/or in direct kinematics with a <sup>9</sup>Be solid target, counting on AGATA, NEDA, and GRIT experimental arrays. We underline that, for the case of direct kinematics, a <sup>9</sup>Be beam should be developed at LNL. The fusion of <sup>9</sup>Be and one α particle can result in different output channels, namely: complete fusion <sup>9</sup>Be+α → <sup>13</sup>C+γ (Q = 10648 keV); <sup>9</sup>Be+α → <sup>12</sup>C+n (Q = 5702 keV); <sup>9</sup>Be+α → α+α+α+n (Q = -1572 keV); <sup>9</sup>Be+α → <sup>8</sup>Be+α+n (Q = -1664 keV); <sup>9</sup>Be+α → <sup>5</sup>He+α+ α (Q = -2308 keV); <sup>9</sup>Be+α → <sup>5</sup>He+<sup>8</sup>Be+γ (Q = -2400 keV). Quantifying the cross section for all exit channels, exploiting coincidence measurements, should be of value to study <sup>9</sup>Be nuclear structure, besides shading some light on the formation of <sup>12</sup>C.

Moreover, using a <sup>6</sup>He<sup>2+</sup> beam, and the AGATA and NEDA multi-detectors, it would be possible to study the reactions <sup>6</sup>He(α,γ)<sup>10</sup>Be (Q = 7409 keV) and <sup>6</sup>He(α,n)<sup>9</sup>Be (Q = 597 keV). This allows not only to analyze the <sup>6</sup>He-α structure of <sup>10</sup>Be, but also to improve the current knowledge on the reaction rates of the two different paths to <sup>12</sup>C formation.

### 3.2.3 The intermediate neutron capture processes

As already remarked, a well established nuclear astrophysics paradigm is that elements beyond iron are made by the s-process and by the r-process, with a comparable contribution to the solar abundances [121, 122]. On the other hand, other neutron-capture processes do happen in stars with intermediate neutron densities between the s-process and the r-process. The intermediate neutron-capture process (i-process, [92]) is defined by neutron densities in the order of 10<sup>14–16</sup> neutrons cm<sup>-3</sup>, and it can be activated by the <sup>13</sup>C(α,n)<sup>16</sup>O following the ingestion of hydrogen in convective He-burning environments. Different types of stars are potential stellar hosts of the i-process: low-mass AGB stars [e.g. 123, 124, 125, 126], post-AGB stars [127], super-AGB stars [128], massive stars [129–131], and rapidly-accreting white dwarfs within binary stellar systems [e.g. 132, 133, 134].
<figure><img src="image_8.png" /><figcaption>**Fig. 6** Summary of nuclear structure activities that could be performed at LNL in the next future, sorted according to the time phase. See text for details</figcaption></figure>

Along the nucleosynthesis path of the i-process, unstable isotopes are made up to 8–10 neutron-rich nuclides far from the valley of stability. Neutron-capture rates of these unstable isotopes are crucial sources of uncertainty, and may be studied at LNL through the surrogate method discussed in previous sections. First specific nuclear sensitivity studies have been made for the i-process: at low metallicities, ref. [135] studied the Ba region and ref. [136] analyzed the abundance distribution for AGB stars. Ref. [137] studied the Sr-Y-Zr region for post AGB stars, ref. [138] studied the mass region 32 < Z < 48 and ref. [139] the mass region 56 < Z < 74. From these studies, depending on the stellar site and on the observation, the authors have indicated as different relevant nuclear reaction rates to measure the $^{75}$Ga(n,γ) and $^{66}$Ni(n,γ) [138]; $^{87}$Kr(n,γ), $^{88}$Kr(n,γ), $^{89}$Rb(n,γ) [137], the $^{135}$I(n,γ) [135], the $^{137}$Cs(n,γ), $^{141}$Ba(n,γ) and $^{141}$La(n,γ) [139].

# 4 Nuclear structure

The knowledge of the nuclear structure is a key ingredient to build a comprehensive microscopic understanding of nuclei, extended nuclear matter and astrophysical phenomena [3], nuclear reactions and decays [5]. Breakthroughs in the experimentation with exotic isotopes, novel theoretical concepts, cross-fertilization in different research areas, and the progress in computer technologies and numerical algorithms, make nuclear structure a modern and lively research field, with exciting prospects spanning from fundamental physics to applications.

In the coming years, Legnaro National Laboratories (LNL) will offer a variety of accelerator facilities and state-of-the-art detection systems, opening the possibility to explore a wide range of nuclear physics and astrophysics processes. Figure 6 and Table 2 provide a view of the possible nuclear structure topics (working groups in Sects. 4.2, 4.3, 4.4, 4.5) which could be explored at LNL in the near, medium and further future (phases A,B and C) using stable and radioactive ion beams. The experimental studies will profit of different, and sometimes complementary, approaches. A detailed description of the future possibilities at LNL is reported in the four following sections, preceded by a theoretical address: Light to medium-mass exotic nuclei (WG1), N~Z nuclei and isospin symmetry breaking (WG2), Shell evolution (WG3) and Shape coexistence (WG4). The topics have been selected to strengthen existing research ambits and open new scenarios, in line with the facility development at LNL.

## 4.1 Nuclear structure theory of relevance to the experimental program

Nowadays, Interacting Shell Models (SM) [140], Energy Density Functional (EDF) theories [141], and ab initio methods [142] can provide complementary microscopic descriptions of nuclear properties in a broad range of masses. Yet, the growing quality of data expected from future campaigns will require sufficiently accurate theoretical predictions to facilitate the interpretation of experimental results. Systematic advances in accuracy and precision are being obtained within ab initio theory, with community efforts going into developing appropriate effective theories of two-, three-, and many-nucleon interactions [143], as well as theory
<table><caption>**Table 2** Summary of key nuclear physics topics and reactions that could be addressed at LNL in the next years. The activities are sorted according to the working group discussing the proposal and the time phase</caption><thead><tr><th>Tag</th><th>Description</th><th>Reaction</th><th>Phase</th></tr></thead><tbody><tr><td>LNL-NS-LMN-a,b,c</td><td>γ decay from near threshold states</td><td><sup>6</sup>Li(<sup>6</sup>Li,p)<sup>11</sup>B, <sup>13</sup>C(<sup>7</sup>Li,p)<sup>19</sup>O, <sup>7</sup>Li(<sup>14</sup>C,p)<sup>20</sup>O</td><td>A,B,C</td></tr><tr><td>LNL-NS-LMN-b</td><td>Particle and γ decay from cluster states</td><td><sup>11</sup>C(α,α'), <sup>15</sup>O(α,α'), <sup>21</sup>Ne inelastic</td><td>B</td></tr><tr><td>LNL-NS-LMN-a0</td><td>Role of 3-body forces in C and O nuclei</td><td><sup>18</sup>O deep inelastic</td><td>A</td></tr><tr><td>LNL-NS-LMN-c0</td><td>Molecular orbitals and di-nucleon correlations</td><td><sup>10</sup>Be(α,α'), <sup>10</sup>Be(p,p')</td><td>C</td></tr><tr><td>LNL-NS-LMN-b,c</td><td>Two-proton giant pairing vibrations</td><td><sup>A</sup>C(<sup>3</sup>He,n)</td><td>B,C</td></tr><tr><td>LNL-NS-LMN-c1</td><td>Resonance in proton-rich nuclei</td><td><sup>26</sup>Si(α,α'), <sup>24,25</sup>Al(p,p')</td><td>C</td></tr><tr><td>LNL-NS-LMN-a1</td><td>Approaching the Island of Inversion at higher spins</td><td>Multi-Nucleon Transfer <sup>22</sup>Ne, <sup>26</sup>Mg, <sup>30</sup>Si</td><td>A</td></tr><tr><td>LNL-NS-LMN-c2</td><td>Proton excitations and 0<sup>+</sup> states in Ar isotopes</td><td>Two-proton transfer <sup>A</sup>Ca(<sup>14</sup>C, <sup>16</sup>O)</td><td>C</td></tr><tr><td>LNL-NS-NZ-a,c</td><td>Isospin-symmetry breaking, shape coexistence</td><td></td><td>A</td></tr><tr><td>LNL-NS-NZ-b</td><td>Fundamental Int. (precision measurement of mirror BR)</td><td><sup>21</sup>Na, <sup>23</sup>Mg, <sup>45</sup>V</td><td>B</td></tr><tr><td>LNL-NS-NZ-c</td><td>T = 0 versus T = 1 proton-neutron pairing</td><td><sup>36</sup>Ar(p, <sup>3</sup>He) and (<sup>3</sup>He,p), <sup>46</sup>V, <sup>50</sup>Mn</td><td>B,C</td></tr><tr><td>LNL-NS-SE-a</td><td>New theory development for shell structure</td><td></td><td>A,B,C</td></tr><tr><td>LNL-NS-SE-b0</td><td>Shell evolution around N = 50: shape coexistence and gap reduction towards <sup>78</sup>Ni</td><td><sup>238</sup>U + <sup>9</sup>Be <sup>78</sup>÷ <sup>82</sup>Zn β decay</td><td>A,B</td></tr><tr><td>LNL-NS-SE-b1</td><td>Shape coexistence and type II shell evolution around N = 60</td><td>Sr, Zr β decay</td><td>B</td></tr><tr><td>LNL-NS-SE-c0</td><td>Shell evolution at N = 82 around <sup>132</sup>Sn</td><td><sup>132</sup>Sn(d,p), (<sup>3</sup>He,d), (<sup>3</sup>H, <sup>4</sup>He)</td><td>C</td></tr><tr><td>LNL-NS-SE-c1</td><td>Lifetimes after transfer for interplay of deformation and single-particle states</td><td></td><td>C</td></tr><tr><td>LNL-NS-DEF-a0</td><td>Jacobi shape</td><td><sup>48</sup>Ca + <sup>48</sup>Ti</td><td>A</td></tr><tr><td>LNL-NS-DEF-a1</td><td>Giant Quadrupole Resonance</td><td><sup>17</sup>O + <sup>40</sup>Ca</td><td>A</td></tr><tr><td>LNL-NS-DEF-b0</td><td>Pygmy Dipole Resonance</td><td>noble gas + <sup>4</sup>He</td><td>B</td></tr><tr><td>LNL-NS-DEF-b1</td><td>Pygmy Dipole Resonance</td><td><sup>142</sup>Cs β decay</td><td>B</td></tr><tr><td>LNL-NS-DEF-c</td><td>Pygmy Dipole Resonance</td><td><sup>94</sup>Sr + <sup>4</sup>He</td><td>C</td></tr></tbody></table>

and methods to solve the nuclear many-body problem [142]. In the first case, Effective Field Theories (EFT) allow to link the nuclear forces directly to the underlying QCD theory, with the aim of minimising modelization and phenomenological contents. Advances in terms of mass number reached over the past few decades by ab initio approaches are shown in Fig. 7. Methods based on handling directly all nucleon degrees of freedom offer, virtually, exact results, but are mostly limited to few-nucleon isotopes. Novel many-body approaches that offer polynomial scaling, by selecting computational degrees of freedom, have quickly extended near the heavy-mass regions, with supercomputing facilities. Full-space computations that need to explicitly account for correlations at play in complex nuclei (superfluidity, deformation, clustering, etc.) have explored the region around the calcium chain [144–149], and are now extending their reach to heavier and doubly open-shell nuclei. Valence-space methods built on the know-how of the empirical shell model have recently completed systematic calculations of the nucleon drip lines up to the iron chain [150].

The frontiers in advancing the above microscopic theory are directly lined to the opportunities that they present in conjunction with experimental programs. Perspectives for ab initio applications from light- to medium-mass nuclei can be identified along three directions:

1. Precision calculations around Z = 20. Progress in the modelling of two- and three-nucleon interactions is providing ab initio calculations with an ever-increasing accuracy, comparable to that of empirical calculations, or even higher. Tools like emulators or Bayesian analysis [153] allow to get systematic feedback from new measurements. Data beyond ground state properties, such as deformation, collective response and electroweak decays, will contribute to assessing theoretical uncertainties stemming from
**Fig. 7** Advances in terms of mass number reached over the past few decades (1980–2022) by ab initio theory. The different classes of methods used to solve the nuclear many-body problem are also displayed, as green dots for wave function-based methods and as yellow and red diamonds for polynomial scaling methods. (Inset) zoom on the early years (1985–2015). Data from Refs. [142, 151–153] and references therein

<figure><img src="image_9.png" /></figure>

the nuclear Hamiltonian. New methods that exploit neural networks and Machine Learning techniques are now being pioneered for light nuclei [154, 155].

2. Discovery calculations around $N = 50$. Ab initio applications in the region $N \approx 50$ will be challenging for two reasons. First, while many systems around calcium remain semi-magic, and can be approximately treated as spherical, the recourse to deformation will be crucial in this mass region. Methods that can explicitly handle deformation are being developed [156–159], together with the associated machinery to describe low-energy spectroscopy. Second, ab initio methods have been used to evaluate optical potentials at low scattering energies, along with structure information. Recent computations up to masses $A = 40$ [160–162] are improving in accuracy and becoming closer to the quality of standard phenomenological scattering. The opportunity to resolve the long-standing issue of consistency between structure and reactions will directly impact the quality of the analysis of experiments at LNL and at similar facilities worldwide.

3. Exploratory calculations around $N = 82$. Only few ab initio calculations have been attempted around $^{132}$Sn, so far [152, 163]. Arguably, this region will constitute the ab initio frontier in the decade to come. Innovative computational techniques, including the exploitation of GPU accelerators, will have to be devised to tackle the increasing number of nucleons or valence space dimensions.

Experimental data in light and medium-mass nuclei, where high-precision ab initio calculations are possible, are then crucial to benchmark more challenging systems, and to improve on the interpretation of structure and reactions. Standard phenomenological mean-field approaches based on EDFs remain the best choice to understand several heavy and deformed systems, as discussed in the following sections for specific cases. Currently, advances are being made in Density Functional Theory with the aim of determining the energy-density functionals directly from ab initio theory, allowing for a similarly solid link with the underlying theory of QCD [164, 165].

## 4.2 Light to medium-mass exotic nuclei

A unified description of the structure of atomic nuclei, from deuteron to superheavy elements, still remains one of the greatest challenges of modern nuclear physics. Light nuclei, with a limited number of protons and neutrons, already provide a unique playground in which to investigate a variety of phenomena appearing in the first portion of the nuclide chart, up to $Z \sim 20$. Among them, the clusterization of nucleons, leading to molecular-like structures, is pivotal for the study of light systems such as Be, C, O, and Ne isotopes [166]. In this context, nuclear excitations in the continuum, in the proximity of particle-emission thresholds, as well as resonances at higher energies, are of particular interest [167, 168]. These states play a major role in nuclear astrophysics [169], as they influence the capture rates of reactions occurring in stars, and hence the abundance of elements in the Universe. The relevant nuclear structure properties may change when heavier systems are considered. Between Mg to Ca isotopes, the study of the interplay between single-particle motion and collective excitations is crucial to pin down the underlying shell structure. The latter is at the basis of the microscopic description of peculiar phenomena, such as the coexistence of different nuclear shapes at similar energies [170]. Overall, the different facets of atomic nuclei can be traced back to the complex nature of nuclear forces and nucleon correlations and interactions. These can be studied at best in light and medium-mass nuclei, with a limited number of degrees of freedom, providing stringent tests for the most advanced nuclear models (see Sect. 4.1).

In the coming years, a large part of the experimental activity at LNL will be devoted to the study of nuclear structure moving away from the valley of stability by employing state-of-the-art $\gamma$-ray and particle detectors, such as AGATA, GRIT, TPCs, etc. Superior sensitivity will be achieved compared to conventional spectrometers, boosting the study of even rarer nuclear phenomena. In this section, selected topics on light and medium-mass nuclei are presented. Possible experiments are discussed combining $\gamma$-ray and particle spectroscopy techniques and exploiting both stable and radioactive beams.
### 4.2.1 Weak gamma-decay branches and particle decays

#### γ decay from near-threshold states

In light neutron-rich nuclei, the investigations of γ decays from unbound near-threshold states is a very relevant topic. Such states are of great importance for the understanding of the onset of clusterization phenomena in molecular-like nuclei and play a key role in nucleosynthesis reactions in star. The most famous example is the Hoyle state in $^{12}$C, lying only 287 keV above the α-decay threshold. The γ decay from near-threshold states is an almost unexplored territory, and AGATA will allow to access electromagnetic decays in neutron-rich B, C, O and N nuclei, with decay branches of the order of $10^{-3} - 10^{-5}$. Fusion reactions induced by intense $^{14}$C and $^{6,7}$Li beams on Be, C, Li and B targets, followed by the evaporation of a single charged particle, detected in the TRACE or GRIT systems, will be exploited. In this context, a very peculiar case is $^{11}$B, where the existence of a narrow near-proton-threshold resonance was proposed on the basis of an unexpectedly high branch (two orders of magnitudes higher than predictions) of the extremely rare process of β-delayed proton emission starting from $^{11}$Be [167, 171, 172]. A preliminary experiment with GALILEO points to a gamma-decay branch of ~$10^{-3}$ which can be further constrained with the AGATA setup, providing a strong benchmark to theory predictions [173, 174].

#### Particle and γ decays from cluster states

The range of light beams produced by the EXOTIC facility is under continuous development, and ideally suited to study near-threshold resonances in compound systems of the type beam+α, when using a helium gas-filled TPC target. These near threshold states are important to understanding the details driving nucleosynthesis processes that take place in stars. One such example is in the $^{15}$O+α reaction that leads to X-ray bursts, some of the most energetic events in the Universe. This process is caused by breakout from the hot-CNO cycle leading to the onset of the rapid-proton capture (rp) process [169] and is thought to be dominated by a single α-clustered state in the $^{19}$Ne compound nucleus [175]. Also possibly on the path of the rp-process are the states in $^{25,26}$Si that can be studied through proton scattering of $^{24,25}$Al SPES beams. Active targets are particularly well adapted to measuring elastic and inelastic resonant scattering: the large target thickness compensates the low intensity of radioactive ion beams, and the tracking of charged particles provides information to determine energies, cross sections and decay channels of the resonant states [176]. Coupling with γ-ray detection is also envisaged, using arrays of high-efficiency scintillators such as LaBr$_3$(Ce) or CeBr$_3$ [177]. Another development that offers significant new opportunities to explore near-threshold states is represented by thin solid noble gas targets that can now be produced [178]. This new technique leads to high-atom ratio ‘gas’ targets on a variety of substrates, such as silicon, aluminium or nitrides, suitable for low-abundance nuclei such as $^{3}$He and $^{21}$Ne. Such targets make novel inelastic and transfer reactions feasible, and, being thin, allow studies with highly segmented germanium detector arrays such as AGATA. This experimental approach opens up investigations of weak γ-decay branches from near-threshold states in both the target and reaction products by distinguishing between collective levels in cluster bands and single-particle states. A deeper understanding of the extent and impact of nuclear clustering in these systems will be obtained [179]. The advantages offered by thin solid noble gas targets to access light nuclei and the high precision achievable in such measurements are expected to challenge advanced theoretical approaches based on ab initio nucleon-nucleon interactions, including also continuum effects [173, 174].

### 4.2.2 Nuclear correlations and nuclear forces

#### Role of 3-body forces in light neutron-rich nuclei

The structural properties of light neutron-rich nuclei have significant impact on nuclear astrophysics and can be used to test the details of the nuclear force, including the three-body term (NNN) of the nucleon-nucleon interaction [180, 181]. In this context, ideal cases are neutron-rich O and C isotopes which can be reached by using deep-inelastic reactions with intense $^{18}$O beams on heavy targets (e.g., $^{238}$U, $^{208}$Pb or $^{198}$Pt) [182]. Here, ab initio calculations have shown a strong sensitivity to electromagnetic properties to NNN forces. By including the NNN term in the calculation the wave function composition can significantly change, thus affecting the lifetime of the excited states [183]. Among the most interesting cases are $^{16}$C and $^{18}$C. In $^{16}$C, the lifetime of the second $2^+$ state, calculated including two-body (NN) forces only, is equal to 230 fs versus 80 fs found including NNN forces. Similar calculations for $^{18}$C provide a lifetime of ~1 ps versus ~2 ps, respectively. Precise lifetimes measurements are therefore needed, which require techniques able to extract information in the time intervals from one hundred femtoseconds to a few picoseconds, based on a detailed study of Doppler broadened γ-peak line shapes. A first experiment of this type was performed at GANIL in 2017, with the AGATA+VAMOS+PARIS setup [181]. The results for $^{20}$O are presented in Fig. 8 (a further support to the need of three-body forces comes from an experiment with AGATA+MUGAST performed at GANIL [184]). At LNL, the larger angular coverage of AGATA, coupled to the PRISMA magnetic spectrometer positioned at forward angle to best profit of enhanced cross sections from deep inelastic processes, will provide a significantly improved sensitivity, crucial for accessing the most exotic cases [185].

#### Molecular orbitals and di-neutron correlations

The $^{8}$Be nucleus is well known for its two-α cluster structure. The neutron-rich $^{10}$Be with two neutrons added to $^{8}$Be is predicted to form neutron molecular orbitals around the two α clusters. According to the molecular orbital model, there are two types of orbitals near the Fermi surface of $^{10}$Be: the bonding π-orbital and the anti-bonding σ-orbital. According to theoretical calculations,
**Fig. 8** Results for $^{20}$O taken from the AGATA+VAMOS+PARIS experiment of Ref. [181]. (Left) Level and decay scheme of $^{20}$O. (Center) Line shape of the 2396-keV $\gamma$ ray de-exiting the $2_2^+$ state in $^{20}$O. The $\chi^2$ lifetime-energy surface is also shown. (Right) Experimental partial lifetime (red) for the $2_2^+ \rightarrow 2_1^+$ decay in $^{20}$O compared with ab initio predictions using different NN and NNN forces (see references in [181])

<figure><img src="image_10.png" /></figure>

the latter is characterized by spatially extended neutron wave functions that stabilizes the two $\alpha$ clusters at a larger distance [186]. The $\pi$-type orbital generates the ground $0^+$ band, whereas the second $0^+$ state at 6.18 MeV is predicted to be the band head of the $\sigma$-type orbital configuration. The experimental data currently available for this latter state are too limited to support or dismiss the enhanced cluster configuration prediction. In addition, a recent theoretical study [187] of the inelastic scattering to the $2_2^+$ state has shown a strong sensitivity to the di-neutron correlation. A very exciting possibility offered by light beams from SPES would be the study of the $^{10}$Be(p,$\gamma\nu$) inelastic scattering reaction, using the GRIT-AGATA set-up to extract the transition strengths from the two types of molecular orbitals and the cross-section to the $2_2^+$ state.

### Two-proton Giant Pairing Vibrations

Pair correlations are known to provide an enhancement in the magnitude of the ground-state to ground-state transition matrix elements between systems that differ by two nucleons [188]. An analogous enhancement is expected from particle–particle correlations involving transitions to higher-lying single-particle shells. A particular mode, the Giant Pairing Vibration (GPV), predicted in the 1970s [189], is described as to the collective superposition of many particle–particle states. The GPV has been searched for in heavy nuclei in the last decades with no success [190]. Its search regained interest with the measurement of a compatible signal in the light carbon isotopes [191]. It was suggested [192] that the GPV is embedded in the continuum and the large background produced by other states makes its identification an experimental challenge. However, a two-proton GPV would be narrower than other nucleon–nucleon modes due to the Coulomb barrier. This offers the possibility to investigate the two-proton GPV in the carbon isotopes, for example, through the ($^{3}$He,$n$) reaction in reverse kinematics using NEDA and GRIT to measure their two-proton decay.

### Giant resonances and deformations in light nuclei

The energy of giant isoscalar modes is closely related to the incompressibility of nuclear matter, a fundamental parameter of the nuclear equation of state [193]. It is thus essential to correctly determine the strength distribution of those modes. Because of the highly collective character of giant resonances (GRs), their strength distributions are strongly dependent on the nuclear shape: a ground-state deformation causes a splitting of the GR line shape. This has been observed for the well-studied isovector giant dipole resonance [194] and for isoscalar modes in medium-mass to heavy nuclei [195]. The unexpected splitting of the isoscalar monopole mode (ISGMR) in $^{154}$Sm was explained as due to the coupling between the $K=0$ components of the monopole and quadrupole resonances. Only recently, this effect has been observed in the deformed light nuclei of $^{24}$Mg [196] and $^{28}$Si [197]. Measurements in inverse kinematics have become possible with the use of active targets [198]. At LNL the method could be used with a stable $^{20}$Ne beam or the radioactive $^{26}$Si beam at SPES. Significant cross sections, however, are only expected for beam energies beyond 50 AMeV.

### 4.2.3 Structure of neutron-rich medium-mass nuclei

#### Approaching the Island of Inversion at higher spins

In Islands of Inversion, across the nuclear chart, ground states of magic nuclei exhibit strong admixtures of intruder configurations from the next higher-lying shell. This results in deformed ground states and in the disappearance of canonical magic numbers. In the original Island of Inversion centered on $^{32}$Mg, the origin of collectivity can be traced back to the mixing of multi-particle-multi-hole configurations with excitations of neutrons from the sd-shell orbitals to the fp shell [199–201]. Nuclei in the Island of Inversion are characterized by deformation as well as configuration mixing and thus the evolution of the single-particle properties is best studied outside of the Island of Inversion. Fusion–evaporation reactions are not ideal to populate neutron-rich nuclei with sizable cross sections, yet allow for the population of high-spin states [202]. A powerful alternative are multi-nucleon transfer reactions which can populate medium-high spin states. Beams of $^{22}$Ne, $^{26}$Mg, and $^{30}$Si are ideally suited to probe the region from O to Si using the
AGATA $\gamma$-ray spectrometer, and PRISMA for channel selection and Q-value measurements. Gamma-ray angular distributions and correlations as well as lifetime measurements using Doppler-shift methods can be employed to extract angular momenta, branching ratios, and reduced transition probabilities. A large and consistent data set, spanning from stability to the borders of the Island of Inversion, and comparisons with state-of-the-art theoretical calculations will be used to track shape change, intruder orbitals, and multi-particle-multi-hole configurations and, thus, infer the underlying structures in the Island of Inversion itself.

### Proton excitations and excited $0^+$ states

Excited $0^+$ states in nuclei are critical signatures indicating shape coexistence. Such $0^+$ states are effectively populated and studied using two-particle transfer reactions such as $(t, p)$ or $(^3\text{He},n)$. An alternative and very powerful probes are the $(^{18}\text{O},^{16}\text{O})$ and $(^{14}\text{C},^{16}\text{O})$, two-neutron (2n) [203, 204] two-proton (2p) [205] transfer reactions, respectively. Pioneering studies at Orsay employed this reaction to discover the first excited $0^+$ state in $^{68}\text{Ni}$ through the selectivity of the reaction and the measured angular distributions of $^{16}\text{O}$ ejectiles, allowing the identification of the momentum transfer [205]. A key nucleus in the understanding of the interplay of spin-orbit, tensor, and central forces and the development of complex shape evolution at $N=28$ is $^{46}\text{Ar}$. While its level structure and neutron properties are well-described by shell-model calculations [206] the B(E2) value is not [207]. The $(^{14}\text{C},^{16}\text{O})$ two-proton transfer reaction on a stable Ca targets is ideally suited to probe the proton hole structure of the Ar isotopes, discover unknown excited $0^+$ states, and resolve the controversy around the structure of $^{46}\text{Ar}$. At LNL, the development of a radioactive $^{14}\text{C}$ beam is planned, and the detector setups of AGATA and GRIT will be available in the coming years. With these, it will become possible to study the $2p-2h$ proton states, search for shape coexisting $0^+$ states and probe their structure through $\gamma$ and conversion-electron spectroscopy, determine branching ratios and lifetimes, and thus extract E2 and E0 reduced transition strengths. The experimental technique is applicable to many cases across the nuclear chart and has a high potential to investigate elusive excited $0^+$ states, also, for example, in $^{34}\text{Si}$, $^{62}\text{Fe}$, $^{74}\text{Zn}$, or $^{80}\text{Ge}$.

## 4.3 $N \sim Z$ nuclei and isospin symmetry breaking

$N \sim Z$ nuclei offer a richness of unique phenomena that allows understanding of specific properties of the nuclear interaction. With protons and neutrons occupying the same orbitals, proton-neutron correlations are enhanced, favouring the development of quadrupole deformation. Regarding pairing correlations, while like-nucleon pairing is of $T=1$ character, proton-neutron pairs can be coupled to $T=0$ and $T=1$. The contribution of both modes of np pairing decreases rapidly moving away from the $N=Z$ line [208]. With exchanged numbers of protons and neutrons, mirror nuclei offer the possibility to extract information about nuclear structure properties and isospin symmetry breaking terms of the nuclear interaction. At LNL, with the advent of the GASP [209] $\gamma$-ray array in the early 90's, nuclei along the $N=Z$ line have been studied up to high spin. These studies continued with EUROBALL [210] and more recently with GALILEO [19]. The main properties studied along the $N=Z$ line have been the high-spin phenomena such as backbending, band termination, and shape coexistence in deformed nuclei, as well as isospin symmetry breaking through the measurement of excited states in mirror nuclei.

In this Chapter we discuss open questions that can be explored in the short and midterm at LNL. The first two regard nuclear collective properties, the third concerns tests of the isospin symmetry of the nuclear interaction, followed by a glance on the search of new physics.

### 4.3.1 Neutron-proton pairing

The nuclear pairing mechanism is a central topic in low-energy nuclear physics [211]. The dominant pairing in almost all known nuclei with $N>Z$ is that in which “superconducting” pairs of neutrons (nn) and protons (pp) couple to a state with angular momentum zero and isospin $T=1$, known as isovector pairing. However, for nuclei with $N \sim Z$, neutrons and protons occupy the same single-particle orbits at their respective Fermi surfaces and Cooper pairs, consisting of a neutron and a proton (np), may form. These pairs may couple in either isovector ($T=1$) or isoscalar ($T=0$) modes, the latter being expected to dominate in $N \sim Z$ nuclei. In spite of the fact that there are convincing arguments for the existence of isovector np pairs, the existence of a correlated isoscalar np pair in condensate form, and the magnitude of such collective pairing remains a controversial and fascinating topic in nuclear structure physics [212].

The lack of experimental confirmation [212, 213] is mainly because the region of the nuclear landscape near the proton drip line, where such phenomena are expected to appear, is largely unreachable, and because the experimental observables are either inconclusive and/or complicated to interpret.

Two-neutron transfer reactions such as $(p, t)$ and $(t, p)$ have provided a unique tool to understand neutron pairing correlations in nuclei [189, 214]. Similarly, the transfer of an np pair from even-even to odd-odd self-conjugate nuclei provides a powerful tool to study np correlations in $N=Z$ nuclei [215, 216]. Some possible reactions are listed in Table 3. Among these the $(p,^3\text{He})$ or $(^3\text{He},p)$ reactions offer the advantage to study, in the same experiment, exclusive cross sections populating the lowest $T=0$ and $T=1$ states in the final nucleus. The corresponding ratio $\sigma(0^+)/\sigma(1^+)$ can provide a model-independent approach to quantify the nature of and interplay between isovector and isoscalar pairing [217]. This ratio plays the role of a Weisskopf unit for np pair transfers.

At LNL, on the short term, high-intensity $N=Z$ stable beams could be used to study the $^{36}\text{Ar}(p,^3\text{He})$ and $(^3\text{He},p)$ reactions to complete the systematics of the sd shell. In the mid-term, radioactive beams of $^{46}\text{V}$ and $^{50}\text{Mn}$, that could be produced at SPES
<table><caption>**Table 3** Possible pair addition and removal reactions to study *np* correlations along the *N* = *Z* line</caption><thead><tr><th>Reaction</th><th>Change in isospin</th></tr></thead><tbody><tr><td>(p,³He); (³He,p)</td><td>0, 1</td></tr><tr><td>(d,α); (α,d)</td><td>0</td></tr><tr><td>(α,⁶Li); (⁶Li,α)</td><td>0</td></tr></tbody></table>

from primary non-fissile targets (TiC, ZrGe...), will provide a complementary probe as in these cases we start from odd–odd $T = 1$ ground states and populate $T = 0$, 1 final states in the even–even $N = Z$ nucleus.

Neutron-proton pairing is also related to α-like quartets in nuclei. Indeed, it was suggested [218, 219] that these can be described as bi-pairs of neutrons-protons. Up to now, the experimental investigation of α clusters in nuclei has mostly focused on excited states of α-conjugate nuclei close to the α thresholds. The α-like quartets, instead, would appear in the ground state of α-conjugate nuclei as a collective state. In the same line as for pairing, the cross-sections for α transfer from α-conjugate nuclei to the 0⁺ ground state should be enhanced with respect to the ones to the first 0⁺ state. The systematic for the α-transfer reaction (⁶Li,d) over the sd shell shows an enhancement very similar to what is obtained from the two-nucleon transfer reaction (t,p). However, existing measurements are not consistent in terms of energy and reaction conditions calling for consistent re-measurements. At LNL, there is the opportunity to revisit the (⁶Li,d) reaction to re-assess the quartet structure of nuclei in the sd shell as a reference baseline to understand this phenomenon beyond ⁴⁰Ca. Further studies with ⁵⁶Ni and ⁵⁸Cu radioactive beams delivered by SPES might be possible.

### 4.3.2 Quadrupole collectivity in $N \sim Z$ nuclei

The development of nuclear deformation is a key property, central to our understanding of the nuclear force. Along the $N = Z$ line quadrupole correlations are quite strong and, in most of the cases, govern the nuclear structure features. This gives rise to different nuclear shapes and their coexistence at similar excitation energies. The study of these properties in medium-mass $N = Z$ nuclei is not straightforward from both theoretical and experimental aspects. It has been shown that the development of quadrupole deformation in nuclei above ⁵⁶Ni involves multi-particle multi-hole excitations across the energy gaps determined by the magic numbers [220, 221]. This is the same mechanism at the origin of the so-called Islands of Inversion. Shell-model calculations are so far the most precise methods to describe spectroscopic properties. Their limitations arise when the model space and the number of valence nucleons to deal with become too large. While new methods are being developed to overcome these limitations [222], we can rely on the predictions based on symmetries, variants of the SU(3) [221]. Large deformation in $N = Z$ nuclei above ⁵⁶Ni develop between ⁷²Kr and ⁸⁰Zr, shape coexistence is predicted in ⁸⁴Mo, and prolate-oblate competition in ⁸⁸Ru and ⁹²Pd. With the exception of ⁷²Kr, in $N = Z$ nuclei with 64 < A < 80 only the $B(E2: 2^+ \rightarrow 0^+)$ has been measured so far. Lifetimes of excited states in $N \sim Z$ nuclei can be measured at LNL using stable beams in fusion–evaporation and multi-nucleon transfer reactions combining AGATA with NEDA or PRISMA with a plunger device, to access levels lifetimes.

### 4.3.3 Isospin-symmetry in isobaric multiplets: transition matrix elements

Isospin symmetry is one of the key concepts in modern nuclear physics [223] and tests of its predictions form an important part of the nuclear-structure programmes at the current and emerging accelerator facilities.

To date, most of these studies have largely focused on measuring the energy differences between analogue states in mirror nuclei and isobaric multiplets. These differences arising from electromagnetic and isospin-non conserving interactions [224–229]. A crucial next phase in the study of isospin physics in nuclei would be to move to precision tests of the isospin symmetry through spectroscopic methods that probe the isospin purity of *wave functions* across isobaric multiplets. For a set of $T \rightarrow T$ analogue EM transitions, a similar linear dependence on $T_z$ is expected for the proton matrix element (proportional to the square root of the reduced EM transition probability):

$$M(T_z)_p = a + bT_z \quad (1)$$

Here, *a* and *b* contain the isoscalar and isovector matrix elements for that specific transition as well as coefficients that depend on *T* but not on $T_z$. Again, deviations from the linear behavior may indicate isospin-symmetry breaking and/or isospin mixing. This rule is difficult to test precisely due to the experimental challenges in performing such measurements in neutron-deficient nuclei. Hence, this presents a major challenge for the next decade. The most straightforward way to test this rule is through the study of a $T = 1$ triplet of nuclei, measuring the analogue $B(E2)$ strengths between the $T = 1, 0^+$ ground state and the $T = 1, 2^+$ first excited state. The linearity rule can be tested by fitting a quadratic expression of the form $M(T_z)_p = a + bT_z + cT_z^2$ and extracting the *c* coefficient, which should be zero in the limit of exact isospin symmetry. Analysis using all available current data (from ref. [230], updated) is shown in Fig. 9, where the ratio $c/|a|$ is plotted. There are two observations from this data. Firstly, the error bars are large (mostly > 10% of the total matrix element), hence, the test of the isospin rule is not, generally, very precise. Secondly, in the case
**Fig. 9** The results of fitting a quadratic expression of the form $M(T_z) = a + bT_z + cT_z^2$ to the transition matrix elements measured in all three members of a $T=1$ triplet. The measurement corresponds to the analogue $B(E2)$ ↑ strengths between the $T=1, 0^+$ ground state and the $T=1, 2^+$ first excited state. A number of outlier cases are visible for which a non-null $c$ parameter is estimated

<figure><img src="image_11.png" /></figure>

of $A = 30, 34, 50, 70$, the deviation from the linearity rule appears to be significant. These await clarification from more precise spectroscopy that could be studied in LNL. In Fig. 9, the large error bars originate from uncertainties in the transition strengths for the $T_z = -1, 0$ members of the triplet and branching-ratio uncertainties in the odd-odd $N = Z, T_z = 0$ cases.

Specific isospin selection rules exist as well for electric dipole transitions, for which there is no isoscalar component. This implies that $T \rightarrow T E1$ transitions in $N = Z$ nuclei should be forbidden, and also that $E1$ transitions should have identical strength in mirror nuclei. Again, deviations from these rules probe isospin mixing. These measurements are hampered by the potential for magnetic quadrupole $M2$ admixtures in the transitions in question. Precision lifetime measurements are required as well. The excellent in-beam $\gamma$-ray resolution of AGATA, in combination with enhanced $\gamma\gamma$ coincidence efficiency, and ability for angular distribution and polarisation measurements, represents an excellent opportunity to address 'isospin physics'. To keep systematic errors at a minimum, experiments should aim at measuring the relevant observables simultaneously across the full isospin multiplet of interest. They should be embedded in experimental campaigns with well-characterized set-ups, ensuring stable conditions for sufficiently long measurements. For most cases considered, combining AGATA with NEDA and a charged-particle array serves channel selection as well as event-by-event determination of recoil vectors. This knowledge can help to further reduce uncertainties in slowing down processes, when applying Doppler-shift based lifetime measurement techniques. Here, statistics should allow for $\gamma\gamma$ coincidences to avoid uncertainties from side-feeding. For a given case, AGATA plus PRISMA, including total kinetic energy cuts, might be a suitable alternative set-up.

### 4.3.4 Fundamental interactions in $\beta$ decay around $N = Z$

The Standard Model (SM) has been a stronghold of particle physics for decades. It shows great success in the prediction of properties on the elementary particles and the mediators of the electroweak interaction. A crucial SM test using $\beta$ decay is the unitarity test of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. A non-unitarity of the matrix would imply the existence of hidden physics such as the existence of the fourth-generation quarks [231]. The unitarity can be tested through the examination of the square sum of the first column elements: $V_{ud}^2 + V_{us}^2 + V_{ub}^2$. Among the matrix elements, the up-down mixing element $V_{ud}$ is critical, because the value and its uncertainty dominate the sum ($|V_{ud}| = 0.97370(25)$ [232]). Presently, the most precise value for $V_{ud}$ comes from superallowed $0^+ \rightarrow 0^+$ nuclear $\beta$ transitions for which the experimental parameters have been measured with increasing precision for many years. It was possible to reach a precision of few parts per $10^4$ for the most favourite cases of superallowed decay from $T_z = -1$ isotopes (see, e.g., fig. 3 in [233]). Improving such high-precision measurements is very challenging and an alternative to the study of the superallowed decay of $T_z = -1$ nuclei is the measurement of the so-called 'mirror' $\beta$ decay, between $T = 1/2$ states in mirror nuclei that can be used to extract another value for $V_{ud}$. These decays include both Gamow-Teller and Fermi transitions, and the measurement of the branching ratios with high precision is needed. A recent publication [234] reports the state-of-the-art, pointing to cases where the uncertainty in the branching ratios ranges from 0.1 to 1.2% (see figs. 2 and 3 in [234]). There will be the possibility for LNL to prepare the setup needed to improve the precision of the branching-ratio measurements for some key cases, exploiting synergies with the $\beta$-decay station in preparation for the SPES facility. With this facility it will be possible to measure the branching ratios in the decay of the isotopes $^{21}$Na, $^{23}$Mg, and $^{45}$V, and the measurement of the lifetime of $^{25}$Al, $^{29}$P, and $^{41}$Sc.

## 4.4 Shell evolution

The present mid-term plan for the study of shell evolution at LNL concentrates at first on the need to precisely define the observables linked to the concept of single-particle shell. The expected evolution of nuclear models in the next years is then presented, in particular pointing out the developments relevant to the future experimental studies with stable and exotic beams at LNL. The plan
then describes the measurements that are envisaged to build a comprehensive picture of shell evolution in exotic neutron-rich nuclei from mass A~70 to mass A~140, highlighting the beams required as well as the experimental setups needed.

### 4.4.1 Observables in shell evolution

Atomic nuclei are strongly-interacting two-components quantum mesoscopic systems whose complexity manifests itself through a rich phenomenology and the non-trivial way A-body observables evolve as a function of, e.g., the number of their constituents.

In this context, the role of any given theoretical scheme is to define and correlate, a priori, disparate experimental observables via a reduced set of building principles: a choice of appropriate effective degrees of freedom (e.g. point-like nucleons in so-called ab initio methods), evolving in a dedicated kinematical space (e.g. tensor product of reduced one-nucleon Hilbert spaces in the so-called valence-space shell model), on the basis of an appropriate kinematical or dynamical laws (time-independent or time-dependent Schrödinger's equations in quantal schemes), governed by their appropriate interactions (e.g. a Hamiltonian rooted into QCD through a specific power counting, in ab initio methods). By construction, any given theoretical scheme attempts to correctly correlate nuclear observables over a limited range of energies and nuclear systems, that shall not be necessarily the same for the various schemes under consideration in low-energy nuclear physics; i.e. each postulated theoretical scheme comes with its own intrinsic limited applicability domain. In this process, one wishes to further correlate the behaviour of *experimentally measurable observables* to a common theoretical construct denoted as *the nuclear shell structure*, the goal being to use a simple one-body quantity to provide a simplified picture of the inherent complexity displayed by actual A-body observables. While this makes the nuclear shell structure and its evolution, e.g., away from $\beta$ stability, a topic of great current interest, two crucial features must be kept in mind when referring to it:

1. While effective single-particle energies (ESPE) making up the nuclear shell structure are unambiguously defined mathematically [235, 236], they constitute a purely theoretical construct and are thus not observable [237, 238], i.e. they only exist within the theory such that their actual values depend on characteristics of the theoretical scheme under consideration that do not however impact actual observables computed within that scheme. Whereas one must expect two different theoretical schemes to reproduce equally well experimental observables (as long as they fall within their respective applicability domains), one must not expect that the shell structure one wishes to correlate them with is the same within the two theoretical schemes. In other words, the simplified picture associated with the shell structure depends on the theoretical scheme used (even if it shall bare qualitative resemblance whenever the theoretical schemes are intrinsically close). This further implies that the evolution of the nuclear shell structure delivered through the study of various nuclei must, in principle, be based on the same, coherent, theoretical scheme.

2. Observables that most strongly correlate with ESPEs, within any given scheme, are cross sections and separation energies associated with one-nucleon addition and removal processes. Given that such spectroscopic data have seldom been accessed in stable nuclei (i) in both the addition and removal channels, (ii) over a large range of excitation energies and (iii) for states characterized by small cross sections [239], reaching more than a few final states via addition and removal experiments on unstable and very exotic nuclei constitutes a tremendous challenge. Because the computation of the nuclear shell structure within standard theoretical schemes (e.g. valence-space shell model, ab initio methods) can however be shown [240] to be sensitive, even in doubly closed-shell nuclei, (a) to states up to more than 10 MeV excitation energies in the main channel, (b) to (at least) the main state in the secondary channel and to states down to 1% spectroscopic strength, taking up this experimental challenge in the years to come is of prime importance to deliver the nuclear shell structure with a small enough theoretical uncertainty.

In conclusion, the study of shell evolution bears some interlaced experimental and theoretical caveats. One the one hand, the determination of energy centroids of effective single-particle energy distribution requires to measure even small nucleon pick-up and stripping cross sections to identify fragments which may imply non negligible shifts on the final energy centroid. On the other hand, ESPE are not an observable, but they acquire a quasi-observable within a given coherent theoretical framework for structure and reaction models. This coherence of the theoretical models employed is particularly relevant for the study of shell evolution on a range of nuclei.

In the following, the opportunites and plans for such detailed measurement at the stable and radioactive ion-beam facilities at LNL will be outlined.

### 4.4.2 Shell evolution with energy density functionals and related techniques

The underlying shell structure obtained from the nuclear interaction is clearly manifested in the properties of nuclei with an odd number of protons and/or neutrons. Therefore, the experimental study of these nuclei will help to determine how shells evolve in different regions of the nuclear chart. Nuclear energy density functionals (EDFs) such as Skyrme, Gogny and/or relativistic Lagrangians [241–244] have been designed to be universally applied once the specific form and parameters of the interaction are fixed. However, the study of bulk and spectroscopic nuclear properties at low excitation energy such as binding energies, radii, excitation energies and transition probabilities with EDFs is scarce for odd nuclei [245–249] or approximations like the equal filling
approximation (EFA) are routinely used [250–252]. The situation is even worse for EDFs that include beyond-mean-field (BMF) effects such as symmetry restoration and configuration mixing [253–255].

There are several technical problems that make these calculations more difficult and time-consuming than those for even–even systems. On the one hand, the most general mean-field transformation must be built with one-quasiparticle intrinsic states (blocking) that breaks the time-reversal symmetry. That means that the EDF solvers have to include time-odd fields [245, 248, 249, 256, 257]. On the other hand, this symmetry breaking normally implies the use of triaxial angular momentum restoration that is involved and computing-demanding [253–255, 258]. Finally, pathologies that may appear in the definition of BMF-EDFs constitute an additional difficulty [259–261].

Currently there are several codes that allow the study of properties of odd nuclei with mean-field EDFs with full blocking although their use has not been very extensive so far and their predictive power is limited. A first mean-field approach to the ground-state of odd-systems can be obtained with self-consistent blocking axial calculations. In such a case, the angular momentum of the state is approximated by the *K*-quantum number (the projection of the angular momentum along the *z*-axis of the intrinsic reference frame) of the blocked quasiparticle state.

Even though these results could give a first attempt to the description of the spectrum of odd systems, this approach lacks for many relevant beyond-mean-field effects, such as symmetry restorations and shape mixing, and cannot provide a quantitative reliable comparison with experimental data. Amongst the beyond-mean-field extensions, one of the most promising techniques is the so-called projected generator coordinate method (PGCM) that is based on the mixing of particle-number and angular momentum restored mean-field wave functions using Hamiltonians instead of EDFs [222, 262–266]. PGCM can provide both observables to be directly compared with experimental data (energies, radii and transition probabilities) and non-observable quantities, e.g., collective wave functions or effective single-particle energies. A lot of work is in progress to extend the applications of mean-field EDFs and PGCM techniques to odd-nuclei. Therefore, the experimental study of such systems will be a very suitable playground to validate these developments and a key tool to study the shell evolution.

### 4.4.3 Shell-evolution around the doubly-magic $^{78}$Ni

Isotopes around $^{78}$Ni are at the very edge of the present knowledge in nuclear shell structure. The *N* = 50 region has been the object of an intense research in the last years, with the first spectroscopic study of $^{78}$Ni having been published recently [267]. The development of deformation around the *N* = 50 shell closure [267–269] as well as the reduction of the *N* = 50 shell gap [270, 271] when approaching $^{78}$Ni have been studied with complementary experimental approaches. Indeed, the first spectroscopy of $^{78}$Ni and $^{79}$Cu has opened some questions. In $^{78}$Ni, recent large-scale shell-model calculations predict an intruder structure close to and even lower than the first $2^+$ state, which is already lying at a somehow low energy of 2.6 MeV [267]. Gamma-ray spectroscopy of $^{78}$Ni has provided tentative evidence of intruder states [267]. In $^{79}$Cu the first spectroscopy via proton-knockout has revealed a plethora of states around the $^{78}$Ni $2^+$ energy quite difficult to disentangle [272]. There was no sign of a low-lying proton $f_{7/2}$ strength coming from a *Z* = 28 core break, which is important for the $^{78}$Ni $2^+$ level energy [267, 269].

A first experimental approach would be the spectroscopy of the yrast states in *N* = 50 isotones. States up to 7–8 units of angular momentum can be populated with $^{208}$Pb, $^{238}$U+$^9$Be fusion–fission reactions. Stable lead or uranium ALPI beams at 6–7 AMeV will impinge on a Be target at the centre of the AGATA-PRISMA setup, to measure the γ-ray decay of fission fragments identified event by event. One could measure states, in $^{80}$Zn, representing a core-breaking excitation which has been used to define a *N* = 50 "spectroscopic" gap size through shell-model calculations. On the other hand, also the spectroscopy of the first excited yrast states in $^{79}$Cu should be accessible, making it possible to study states coupled to the $^{78}$Ni core excitations.

With the advent of radioactive beams from the SPES facility, neutron-rich nuclei around *N* = 50 can also be studied by means of β-decay studies. The large Q value (≈ 8–10 MeV) available for β-decay in nuclei produced by SPES like $^{78–80}$Cu, $^{78–82}$Zn, $^{80–87}$Ga, $^{83–87}$Ge, $^{84–89}$As, $^{94–102}$Rb makes it possible to observe a significant Gamow-Teller strength (GT) in the β-decay. These allowed decay proceed through “doorway states”. i.e. states coupled to particle-hole excitations across the *N* = 50 core. As a result, the GT strength distribution becomes a sensitive probe of the correlations arising from intruder states close to $^{78}$Ni [273, 274]. The decay spectroscopy requires the SPES Decay Station coupled to a neutron time-of-flight detector for β-delayed neutron spectroscopy, since the decreasing neutron-separation threshold in exotic nuclei implies that a significant part of the GT strength could lead to neutron emission from highly excited states in the daughter nuclei.

### 4.4.4 Characterization of the *N* = 50 shell closure

Characterizing the evolution of the *N* = 50 shell closure towards $^{78}$Ni and the possible appearance of unexpected intruder states at rather low energy is essential if one aims at predicting the structure of nuclei further away from stability, including those involved during nucleosynthesis processes. While transfer reactions, such as (d,p) nucleon addition, were largely used to quantify precisely how valence orbitals evolves along isotonic chain in lighter regions, the *N* = 50 chain towards $^{78}$Ni remains poorly studied. The distribution of single-particle strength for valence orbitals (2d$_{5/2}$, 3s$_{1/2}$, 2d$_{3/2}$, 1g$_{7/2}$) in *N* = 51 nuclei is only studied in details for $^{91}$Zr, $^{89}$Sr, $^{87}$Kr [275] still far from *Z* = 28. For the more exotic $^{85}$Se and $^{83}$Ge, only the ground and first excited states were
populated, by nucleon addition, for the first time in Oak Ridge in a pioneering experiment with rather limited statistics and excitation energy resolution [276].

SPES high intensity beams of $^{84}$Se of $^{82}$Ge (~10$^5$ to 10$^6$ pps), combined with the state-of-the-art particle-$\gamma$ detection setup GRIT+AGATA, will be ideally suited to reach a considerably higher resolving power and statistics to precisely extract, for the first time, a large fraction of the single-particle strength distributions in $^{85}$Se and $^{83}$Ge.

### 4.4.5 Shape coexistence

Shape coexistence in nuclei is a widespread feature that may occur in nearly all nuclei. It is associated with the fundamental tendency of nuclei to deform, if not in their ground states, in their excited states. The distinctive character of shape coexistence lies in the interplay between two opposing trends: shell and subshell closures have a stabilizing effect leading to sphericity, while residual interactions between protons and neutrons outside closed shells drive the nucleus to deformation. Valuable data in support of this idea are available, for example, in the region $Z \sim 40, N \sim 60$ (see e.g. ref. [277]), which show that nuclei at, and close, to double-subshell gaps can exhibit shape coexistence via the suppression of ground-state collectivity. The main observables related to shape coexistence are the strength of the electric monopole transitions (E0) and of electric quadrupole (E2) and magnetic dipole (M1) transitions.

An exclusive contribution to clarify the configuration of low-energy states can be obtained from the analysis of their electric monopole (E0) decay [278, 279]. Precise measurements of the E0 strength required the use of electron spectrometers, as the newly developed SLICE [37].

As an example of the investigation of nuclear shape coexistence that can be performed via measurements of the electric monopole strength, we refer to the Sr isotope case, which can be populated via $\beta$-decay of the father Rb nuclei, produced at the SPES facility.

Another key observable related to shape coexistence is provided by reduced transition probabilities, which give information on the shape of the nucleus, allowing to study phenomena such as nuclear deformation and shape coexistence [277, 280]. The fast-timing technique is a powerful tool that provides access to nuclear lifetimes spanning a range going from few picoseconds to nanoseconds [281–283]. In recent years, new technologies such as state-of-the-art fast scintillator materials (LaBr$_3$:Ce, CeBr$_3$) and digital electronics are being exploited to obtain improved time resolutions [281, 284–287]. Such improvements allowed precise lifetime measurements, for instance in the mass regions $A \simeq 70,100–110,180$ [288–291].

SPES non post-accelerated beams will provide the possibility of accessing key regions of the nuclear chart where shape coexistence phenomena are predicted, such as the region comprising Kr, Zr, Mo, Pd and Cd isotopes around mass $A = 100$, exploiting the resident $\beta$-DS decay station array equipped with LaBr$_3$:Ce detectors. The possible coupling of these detectors to the resident $\gamma$ spectrometer GALILEO will further expand the use of fast-timing techniques at LNL.

### 4.4.6 Coulomb excitation for deformation and shape coexistence

Low-energy Coulomb excitation is one of the most well established experimental techniques used for studying the nuclear structure and, still to this day, one of the most widely employed. By carefully choosing the beam energy to guarantee the so-called *safe* condition [292] (typically a few AMeV), the nuclear interactions become negligible in the Coulomb-excitation scattering process and the observables of interest can be extracted in a model-independent way. The technique allows for determining reduced transition probabilities and spectroscopic quadrupole moments. Also, it is the only experimental technique allowing for the model-independent extraction of relative signs of E2 matrix elements, needed to link transitional and diagonal E2 matrix elements to the Hill-Wheeler parameters ($\beta_2, \gamma$) [292, 293], which identify any quadrupole shape. These unique features make low-energy Coulomb excitation a powerful tool to investigate phenomena such as shape coexistence, shape transitions, superdeformation, and octupole collectivity (see, for instance, refs. [294–296]). Very interesting and well beyond the scope of nuclear physics, are transitional nuclei, for which the octupole-deformation parameter $\beta_3$ [297] is sizable [296, 298–300], and [301]. These nuclei are predicted to enhance a CP-violating nuclear Schiff moment, e.g., see ref. [302] and references therein. Due to the vanishing small intensities of E3 transitions, when compared to dominant fast E1-decay paths, in general, a direct experimental determination of the electric-octupole moment requires the measurement of excitation paths using the technique of safe Coulomb-excitation (Coulex).

SPES will offer advantages in terms of beam energy and intensity for Coulomb excitation in key nuclei with respect to previous experiments at other ISOL facilities. Examples of isotopes that could be further investigated with this technique in the near future at LNL are neutron-rich Zn and Sn isotopes previously studied at ISOLDE and HRIBF (see, for instance, refs. [303, 304]). In addition, the measurement of spectroscopic quadrupole moments and, possibly, Hill-Wheeler parameters would directly probe the collective character of these isotopes, which is also relevant for r-process calculations [305–307]. It is also clear that from the expected high-energy and high-intensity SPES beams close to $^{78}$Ni and $^{132}$Sn, several nuclei in these regions of the nuclide chart will be studied with Coulomb excitation for the very first time. Other region of interest for octupole deformation will be also accessible, for example the region of Ba nuclei, with much larger statistics than presently available [299].
### 4.4.7 Nuclear deformation around $N = 60$

When going to deformed or shape-coexisting systems, nucleon transfer reactions are still extremely useful, although more challenging to perform and interpret. A first illustration is a recent study of the $^{94,95,96}$Sr(d,p) reactions [308, 309] before the $N = 60$ shape transition, in which nucleon transfer region provided additional insight on the microscopic nature of coexisting configurations. At SPES, beams of $^{94,95,96}$Kr, $^{96,97,98}$Sr should be produced with high intensities and represent good candidates to investigate this transfer technique below Zr ($Z = 40$), in inverse kinematics. This would allow to better characterize how proton vacancies impact neutron configurations and consequently affect this transitional phenomenon. The combined use of direct nucleon transfer to study single-particle configurations and the above-mentioned Coulomb excitation studies to precisely characterize collectivity represents the optimal strategy to firmly enhance our microscopic understanding of the structural mechanism at play in this sudden phase/shape transition.

### 4.4.8 Shell-evolution around the doubly-magic $^{132}$Sn

The region around the doubly-magic $^{132}$Sn has been the object of many studies to probe both the neutron and proton shell structure at the $N = 82$ and $Z = 50$ shell closures. Generally, nuclei around doubly closed shells play a crucial role in establishing the two-body matrix elements of the effective nuclear interactions [310]. As described in Sect. 4.1, ab initio methods start to be applied also to this relatively heavy nuclei [152, 163], making it possible to compare such predictions to spectroscopic data from direct transfer reactions. The large angular momentum of the nuclear orbitals in this region ($ℓ = 3, 5, 6$) suggests the use of neutron adding reactions with heavier target nuclei like ($^{4}$He, $^{3}$He), ($^{13}$C, $^{12}$C) and cluster transfer on weakly-bound $^{7}$Li targets [311], together with the more standard (d,p) reactions [312, 313]. In this context, of particular interest are one-proton-valence nuclei of Sb, with $A = 127-134$, and two-proton-valence nuclei of Te, with $A = 129-135$. For example, in the case of the $^{132}$Sb nucleus (one-proton-particle, one-neutron-hole with respect to the $^{132}$Sn core), the level structure at low excitation energies arises from 1p-1 h couplings involving $1g_{7/2}$, $2d_{5/2}$, and $1h_{11/2}$ proton particles, and $3s_{1/2}$, $2d_{3/2}$, and $1h_{11/2}$ neutron holes. Most of the 1p-1 h states involving the $g_{7/2}$ proton and $d_{3/2}$ neutron hole have been tentatively located, while the information about other multiplets is largely missing. The one-proton, one-neutron nucleus $^{134}$Sb is not well known either. We note that one-nucleon valence systems also play a key role in understanding complex excitations arising from the coupling to the excited $^{132}$Sn core [314].

Considering the SPES beam intensities and energies of re-accelerated beams around $^{132}$Sn, reactions envisaged are the neutron adding transfers $^{132-134}$Sn(d,p); $^{4}$He, $^{3}$He; $^{13}$C, $^{12}$C)$^{133-135}$Sn. They can probe the neutron $1f_{7/2}$, $2p_{3/2}$, $2p_{1/2}$, $0h_{9/2}$, $1f_{5/2}$, $0t_{13/2}$ shells beyond $N = 82$. Proton stripping reactions, like $^{132}$Sn($^{3}$H, $^{4}$He)$^{131}$In, and proton adding transfers, like $^{132}$Sn($^{3}$He,d)$^{133}$Sb, can instead help to understand the shell evolution both below and above $Z = 82$. These reactions will exploit the unprecedented efficiency and granularity of the AGATA-GRIT setup. The use of exotic beams with intensities as low as $10^4$ pps implies the need of dense helium targets, at least $10^{20}$ at/cm$^2$, to have a sufficient luminosity for direct reactions with cross sections of ~1 mbarn. The CTADIR cryogenic target, being built at LNL and financed by the PRIN2017 call for funding, will allow the use of a 4 mm thick $^{3,4}$He target kept at a temperature of 9 K by a cryocooler with up to $10^{21}$ atoms/cm$^2$. The target is designed to be compatible with the AGATA-GRIT setup.

## 4.5 Deformation and collective modes

Studying the emergence of collective behaviour in atomic nuclei allows to address the more general investigation of complex many-body systems, that could manifest astonishing simplicities and regularities. One of the best examples of collective modes in nuclei is the Isovector Electric Giant Dipole Resonance (IVGDR), interpreted as an oscillation of all the neutrons against all the protons (see Fig. 10). This phenomenon, and its rather simple patterns, has been extensively used to extract valuable information focusing on both zero and finite temperature [194, 315]. However, there are aspects which are still subject of modern large-impact research. They concern, for example, the understanding of the IVGDR evolution as a function of Isospin (e.g. in exotic neutron-rich nuclei) and the study of the low-lying electric dipole strength (Pygmy Dipole Resonance) [316, 317]. An important feature of the IVGDR is also the dependence of its properties on the nuclear shape, which makes it a good tool for the studies of nuclear deformation [318–321]. In the following, a list of physics cases will be presented. They represent interesting possibilities to advance our understanding of nuclear structure by means of specific gamma-ray spectroscopy studies. These experiments can be performed using accelerator facilities and instruments that are presently available, or will be available in the mid-term, at LNL. Experiments to be performed with SPES radioactive neutron-rich beams are highlighted, while stressing the relevance that experiments using stable beams still have.

### 4.5.1 Selected theoretical methods

The random phase approximation (RPA) and the quasiparticle RPA (QRPA) are well known and largely applied microscopic methods to describe nuclear excitations [323]. Their main advantage, in comparison to other nuclear structure models, is that large single-particle spaces can be used, allowing thus for a full description of the total excitation strength and the corresponding energy
<figure><img src="image_12.png" /><figcaption>**Fig. 10** Left panel: schematic drawing of the PDR and IVGDR modes overlaid in the electric-dipole excitation spectrum of a nucleus. Next to the peaks there are two sketches representing their associated macroscopic interpretations. Right panel: RPA calculations of the strength distributions of the unstable nucleus $^{94}$Sr [322], showing the isovector (top) and isoscalar (bottom) responses. A clear increase is seen in the 5–10 MeV PDR energy region (marked in green)</figcaption></figure>

weighted sum rules. In the RPA and QRPA, excited states are approximated by a linear superposition of one-particle one-hole and two-quasiparticle excitations, respectively, neglecting higher order configurations of the many-particle many-hole type. This picture has been shown to successfully describe the Giant Resonances. Extensions, such as the Particle Vibration Coupling (PVC) [324], the Second RPA (SRPA) [325], the Quasiparticle Time Blocking Approximation [326] or the Quasiparticle Phonon Model [327], aim at describing the spreading widths of collective excitations and their fragmentation, due to the coupling to more complex states, like 2p-2 h or 4-quasiparticle configurations. In order to support the experimental activities proposed in the present manuscript, a QRPA code based on the self-consistent solution of the Skyrme-Hartree-Fock plus BCS equations has become recently available to the community [328]. Further developments to improve the treatment of pairing within the Bogoliubov approximation are envisaged within the time scale of the mid term plan (see, e.g., ref. [329]). PVC codes could also become available [330].

### 4.5.2 Pygmy resonances

In recent years the study of the low-energy electric dipole response in nuclei attracted strong interest. This is mainly associated to the phenomenon of the Pygmy Dipole Resonance (PDR) [316, 317]: the observation of the systematic presence of resonance-like structures at energies around the nucleon emission threshold in the excitation spectra of neutron-rich nuclei. A simple interpretation describes this phenomenon as related to a new collective mode, originating from the oscillation of the $N=Z$ core against the neutron skin of neutron-rich nuclei (see Fig. 10), but this is still under debate. Independently on the success of such particular description, these experimental studies are a very good testing ground for the problem of emergence of collectivity in nuclear structure. It was shown, in fact, already long time ago, that the inclusion of the PDR in the calculations of neutron-capture cross sections results in a better reproduction of the experimental data [331]. More recently, growing interest was prompted by theoretical works showing the possible impact of the PDR also beyond nuclear structure. For example, a collective mode involving the presence of the neutron skin, would allow to extract information on its thickness, which is determined by the symmetry energy of the equation of state (EOS) and directly linked to its parameters [332–334]. This has implications on the description of relevant astrophysics objects, like neutron stars. Experimental data on the PDR in neutron-rich exotic nuclei are still scarce. For this reason, measurements that can be performed with SPES radioactive beams are a great scientific opportunity to extend the systematics obtained with $(\alpha, \alpha'\gamma)$ reactions on stable target nuclei [316]. To study the PDR in radioactive nuclei, the experiments must be performed in inverse kinematics, requiring a target made of $^{4}$He (or $^{3}$He) with sufficiently high density. The CTADIR cryogenic target [113] will complement an experimental setup composed by AGATA [9] and the GRIT advanced silicon array [335], for the detection of the scattered particles. The additional presence of a highly efficient scintillator array (like PARIS [11, 336]) would allow to increase even further the experimental sensitivity of the setup for in-beam high-resolution $\gamma$ spectroscopy studies. Inelastic scattering experiments can be realized in inverse kinematics to study the structure of unstable nuclei, such as $^{94}$Sr and $^{132}$Sn. In particular, for the case of $^{94}$Sr, calculations [322] show that the cross section for the population of PDR states in these experimental conditions is sizable (see right panel of Fig. 10). It has to be said that for the case of $^{132}$Sn, published data already exist [337]. However, the experimental conditions were completely different than those at SPES (i. e., relativistic Coulomb excitation with exotic beams at GSI). While the cross section for the population of the PDR states at these extremely high energies is much larger, the increased sensitivity brought to the LNL setup by the availability of AGATA, and the dominant role of the nuclear interaction at SPES energies, give the possibility to extract complementary nuclear structure information. We note that not only the $1^{-}$ PDR states will be populated, but also states of other multipolarity. This means that the same experiments would allow to study at the same time also the phenomenon of the Pygmy Quadrupole Resonance [338]. As stated in [339], one thing that became clear in the study of the phenomenon of the PDR is the need of a sort of “multimessanger approach”, meaning that information on the structure of the PDR can be obtained populating the same states with different, complementary, nuclear reactions (thus having different population cross sections, see e.g. also [340]). In this view, for example, nucleon transfer reactions can be useful to probe the single particle nature of PDR states, as already demonstrated
in [341]. Some stable nuclei (noble gasses, for example), rarely studied in the past on this respect, can be accessed with experiments in inverse kinematics.

Another recent question around the PDR regards whether this type of excitation survives in nuclei at finite temperature. This issue is of basic relevance for astrophysical processes that mostly take place in a finite temperature environment. Predictions [342–345] indicate the presence of PDR states at finite temperature and even an increase in strength with temperature, but no measurements are available so far. In addition, no predictions combining thermal fluctuations and spin effects to the intrinsic dipole response at finite temperature are available. To search for an experimental signal of the PDR at finite temperature the predicted difference between a chain of nuclei should be measured as function of the increasing number of neutrons. In a first step one could use fusion evaporation reactions and observe the subsequent statistical $\gamma$-decay yield. Indeed, the comparison of different reactions could provide a way to entangle the features of the pygmy strength with temperature.

Finally, PDR states can be studied also in decay spectroscopy measurements [346]. SPES has a dedicated $\beta$-decay station that has been built to perform this kind of experiments, also using non re-accelerated beams [346, 347]. Beta decay represents a further experimental probe, which allows the population of two-particle two-hole configurations, not reached by inelastic scattering experiments. Examples of possible nuclei to be studied with this method can be found in [346].

### 4.5.3 Jacobi shape transition

The Jacobi shape transition is a phenomenon consisting in an abrupt change, as a function of angular momentum, of the nucleus shape from oblate, through tri-axial, to more and more elongated shapes. Its existence is predicted to occur for many nuclei at high angular momenta [318, 348, 349] in the region of highest possible deformations of the nucleus before it fissions. So far, this phenomenon was observed only in the light mass nuclei ($A\sim40$) [318–321]. Another region, where very extreme spins can be reached, corresponds to $90<A<140$, as here the limiting angular momentum for fission process is very high. Stable beams at LNL can therefore be used to investigate the shape evolution of hot nuclei in the $A\sim100$ and $A\sim130$ mass regions, at extreme angular momenta, via the measurement of high-energy $\gamma$ rays from the GDR decay in coincidence with light charged particles and discrete transitions in evaporation residues, using AGATA [9] coupled to PARIS [11, 336], and EUCLIDES [21] silicon particle detectors. The research on the Jacobi shape transition was proposed for nuclei selected on the basis of calculations of the total energy surfaces, as a function of quadrupole deformation parameters $\beta$ and $\gamma$, for increasing spin with the Lublin-Strasbourg Drop (LSD) model [349]. In the mass region $A\sim100$, the Jacobi shape transition can be studied in the $^{96}\text{Mo}$ nucleus using a $^{48}\text{Ca}$ beam at 250 MeV energy impinging on a $^{48}\text{Ti}$ target, leading to the $^{96}\text{Mo}$ compound nucleus at 120 MeV excitation energy and with maximum angular momentum of $80\,\hbar$. Nuclei with heavier masses could also be populated in a similar manner, for example $^{130}\text{Ba}$ and $^{142}\text{La}$. To study the Jacobi shape transition, the high-energy $\gamma$ rays from the GDR decay will be measured with the use of PARIS detectors. The experimental selection of events corresponding to high angular momenta will be possible by gating on multiplicity, using PARIS as a multiplicity filter, or choosing particular decay channels, especially those with one alpha-particle emission (in case of $^{98}\text{Mo}$) detected with use of EUCLIDES. The low spin gamma transitions in the final reaction products, measured in coincidence with AGATA, will help to determine the residue by the coincidence gating on discrete $\gamma$-ray transitions.

### 4.5.4 Gamma decay from Giant Quadrupole Resonance excitation

Despite the Giant Quadrupole Resonances (GQRs) have been widely studied in the past, experimental data on their gamma decay are extremely scarce. This is mainly due to the experimental difficulties originated by the small gamma branching, which is obscured by the strongly competing channel of neutron emission. However, performing such experiments is very appealing due to the unique features and illuminating features associated with the detection of the electromagnetic decay. Experiments of this kind were recently performed at CCB Krakow [350], following the pioneering work of J. Beene and collaborators [351] (done in this case with the $^{17}\text{O}$ nucleus as GR exciting probe). Recent theoretical work has also been done [352], showing the importance of obtaining these kind of experimental data. In the mid term it will be available at LNL an experimental setup made of the composite system of AGATA coupled with a scintillation detector array like PARIS [11, 336] or HECTOR+ [353], in order to guaranty the necessary efficiency at high energy. The reaction used would be inelastic scattering of $^{17}\text{O}$ at 20 AMeV bombarding energy to study the gamma decay of the GQR populated in stable nuclei of various masses (e.g. $^{40}\text{Ca}$). In addition, a silicon detector array would be needed to detect the inelastically scattered $^{17}\text{O}$ ions and eventually also the charged particles emitted following the GR decay (allowing to study also other GR decays in addition to the gamma type). The proposed studies will be complementary to that carried out at CCB IFJ PAN with the use of proton beam [350].

### 4.5.5 Isospin mixing

The concept of Isospin was introduced by Heisenberg in 1932 and it is an extremely useful tool to describe and predict the structure of nuclei, exploiting the fact that the interactions among nucleons are to a large extent independent from the considered particles being protons or neutrons (see also Sect. 4.3). However, Isospin is not a perfect symmetry. It is broken, in the first instance, by
**Fig. 11** Schematic view of reaction mechanism phenomenology at Coulomb and Fermi energies. The horizontal axis ideally represents the energy of the projectile, expressed in MeV/u, while the vertical axis indicates the semi-classical impact parameter. Each cloud schematically indicates the energy and impact parameter region where a given reaction mechanism dominates. Semi-transparent green and grey squares are unavoidable sources of background. LNL energies range from deep-sub-Coulomb energies up to the onset of multi-fragmentation phenomena

<figure><img src="image_13.png" /></figure>

the Coulomb force. This causes the mixing. Significant effort was made to quantify the Isospin mixing for nuclei in different mass regions [225, 354, 355]. In particular, for studying Isospin symmetry breaking in electric dipole (E1) transitions, the giant dipole resonance mode (GDR), where approximately all the electric dipole harmonic oscillator strength is concentrated, is a favourable case for searching for small effects in the violation of the associated selection rule [356–358]. It was pointed out that these studies have also consequences that go beyond nuclear structure. In particular, one of the (small) corrections to the first term of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $V_{ud}$ value, actually depends on the Isospin mixing [359, 360]. These kind of experiments are performed using fusion evaporation reactions. The main requirement from the point of view of the experimental setup is to have a combination of an highly efficient system for the detection of gamma rays in the range up to 20 MeV and a high resolution gamma spectrometer to detect discrete, lower energy, lines (thus allowing to identify the residue nuclei of the fusion evaporation reactions). An array of large volume scintillators like PARIS or HECTOR+ [353], coupled with a high resolution spectrometer as AGATA would perfectly fit the experimental needs.

# 5 Nuclear reactions and dynamics

Section 4 has focused on experiments to probe the fine details of the nuclear structure which are related to the properties of a specific nuclear system. In this section we discuss the interaction between colliding nuclei by studying the dynamical evolution of nuclear reactions. The proper description of such evolving systems depends directly on our basic knowledge of the nuclear potential and it is linked to the nucleon-nucleon potential emerging from the residual strong interaction. A detailed knowledge of the reaction mechanisms is also necessary to correctly interpret the results in experiments attempting to probe nuclear structure aspects and vice-versa. Nuclear reactions, indeed, are a powerful tool to produce nuclei in conditions away from the ground state, providing access to excited nuclear levels, and it is well known that the interplay between nuclear structure and reaction dynamics is a key ingredient for a proper interpretation of the experimental results. Moreover, at higher energies, the study of reaction dynamics and thermodynamics is crucial to constrain the Equation of State of nuclear matter.

In this framework, LNL is the ideal playground infrastructure to probe dynamical aspects of nuclear systems and nuclear reactions at low energies (i.e. $E_{beam} \le 15-20$ MeV/u). In this energy regime, several dynamical processes can influence the outcome of a nuclear reaction, which is made more complex by the existence of a strong interplay with the structure of nuclei involved in the collision. Figure 11 schematically depicts the various reaction mechanisms that usually occur at low-to-medium incident energies. On a qualitative point of view, but useful to illustrate the main topics that are of interest for the investigations proposed in this section, the reaction mechanism is mainly affected by the velocity of the beam (i.e. its kinetic energy per unit mass) and the semi-classical centrality of the collision (i.e. its impact parameter). Figure 11 describes this point by using a centrality (vertical axis) and energy (horizontal axis) plane. In this schematic view, for the sake of clarity, we avoided representing other crucial parameters of the collision (such as size, charge and isospin of the entrance channel, as well as the structure of entrance and exit channels). Each cloud indicates the impact parameter and energy region where a given reaction mechanism dominates, while the green and grey squares
<figure><img src="image_14.png" /><figcaption>**Fig. 12** Summary of the nuclear reactions studies that will be performed at LNL in the next future, sorted according to the time phase</figcaption></figure>

<table><caption>**Table 4** Summary of key topics on nuclear reactions and dynamics that will be addressed at LNL in the mid term future. The activities are sorted according to the working group discussing the proposal: (i) dissipative collisions and pre-equilibrium emissions; (ii) transfer reactions; (iii) fission and sub-barrier fusion. The three phases represent the readiness of the experimental campaigns</caption><thead><tr><th>Tag</th><th>Description</th><th>Reactions/beams</th><th>Phase</th></tr></thead><tbody><tr><td>LNL-RD-FU-a0</td><td>α-correlations and clustering in light/medium mass nuclei</td><td>16<sup>-18</sup>O at 10 MeV/u</td><td>A</td></tr><tr><td>LNL-RD-FU-a1</td><td>Onset of pre-equilibrium and clustering</td><td>16<sup>-18</sup>O, <sup>22</sup>Ne at 18-20 MeV/u, exotic Sn and Rb isotopes</td><td>A</td></tr><tr><td>LNL-RD-FU-a2</td><td>α emission at high spins</td><td>Ti, Ni at 10 MeV/u</td><td>A</td></tr><tr><td>LNL-RD-FU-b0</td><td>Complete and Incomplete Fusion</td><td></td><td>B</td></tr><tr><td>LNL-RD-FU-b1</td><td>Isospin dependence of CN formation and decay</td><td><sup>88</sup>Kr and <sup>94</sup>Kr at 10 MeV/u on <sup>40-48</sup>Ca</td><td>B-C</td></tr><tr><td>LNL-RD-TR-a0</td><td>Population of n-rich heavy nuclei via multi-nucleon transfer reactions</td><td>Beams: <sup>48</sup>Ca, <sup>94</sup>Rb, <sup>124-132</sup>Sn, <sup>136-144</sup>Xe, <sup>208</sup>Pb. Targets: <sup>48</sup>Ca, <sup>124</sup>Sn, <sup>208</sup>Pb</td><td>A</td></tr><tr><td>LNL-RD-TR-a1</td><td>Nucleon-nucleon correlations in transfer reactions</td><td><sup>88</sup>Sr+<sup>144</sup>Sm, <sup>48</sup>Ca+<sup>208</sup>Pb, <sup>40</sup>Ca+<sup>132</sup>Sn, <sup>60</sup>Ni+<sup>116</sup>Sn</td><td>A</td></tr><tr><td>LNL-RD-TR-a2</td><td>Competition between transfer and near-barrier fusion</td><td>58, 69, <sup>70</sup>Ni+<sup>124</sup>Sn</td><td>A</td></tr><tr><td>LNL-RD-TR-b0</td><td>Transfer reactions to constrain the Asymptotic Normalization Constant</td><td><sup>7</sup>Li(d,p)<sup>8</sup>Li, <sup>7</sup>Be(d,n)<sup>8</sup>B, <sup>16</sup>O(<sup>3</sup>He,d)<sup>17</sup>F @ 10 MeV/u</td><td>B-C</td></tr><tr><td>LNL-RD-FF-a0</td><td>Fusion-induced fission</td><td>Pb beam</td><td>A</td></tr><tr><td>LNL-RD-FF-b0</td><td>Transfer-induced fission</td><td><sup>238</sup>U beam</td><td>B</td></tr><tr><td>LNL-RD-FF-c0</td><td>Isomers measured at the focal plane of PRISMA</td><td></td><td>C</td></tr><tr><td>LNL-RD-FF-a1</td><td>Fusion far below the barrier by particle-γ coincidences</td><td><sup>16</sup>O, <sup>19</sup>F, <sup>12</sup>C, <sup>13</sup>C beams on light targets</td><td>A</td></tr><tr><td>LNL-RD-FF-b1</td><td>Sub-barrier fusion with exotic neutron-rich nuclei</td><td><sup>96</sup>Sr, <sup>94</sup>Kr beams on <sup>40</sup>Ca, <sup>28</sup>Si</td><td>B</td></tr><tr><td>LNL-RD-FF-c1</td><td>Beyond the limits on heavy-ion fusion at SPES</td><td>24<sup>-26</sup>Al beams on <sup>12</sup>C, <sup>19</sup>F, <sup>26</sup>Mg</td><td>C</td></tr></tbody></table>

represent unavoidable competing processes. The following paragraphs describe the state of the art and the future plans for the study of these mechanisms. The topics have been mainly arranged according to the experimental techniques used and include the study of: dissipative collisions and pre-equilibrium emissions (WG1); transfer processes and particle spectroscopy (WG2); fission and sub-barrier fusion (WG3). The physics cases that are summarized in Table 4 and reported in Fig. 12.
## 5.1 Dissipative collisions and pre-equilibrium emissions

### 5.1.1 Fusion reactions and compound nucleus decay

Fusion reactions above the Coulomb barrier have been the subject of intense experimental campaigns, especially during the '70s and the '90s of the past century [361-365], providing data in hundreds of systems and collisions [366, 367]. A detailed analysis of the systematic trends shows that the fusion cross section has a different behaviour dependent on the energy regimes, which can be described by a number of models based on several phenomenological approaches [361, 368-373]. Those can be microscopical (as TDHF, see [374, 375]), molecular dynamics (see [376, 377]), or macroscopical (such as critical distance models, based on the occurrence of entrance channel effects [378, 379] or more basic approaches based on the liquid drop model [380]).

Recently, state-of-the-art artificial intelligence approaches based on a hybridization of genetic programming and artificial neural networks [381-383] have been successfully adopted to model the fusion cross section, exploiting a large number of collision systems [384]. These techniques are particularly interesting as they allow to derive, in a completely data-driven way, a mathematical expression for the description of experimental data, even in presence of particularly complicated problems. In addition to these aspects, the underlying methods also allow to suitably select the variables needed to predict the output (see e.g. [385-387]). This is extremely relevant for the modeling of nuclear physics data, as it allows to effectively probe correlations between nuclear variables and to drive theories towards the description of nuclear properties. The analytical model derived in Ref. [384] had a discrete success in predicting the cross section of the fusion between light-to-medium mass nuclei above the Coulomb barrier. A detailed analysis of the new model in the high energy region ($E_{beam} \approx 5-10$ MeV/u) shows the presence of large discrepancies for several collision systems, which were also evidenced in other recent studies [373].

The aforementioned discrepancies clearly demand for further experimental campaigns to investigate the complete fusion cross section at high energies. However, these investigations are made particularly complex by the underlying mechanisms. In fact, while at lower energy (for medium-mass systems, like those considered in ref. [373]) the dominant reaction mechanism is that of the complete fusion, at energies over a few MeV/u the complete fusion is hindered and incomplete processes become dominant. The emission of few particles before thermalization, known as out-of-equilibrium emission, for example, can contaminate fusion-evaporation data. These phenomena are possibly enhanced by the occurrence of clustering [388], which have a strong interplay with the formation and decay of hot nuclear states. On the other hand, quasi-fission mechanisms, in which few nucleons are exchanged between projectile and target without the formation of a thermally equilibrated compound nucleus, also gain importance at increasing energies, and increasing masses of the reaction partners. The latter are, moreover, particularly difficult to disentangle from fusion-fission mechanisms, which instead involve the formation and decay of a fully equilibrated compound nucleus. It is therefore clear that a solid description of these competing mechanisms is mandatory to clarify the full picture. The following paragraphs summarize the open questions that will be subject of studies in the medium term future at LNL.

### Complete and incomplete fusion (LNL-RD-FU-b0)

Absolute fusion cross-section measurements can be effectively exploited in the study of nuclear properties but particular care has to be put in understanding the reaction mechanism. Indeed, open questions on the correct values of the fusion cross sections close to its maximum are still present, even for reactions induced by stable nuclei. Moreover, measurements involving Radioactive Ion Beams (RIB) can highlight exotic nuclear properties, such as the presence of halo nuclei.

The collision of heavy ions can lead to incomplete fusion where projectile and target exchange few nucleons but never form a compound nucleus. This process, called *quasi-fission* is faster then the complete fusion leading to fission (fusion-fission), but final products are similar to the fission fragments. While fusion-fission is ruled by the thermodynamics of the compound system and by nuclear structure properties, quasi-fission is mainly a dynamical process that mixes with the complete fusion cross section, possibly altering the outcome of the measurement. A possible way to identify quasi-fission phenomena has been recently proposed [389]: the idea is based on the exchange of nucleons between the partners of a di-nuclear system, which tends to equalize their masses, and involves the measurement of the mass distribution for several angles. Mass-angle distributions should be linked to the lifetime of the process, which is rather short for quasi-fission mechanisms and longer for fully equilibrated systems.

Traditional fusion cross-section experiments are performed using thin targets and telescope detectors that cover only a limited portion of the full solid angle. As a consequence, to extract the fusion cross section the integration of the angle and energy distribution of the detected products is mandatory. Eventually, in order to build the excitation function the beam energy should be changed several times. Such issues can be overcome exploiting an active target for fusion cross section measurement [176]. Moreover, the isovector giant dipole resonance (IVGDR) represents a promising observable to describe the collective behavior of the composite system on its way to fusion. The IVGDR is, indeed, a collective excitation mode of the nucleus in which protons and neutrons are moving out of phase. According to the Brink-Axel hypothesis, the properties of the IVGDR are the same, whether the IVGDR is built on the ground state or on an excited state. Applying this hypothesis to highly excited compound nuclei formed in fusion reactions, the IVGDR could help answering questions related to the deformation and to the fission dynamics. In addition, this approach is particularly interesting for very high masses since nuclear structure data on super-heavy nuclei (SHN) are very scarce and generally limited to the low excitation energies due to the low production cross sections and to competing processes. To characterize the IVGDR in SHN and get hint on the temperature at which the CN is formed, we plan to extract the pre-fission $\gamma$-ray energy spectra