**Fig. 34** CoMD calculations for the collision $^{48}$Ca + $^{27}$Al at 40 MeV/nucleon and impact parameter 4 fm. We plot as a function of time: **a** $D_Z$, projection along the beam axis of $\vec{D}$ and **b** the density $\rho$ evaluated in the center of mass. The dashed horizontal line in the **a** represents the asymptotic value of $D_Z$

<figure><img src="image_33.png" /></figure>

In particular, when different charged particles and fragments are produced through the collision, its asymptotic value $\vec{D}_a$ can be expressed (in units of the elementary charge) as:

$$ \vec{D}_a = \sum_{i=1}^{m_c} \frac{Z_i}{M_i} \vec{P}_i \quad (3) $$

In the previous expression $m_c$, $M_i$, $Z_i$ and $\vec{P}_i$ indicate the multiplicity of charged particles, the mass, the charge and the momentum of the generic particle, respectively. $\vec{P}_i$ is evaluated in the center of mass reference frame. Finally the over-line symbol indicates the average on the events.

$\vec{D}_a$ can therefore furnish a measure of the average degree of isospin or charge/mass equilibration (i.e., redistribution of the neutron excess) in the momentum space as the result of the collision process. According to the definition (3) we can extract the asymptotic value measuring the velocity and charge of all reaction products. Both the pre-equilibrium $\gamma$-ray emission and $\vec{D}_a$ can be considered therefore as signals globally characterizing the charge/mass equilibration process of which the first one can be considered as a heralding messenger. Recently, $\vec{D}_a$ has been measured in mid-peripheral collisions induced on the system $^{48}$Ca + $^{27}$Al at 40 AMeV with the CHIMERA multidetector [96]. The reconstructed average dipolar signal has been reproduced through CoMD calculations [96, 97, 256]. The discussion about the dependence from EOS parameters of the average dipolar signal is reported in Sect. 3.1.5.

In future, we would measure both pre-equilibrium $\gamma$-rays emission and the asymptotic value $\vec{D}_a$ in the same experiment. This will be possible by detecting the $\gamma$-rays by means of the CSI crystals of the multidetector CHIMERA in coincidence with the produced particles. These combined measurements could furnish, especially for central/semi-central collisions, a sort of complete time evolution of $\vec{D}$. Moreover, through the CoMD model, we have also the possibility to evaluate the explored densities during the pre-equilibrium stage in which the $\gamma$-rays are emitted [257] (see Fig. 34). The need to perform a complete reconstruction of the event, and the weakness of the pre-equilibrium $\gamma$-ray emission ask for high-intensity beams (of the order of 10–20 nA) as for instance of stable Ar, Ca isotopes; the use of Ca, Ni target nuclei will allow to span rather large charge/mass asymmetries.

### 4.2.3 Exploring the breathing mode in exotic nuclei

Among the nuclear collective modes the ISGMR, also called the breathing mode of nuclei, is of major importance because its properties are related to the nuclear matter incompressibility $K_\infty$. The latter is a fundamental ingredient in defining the EOS for nuclear matter and it is also a basic parameter in the description of neutron stars and supernovae [258]. The energy of the resonance in the mass A nucleus give the information about $K_A$ connected to $K_\infty$ by the following relation:

$$ K_A = K_\infty + K_{\text{surf}} A^{-1/3} + K_\tau \delta^2 + K_{\text{Coul}} \frac{Z^2}{A^{4/3}} \quad (4) $$

being Z the charge of the nucleus and $\delta$ its asymmetry term. The question about the proper value of $K_\infty$ is still open. Part of the existing uncertainty is due to our poor knowledge of the symmetry energy [259]. The $K_\tau$ asymmetry term contribution in Eq. (4) has been poorly determined, since it requires accurate studies of the compression modes in an isotopic chain spanning a wide range of $(N-Z)/A$ values. This was recently done for the stable Sn isotopes and a value of $K_\tau = -550 \pm 100$ MeV was obtained
<figure><img src="image_33.png" /><figcaption>**Fig. 34** CoMD calculations for the collision $^{48}$Ca + $^{27}$Al at 40 MeV/nucleon and impact parameter 4 fm. We plot as a function of time: **a** $D_Z$, projection along the beam axis of $\vec{D}$ and **b** the density $\rho$ evaluated in the center of mass. The dashed horizontal line in the **a** represents the asymptotic value of $D_Z$</figcaption></figure>

In particular, when different charged particles and fragments are produced through the collision, its asymptotic value $\vec{D}_a$ can be expressed (in units of the elementary charge) as:

$$ \vec{D}_a = \sum_{i=1}^{m_c} \frac{Z_i}{M_i} \vec{P}_i \qquad (3) $$

In the previous expression $m_c$, $M_i$, $Z_i$ and $\vec{P}_i$ indicate the multiplicity of charged particles, the mass, the charge and the momentum of the generic particle, respectively. $\vec{P}_i$ is evaluated in the center of mass reference frame. Finally the over-line symbol indicates the average on the events.

$\vec{D}_a$ can therefore furnish a measure of the average degree of isospin or charge/mass equilibration (i.e., redistribution of the neutron excess) in the momentum space as the result of the collision process. According to the definition (3) we can extract the asymptotic value measuring the velocity and charge of all reaction products. Both the pre-equilibrium $\gamma$-ray emission and $\vec{D}_a$ can be considered therefore as signals globally characterizing the charge/mass equilibration process of which the first one can be considered as a heralding messenger. Recently, $\vec{D}_a$ has been measured in mid-peripheral collisions induced on the system $^{48}$Ca + $^{27}$Al at 40 AMeV with the CHIMERA multidetector [96]. The reconstructed average dipolar signal has been reproduced through CoMD calculations [96, 97, 256]. The discussion about the dependence from EOS parameters of the average dipolar signal is reported in Sect. 3.1.5.

In future, we would measure both pre-equilibrium $\gamma$-rays emission and the asymptotic value $\vec{D}_a$ in the same experiment. This will be possible by detecting the $\gamma$-rays by means of the CsI crystals of the multidetector CHIMERA in coincidence with the produced particles. These combined measurements could furnish, especially for central/semi-central collisions, a sort of complete time evolution of $\vec{D}$. Moreover, through the CoMD model, we have also the possibility to evaluate the explored densities during the pre-equilibrium stage in which the $\gamma$-rays are emitted [257] (see Fig. 34). The need to perform a complete reconstruction of the event, and the weakness of the pre-equilibrium $\gamma$-ray emission ask for high-intensity beams (of the order of 10–20 nA) as for instance of stable Ar, Ca isotopes; the use of Ca, Ni target nuclei will allow to span rather large charge/mass asymmetries.

### 4.2.3 Exploring the breathing mode in exotic nuclei

Among the nuclear collective modes the ISGMR, also called the breathing mode of nuclei, is of major importance because its properties are related to the nuclear matter incompressibility $K_\infty$. The latter is a fundamental ingredient in defining the EOS for nuclear matter and it is also a basic parameter in the description of neutron stars and supernovae [258]. The energy of the resonance in the mass A nucleus give the information about $K_A$ connected to $K_\infty$ by the following relation:

$$ K_A = K_\infty + K_{\text{surf}} A^{-1/3} + K_\tau \delta^2 + K_{\text{Coul}} \frac{Z^2}{A^{4/3}} \qquad (4) $$

being Z the charge of the nucleus and $\delta$ its asymmetry term. The question about the proper value of $K_\infty$ is still open. Part of the existing uncertainty is due to our poor knowledge of the symmetry energy [259]. The $K_\tau$ asymmetry term contribution in Eq. (4) has been poorly determined, since it requires accurate studies of the compression modes in an isotopic chain spanning a wide range of $(N-Z)/A$ values. This was recently done for the stable Sn isotopes and a value of $K_\tau = -550 \pm 100$ MeV was obtained
[56]. In order to determine $K_τ$ with more accuracy and to probe the role of the symmetry energy in the $K_∞$, extending the ISGMR measurement to unstable nuclei is mandatory.

Although extremely appealing, the ISGMR measurement in unstable nuclei remains a major experimental challenge due to the low radioactive beam intensities and the unfavorable conditions in inverse kinematics. Indeed, the ISGMR cross section peaks at 0°, resulting in very low recoil velocities for the light isoscalar probes, i.e., deuterons, $\alpha$ particles and $^6$Li [260].

At the LNS the In-Flight FraISe facility will produce radioactive ion beams at Fermi energies with enough intensity to successfully perform challenging nuclear physics experiments. Moreover, we have already demonstrated the capability of the MAGNEX [25] large acceptance spectrometer to perform, with high sensitivity, experiments with beams accelerated by the SC, at 0° [261].

On the basis of such considerations, we plan to measure the ISGMR in exotic nuclei via deuteron inelastic scattering, detecting the recoiling deuterons emitted at around 0° by MAGNEX. A challenging aspect of this technique is the detection of deuterons at low kinetic energy. This is possible with the present MAGNEX FPD detector, but it should be specifically proven after the foreseen upgrade. The in-flight production method of FraISe allows to accelerate various isotopes at the same time with rates of hundreds of kHz, which is enough for a statistically significant exploration of ISGMR in few days of data taking, assuming typical differential cross sections of about 80–100 mb/sr at 0°. For instance, by selecting the $^{38}$S as main isotope we can get adequate fluxes of $^{37}$S, $^{34,35}$P, $^{31,32}$Si, $^{29}$Al. By tagging and tracking the transported fragments on an event-by-event basis, we plan to investigate the ISGMR spectral features in many exotic nuclei in the same experiment.

The target we plan to use is a deuterated polyethylene CD₂ film of about 1 mg/cm² thickness. The thickness is chosen in order to ensure a reasonable counting rate without limiting too much the energy resolution in the $^{38}$S energy spectrum. This is expected to be about 400 keV, mainly due to the uncertainty associated with the reconstruction of the beam energy.

The energy of the $^{38}$S impinging on the target is expected to be in the 1 GeV range. Then to measure its excitation energy spectrum between 10 and 30 MeV, where the ISGMR is expected, it is necessary to detect the recoiling deuterons with energies ranging from about 1 to 10 MeV, in the laboratory angular region between 0° and 10°. The spectrometer will be set at a fixed position, with the optical axis at 3°, working in full acceptance mode (50 msr solid angle). In this way the whole angular region of interest will be covered. Four magnetic field settings will be used to transport deuterons from 1 to 10 MeV to the focal plane detector (FPD), where they will be tracked and identified, so to have a complete reconstruction of their momentum [262].

In order to disentangle between monopole and quadrupole resonances and to extract the ISGMR strengths, we plan to measure the angular distributions and the excitation energy spectrum selecting different scattering angle ranges.

### 4.2.4 Study of isovector giant dipole resonance with stable and unstable nuclei

The GDR is the most investigated collective motion both on the ground state and on excited states. It was used to probe basic nuclear properties at finite temperature and angular momentum (e.g., nuclear shapes fluctuations and shape evolution, Jacobi transitions, fission timescales, loss of collectivity and phase transitions). From the experimental side, new experiments will be beneficial at various excitation energies to test model predictions (EDF or RPA approaches) and to solve open issues [263]. In particular, at moderate excitation, recent results showed contrasting evidence concerning the saturation of the GDR width at temperatures $T \approx 2.5$ MeV [264–266] for nuclei with mass around $A = 100$ and further experiments in this mass region could clarify the specific issue. Future studies can be also envisaged at higher excitation energies where, around $E^* = 230–250$ MeV, a sudden quenching (up to the complete disappearance) of the GDR $\gamma$-ray yield was observed [263], at odds with the prediction of the statistical model, possibly due to a competition between the equilibration of collective motion and particle decay [267]. A link between such a disappearance and the liquid-gas phase transition is still an open question, triggered by the similarities between the limiting temperature emerging from the caloric curve and the limiting excitation energy for collective motions. Therefore, dedicated experiments in different mass regions ($A \approx 50–60$ and $A \approx 180–190$), where data are lacking, are indeed necessary. Moreover, the study of the GDR features of light nuclei with cluster structures [268] and the role of collectivity toward the p-dripline are among the main topics to face with the new facility upgrade at LNS, complemented with the investigation of the heavy-mass zone (accessible via the incomplete fusion channel), which is relatively unexplored. Possible beams could consist of high-intensity Ar, Ni and Zn isotopes (1–10 pnA) at energies 17–30 AMeV.

For such future experiments a composite setup for charged species and $\gamma$-rays up to 60–70 MeV is mandatory, in order to identify in charge (and in mass) the emitting sources, generally produced via (complete or incomplete) fusion processes [2]. Also, light charged particles must be detected, to estimate the pre-equilibrium contribution. At Fermi energies also the GDR built on the quasi-projectiles (QP) in semi-peripheral collisions far from the stability valley could be investigated, exploiting the FraISe exotic beams [17, 18]. For the detection of charged species, good candidates are FAZIA-like telescopes [101], capable of isotopic separation up to and beyond Ca isotopes and to resolve the charge of heavier fragments with very low thresholds, thus being a valuable asset to detect both forward emitted QPs and fusion residues. For the latter case, also the TOF method, as exploited by the CHIMERA array [2], might help to put coarse gates on the size of the residues (unit mass resolution from E-TOF is possible only for light nuclei). Concerning hard $\gamma$-ray detection, an efficient solution is represented by large BaF₂ scintillators, such as those of MEDEA [239], possibly with new and versatile readout, in order to greatly simplify their use under vacuum. Alternatively, new hard $\gamma$ sensors can be used such as GAGG crystals, anyhow requiring specific and accurate performance tests. A preliminary rendering of the conceptual detection system is shown in Fig. 35. Finally, whatever the final setup architecture, a well-equipped and large scattering chamber
[56]. In order to determine $K_τ$ with more accuracy and to probe the role of the symmetry energy in the $K_∞$, extending the ISGMR measurement to unstable nuclei is mandatory.

Although extremely appealing, the ISGMR measurement in unstable nuclei remains a major experimental challenge due to the low radioactive beam intensities and the unfavorable conditions in inverse kinematics. Indeed, the ISGMR cross section peaks at 0°, resulting in very low recoil velocities for the light isoscalar probes, i.e., deuterons, $\alpha$ particles and $^6$Li [260].

At the LNS the In-Flight FraISe facility will produce radioactive ion beams at Fermi energies with enough intensity to successfully perform challenging nuclear physics experiments. Moreover, we have already demonstrated the capability of the MAGNEX [25] large acceptance spectrometer to perform, with high sensitivity, experiments with beams accelerated by the SC, at 0° [261].

On the basis of such considerations, we plan to measure the ISGMR in exotic nuclei via deuteron inelastic scattering, detecting the recoiling deuterons emitted at around 0° by MAGNEX. A challenging aspect of this technique is the detection of deuterons at low kinetic energy. This is possible with the present MAGNEX FPD detector, but it should be specifically proven after the foreseen upgrade. The in-flight production method of FraISe allows to accelerate various isotopes at the same time with rates of hundreds of kHz, which is enough for a statistically significant exploration of ISGMR in few days of data taking, assuming typical differential cross sections of about 80–100 mb/sr at 0°. For instance, by selecting the $^{38}$S as main isotope we can get adequate fluxes of $^{37}$S, $^{34,35}$P, $^{31,32}$Si, $^{29}$Al. By tagging and tracking the transported fragments on an event-by-event basis, we plan to investigate the ISGMR spectral features in many exotic nuclei in the same experiment.

The target we plan to use is a deuterated polyethylene CD₂ film of about 1 mg/cm² thickness. The thickness is chosen in order to ensure a reasonable counting rate without limiting too much the energy resolution in the $^{38}$S energy spectrum. This is expected to be about 400 keV, mainly due to the uncertainty associated with the reconstruction of the beam energy.

The energy of the $^{38}$S impinging on the target is expected to be in the 1 GeV range. Then to measure its excitation energy spectrum between 10 and 30 MeV, where the ISGMR is expected, it is necessary to detect the recoiling deuterons with energies ranging from about 1 to 10 MeV, in the laboratory angular region between 0° and 10°. The spectrometer will be set at a fixed position, with the optical axis at 3°, working in full acceptance mode (50 msr solid angle). In this way the whole angular region of interest will be covered. Four magnetic field settings will be used to transport deuterons from 1 to 10 MeV to the focal plane detector (FPD), where they will be tracked and identified, so to have a complete reconstruction of their momentum [262].

In order to disentangle between monopole and quadrupole resonances and to extract the ISGMR strengths, we plan to measure the angular distributions and the excitation energy spectrum selecting different scattering angle ranges.

### 4.2.4 Study of isovector giant dipole resonance with stable and unstable nuclei

The GDR is the most investigated collective motion both on the ground state and on excited states. It was used to probe basic nuclear properties at finite temperature and angular momentum (e.g., nuclear shapes fluctuations and shape evolution, Jacobi transitions, fission timescales, loss of collectivity and phase transitions). From the experimental side, new experiments will be beneficial at various excitation energies to test model predictions (EDF or RPA approaches) and to solve open issues [263]. In particular, at moderate excitation, recent results showed contrasting evidence concerning the saturation of the GDR width at temperatures $T \approx 2.5$ MeV [264–266] for nuclei with mass around $A = 100$ and further experiments in this mass region could clarify the specific issue. Future studies can be also envisaged at higher excitation energies where, around $E^* = 230–250$ MeV, a sudden quenching (up to the complete disappearance) of the GDR $\gamma$-ray yield was observed [263], at odds with the prediction of the statistical model, possibly due to a competition between the equilibration of collective motion and particle decay [267]. A link between such a disappearance and the liquid-gas phase transition is still an open question, triggered by the similarities between the limiting temperature emerging from the caloric curve and the limiting excitation energy for collective motions. Therefore, dedicated experiments in different mass regions ($A \approx 50–60$ and $A \approx 180–190$), where data are lacking, are indeed necessary. Moreover, the study of the GDR features of light nuclei with cluster structures [268] and the role of collectivity toward the p-dripline are among the main topics to face with the new facility upgrade at LNS, complemented with the investigation of the heavy-mass zone (accessible via the incomplete fusion channel), which is relatively unexplored. Possible beams could consist of high-intensity Ar, Ni and Zn isotopes (1–10 pnA) at energies 17–30 AMeV.

For such future experiments a composite setup for charged species and $\gamma$-rays up to 60–70 MeV is mandatory, in order to identify in charge (and in mass) the emitting sources, generally produced via (complete or incomplete) fusion processes [2]. Also, light charged particles must be detected, to estimate the pre-equilibrium contribution. At Fermi energies also the GDR built on the quasi-projectiles (QP) in semi-peripheral collisions far from the stability valley could be investigated, exploiting the FraISe exotic beams [17, 18]. For the detection of charged species, good candidates are FAZIA-like telescopes [101], capable of isotopic separation up to and beyond Ca isotopes and to resolve the charge of heavier fragments with very low thresholds, thus being a valuable asset to detect both forward emitted QPs and fusion residues. For the latter case, also the TOF method, as exploited by the CHIMERA array [2], might help to put coarse gates on the size of the residues (unit mass resolution from E-TOF is possible only for light nuclei). Concerning hard $\gamma$-ray detection, an efficient solution is represented by large BaF₂ scintillators, such as those of MEDEA [239], possibly with new and versatile readout, in order to greatly simplify their use under vacuum. Alternatively, new hard $\gamma$ sensors can be used such as GAGG crystals, anyhow requiring specific and accurate performance tests. A preliminary rendering of the conceptual detection system is shown in Fig. 35. Finally, whatever the final setup architecture, a well-equipped and large scattering chamber
**Fig. 35** Rendering of the concept of the new composite setup. The beam enters from left and hits the target (not visible) positioned between the two wheel arrays. The back wheel array could host crystals for hard $\gamma$ while the forward one contains $CsI(Tl)$ crystals. The four FAZIA blocks cover some forward angles and can be used to trigger the measurement on heavy QP or ER products. Drawing made by Carlo Cialdai, INFN Florence

<figure><img src="image_34.png" /></figure>

will be mandatory for those experiments. The minimum length for such a chamber, assumed hosting a multidetector of the type reported in the figure, should be about 250 cm in length and 100 cm wide. The target system should be remotely controlled and the complete beam diagnostics should be available.

# 5 Nuclear astrophysics

Several astrophysics theoretical predictions are strictly dependent on the availability of theoretical/experimental information about reaction cross sections at energies of astrophysical interest.

Nuclear astrophysics studies constitute an interdisciplinary field where knowledge and investigations of different fields of astro-physics (mainly stellar physics and cosmological nucleosynthesis) merge with experimental nuclear physics and theory. Through this synergic effort, in the last twenty years, the overall understanding of many astrophysical phenomena was greatly improved. However, in many practical cases, the still-existing uncertainty affects the predictions of stellar models and element nucleosynthesis. LNS has undoubtedly played a leading role within this framework.

We hereby summarize the possible outcome of this research arising from the upgrading of LNS facilities. In details, it will cover the fundamental topics listed below:

* Quiescent stellar burning: stellar models are investigated with a balanced focus on both massive and smaller mass stars. Their importance for nucleosynthesis is examined in details with big attention paid to the role of nuclear and atomic inputs in different phases of stellar evolution. In particular, contributions by indirect methods, the asymptotic normalization coefficient (ANC) or Trojan horse method (THM), which may solve puzzles of great importance for stellar structure and evolution as for the $^{12}\text{C} + ^{12}\text{C}$ and $^{12}\text{C} + ^{16}\text{O}$ reactions (tag LNS-NA-NAI-a1 in Table 6) are discussed in Sect. 5.1.3.

The possibility to accelerate $^{20}\text{Ne}$ in the Tandem thanks to the NESTOR source will allow indirect studies of the $^{16}\text{O} + ^{16}\text{O}$ fusion by means of the THM which may uncover important features still unknown for this reaction rate (tag LNS-NA-NAI-c0 in Table 6) as extensively discussed in Sect. 5.1.3. The NESTOR source providing He$^{-}$ ion beams will be extremely useful to investigate (p, $\gamma$) transfer reactions of interest for nuclear astrophysics (tag LNS-NA-NAI-c2 in Table 6) as discussed in Sect. 5.1.4. Another important problem which can be addressed with multimethodical approaches (indirect methods, laser-induced reactions) is the study of light elements depletion which is strongly related to the cosmological lithium problem (tag LNS-NA-NAI-b0 in Table 6) as discussed in Sect. 5.1.1. Advanced experimental techniques, like those provided by PANDORA, which will be present at LNS in the next 5–7 years and will allow the study of $^{7}\text{Be}$ decay time in plasma conditions, will be presented in Sect. 5.1.2 (tag LNS-NA-NAI-c1 in Table 6). Later stages of stellar evolution give the possibility to investigate reactions involving Ne and Na (tag LNS-NA-NAI-a0 in Table 6) as reported in Sect. 5.1.4;

* Primordial and explosive nucleosynthesis: the formation of elements in the early universe will be explored at LNS by means of different methods ranging from indirect ones, to studies in laser-induced plasma and PANDORA in Sect. 5.2.1 (tag LNS-NA-EXN-b0 in Table 6). The explosive nucleosynthesis, which is crucial in explaining several dramatic phenomena which take place in the universe–novae (tag LNS-NA-EXN-a1 in Table 6) as discussed in Sect. 5.2.2, X-Ray Bursts, and Core-Collapse SuperNovae (CCSN)–will also be studied at LNS with the possibility of accelerating long-lived isotopes at Tandem ($^{26}\text{Al}$, $^{10}\text{Be}$, $^{44}\text{Ti}$) (tag LNS-NA-EXN-a0 in Table 6–see Sect. 5.2.2) or producing unstable beams from FraISe for studying X-Ray Bursts nucleosynthesis like in the case of the $^{14}\text{O}(p,\alpha)^{17}\text{O}$ and $^{18}\text{Ne}(\alpha,p)^{21}\text{Na}$ reactions (see Sect. 5.2.2 with tag LNS-NA-EXN-c0 in Table 6);

* Neutron-induced reactions and their consequent importance for s- and r-process will also be examined to the light of multimes-senger astronomy achievements of the last years when neutron star mergers in binary systems emerged recently as a fundamental mechanism for nucleosynthesis of heavy elements in the Universe. As regards the s-processes, the PANDORA facility will allow very precise half-life/branching measurements in stellar plasma for elements which are determinant for heavy elements production like Cs, Ba, Hf (see Sect. 5.3.1 tag LNS-NA-NIN-a1 in Table 6). In the same context, the PANDORA facility may allow the measurement of opacities at electron densities and temperatures resembling some ejecta plasma conditions, shedding light on r-process-generated metallic species at specific time stages of the Kilonovae diffusion (tag LNS-NA-NIN-b0 in Table 6) as it is
**Fig. 35** Rendering of the concept of the new composite setup. The beam enters from left and hits the target (not visible) positioned between the two wheel arrays. The back wheel array could host crystals for hard $\gamma$ while the forward one contains $CsI(Tl)$ crystals. The four FAZIA blocks cover some forward angles and can be used to trigger the measurement on heavy QP or ER products. Drawing made by Carlo Cialdai, INFN Florence

<figure><img src="image_34.png" /></figure>

will be mandatory for those experiments. The minimum length for such a chamber, assumed hosting a multidetector of the type reported in the figure, should be about 250 cm in length and 100 cm wide. The target system should be remotely controlled and the complete beam diagnostics should be available.

# 5 Nuclear astrophysics

Several astrophysics theoretical predictions are strictly dependent on the availability of theoretical/experimental information about reaction cross sections at energies of astrophysical interest.

Nuclear astrophysics studies constitute an interdisciplinary field where knowledge and investigations of different fields of astro-physics (mainly stellar physics and cosmological nucleosynthesis) merge with experimental nuclear physics and theory. Through this synergic effort, in the last twenty years, the overall understanding of many astrophysical phenomena was greatly improved. However, in many practical cases, the still-existing uncertainty affects the predictions of stellar models and element nucleosynthesis. LNS has undoubtedly played a leading role within this framework.

We hereby summarize the possible outcome of this research arising from the upgrading of LNS facilities. In details, it will cover the fundamental topics listed below:

* Quiescent stellar burning: stellar models are investigated with a balanced focus on both massive and smaller mass stars. Their importance for nucleosynthesis is examined in details with big attention paid to the role of nuclear and atomic inputs in different phases of stellar evolution. In particular, contributions by indirect methods, the asymptotic normalization coefficient (ANC) or Trojan horse method (THM), which may solve puzzles of great importance for stellar structure and evolution as for the $^{12}\text{C} + ^{12}\text{C}$ and $^{12}\text{C} + ^{16}\text{O}$ reactions (tag LNS-NA-NAI-a1 in Table 6) are discussed in Sect. 5.1.3.

The possibility to accelerate $^{20}\text{Ne}$ in the Tandem thanks to the NESTOR source will allow indirect studies of the $^{16}\text{O} + ^{16}\text{O}$ fusion by means of the THM which may uncover important features still unknown for this reaction rate (tag LNS-NA-NAI-c0 in Table 6) as extensively discussed in Sect. 5.1.3. The NESTOR source providing He$^{-}$ ion beams will be extremely useful to investigate (p, $\gamma$) transfer reactions of interest for nuclear astrophysics (tag LNS-NA-NAI-c2 in Table 6) as discussed in Sect. 5.1.4. Another important problem which can be addressed with multimethodical approaches (indirect methods, laser-induced reactions) is the study of light elements depletion which is strongly related to the cosmological lithium problem (tag LNS-NA-NAI-b0 in Table 6) as discussed in Sect. 5.1.1. Advanced experimental techniques, like those provided by PANDORA, which will be present at LNS in the next 5–7 years and will allow the study of $^{7}\text{Be}$ decay time in plasma conditions, will be presented in Sect. 5.1.2 (tag LNS-NA-NAI-c1 in Table 6). Later stages of stellar evolution give the possibility to investigate reactions involving Ne and Na (tag LNS-NA-NAI-a0 in Table 6) as reported in Sect. 5.1.4;

* Primordial and explosive nucleosynthesis: the formation of elements in the early universe will be explored at LNS by means of different methods ranging from indirect ones, to studies in laser-induced plasma and PANDORA in Sect. 5.2.1 (tag LNS-NA-EXN-b0 in Table 6). The explosive nucleosynthesis, which is crucial in explaining several dramatic phenomena which take place in the universe–novae (tag LNS-NA-EXN-a1 in Table 6) as discussed in Sect. 5.2.2, X-Ray Bursts, and Core-Collapse SuperNovae (CCSN)–will also be studied at LNS with the possibility of accelerating long-lived isotopes at Tandem ($^{26}\text{Al}$, $^{10}\text{Be}$, $^{44}\text{Ti}$) (tag LNS-NA-EXN-a0 in Table 6–see Sect. 5.2.2) or producing unstable beams from FraISe for studying X-Ray Bursts nucleosynthesis like in the case of the $^{14}\text{O}(p,\alpha)^{17}\text{O}$ and $^{18}\text{Ne}(\alpha,p)^{21}\text{Na}$ reactions (see Sect. 5.2.2 with tag LNS-NA-EXN-c0 in Table 6);

* Neutron-induced reactions and their consequent importance for s- and r-process will also be examined to the light of multimes-senger astronomy achievements of the last years when neutron star mergers in binary systems emerged recently as a fundamental mechanism for nucleosynthesis of heavy elements in the Universe. As regards the s-processes, the PANDORA facility will allow very precise half-life/branching measurements in stellar plasma for elements which are determinant for heavy elements production like Cs, Ba, Hf (see Sect. 5.3.1 tag LNS-NA-NIN-a1 in Table 6). In the same context, the PANDORA facility may allow the measurement of opacities at electron densities and temperatures resembling some ejecta plasma conditions, shedding light on r-process-generated metallic species at specific time stages of the Kilonovae diffusion (tag LNS-NA-NIN-b0 in Table 6) as it is
<table><caption>**Table 6** Tables with priorities and feasibility as addressed in the working group</caption><thead><tr><th>Tag</th><th>Description</th><th>Reaction</th><th>Phase</th></tr></thead><tbody><tr><td>LNS-NA-EXN-a0</td><td><sup>26</sup>Al<sub>gs</sub> Nucleosynthesis</td><td><sup>26</sup>Al(n,α)<sup>23</sup>Na</td><td>A</td></tr><tr><td>LNS-NA-EXN-a1</td><td>Novae nucleosynthesis</td><td><sup>31</sup>P(p,α)<sup>28</sup>Si</td><td>A</td></tr><tr><td>LNS-NA-NAI-a0</td><td>Advanced burning—AGB</td><td><sup>23</sup>Na(p,α)<sup>20</sup>Ne, <sup>23</sup>Na(p, γ)<sup>24</sup>Mg</td><td>A</td></tr><tr><td>LNS-NA-NAI-a1</td><td>He and C burning</td><td><sup>16</sup>O + <sup>12</sup>C, Hoyle state studies</td><td>A</td></tr><tr><td>LNS-NA-NIN-a0</td><td>Neutron poison reaction</td><td><sup>25</sup>Mg (n, γ) <sup>26</sup>Mg, <sup>22</sup>Ne (n, γ) <sup>23</sup>Ne</td><td>A/B</td></tr><tr><td>LNS-NA-NIN-a1</td><td>Half-life/branching in stellar plasma (PANDORA)</td><td><sup>134, 135</sup>Cs(β<sup>-</sup>)<sup>134, 135</sup>Ba<br><sup>176</sup>Lu(β<sup>-</sup>)<sup>176</sup>Hf<br><sup>85</sup>Kr(β<sup>-</sup>)<sup>85</sup>Rb</td><td>A/B</td></tr><tr><td>LNS-NA-NIN-b0</td><td>Plasma opacity measurement (PANDORA)</td><td>Se, Sr, Nb elements</td><td>B</td></tr><tr><td>LNS-NA-NAI-b0</td><td>Light elements depletion</td><td>LiBeB with NESTOR/ i-LUCE)</td><td>B/C</td></tr><tr><td>LNS-NA-EXN-b0</td><td>Multimodal BBN</td><td>BBN network, <sup>7</sup>Be decay)</td><td>B/C</td></tr><tr><td>LNS-NA-NAI-c0</td><td>O burning</td><td><sup>16</sup>O + <sup>16</sup>O</td><td>C</td></tr><tr><td>LNS-NA-NAI-c1</td><td><sup>7</sup>Be decay in stellar plasma (PANDORA)</td><td><sup>7</sup>Be(e<sup>-</sup>,γ)<sup>7</sup>Li</td><td>C</td></tr><tr><td>LNS-NA-NAI-c2</td><td>Spectroscopy of medium mass</td><td><sup>34</sup>S(p,γ)<sup>35</sup>Cl</td><td>C</td></tr><tr><td>LNS-NA-EXN-c0</td><td>X-Ray Bursts</td><td><sup>14</sup>O(p,α)<sup>17</sup>O, <sup>18</sup>Ne (α, p) <sup>21</sup>Na</td><td>C</td></tr><tr><td>LNS-NA-NIN-c0</td><td>Neutron source reactions</td><td><sup>22</sup>Ne (α, n) <sup>26</sup>Mg</td><td>C</td></tr><tr><td>LNS-NA-NIN-c1</td><td>R-process investigations with POLYFEMO</td><td>β-delayed neutron decay</td><td>C</td></tr><tr><td>LNS-NA-NIN-c3</td><td>Continuous and pulsed neutron sources<br>Driven by laser and ion beams</td><td><sup>140</sup>Ce (n, γ) <sup>141</sup>Ce and <sup>94</sup>Zr (n, γ) <sup>95</sup>Zr</td><td>C</td></tr></tbody></table>

extensively discussed in Sect. 5.3.3. Neutron-induced reactions are also important for understanding the role of neutron-poison reactions in stellar environment (tag LNS-NA-NIN-a0 in Table 6) as discussed in Sect. 5.3. In this framework an important role can be played by lasers for driving continuous and pulsed neutron sources as reported in Sect. 5.3.2 (tag LNS-NA-NIN-c3 in Table 6). Naturally also for n-producing reactions like the <sup>22</sup>Ne(α,n)<sup>25</sup>Mg, astrophysical studies will benefit from LNS facilities as for Ne-implantation from NESTOR or experiments using MAGNEX (tag LNS-NA-NIN-c0 in Table 6) as explained in details in Sect. 5.3.1. The FraISe facility will also offer relevant possibilities of studying the nucleosynthesis connected to r-process using the POLYFEMO neutron detector as it is reported in Sect. 5.3.4 (see tag LNS-NA-NIN-c1 in Table 6).

We believe that the synergistic efforts of the nuclear and astrophysical or theoretical communities, as well as the building up of a *common foundation* for new generations of investigators, will lead to a stronger nuclear astrophysical community which may be one of the keys to a better understanding of the physical processes taking place in the Universe. The planned activities have been organized into 3 phases, from phase 1 (experiments which can be performed as soon as machines will be restarted) to phase 3 (experiments where a longer R & D is required). This is synthesized in Fig. 36.

## 5.1 Nuclear and atomic inputs for quiescent stellar evolution

Most of stellar evolution proceeds via quiescent burnings which produce the largest part of the energy released by a stellar object in its lifetime. Moreover, a large part of nuclides production is strongly related to it, especially in the light elements regime (A ≤ 56). In those processes, nuclear and atomic inputs determine many aspects of the overall stellar evolution [269].

### 5.1.1 Light elements depletion

Important information ranging from the primordial nucleosynthesis to the still-on-going galactic cosmic ray (GCR) and stellar nucleosynthesis are retrieved from the study of lithium, beryllium and boron (hereafter LiBeB) abundances. Those light elements are destroyed during stellar evolution via nuclear processes at temperatures around few $10^6$ K ($T \approx 2 \times 10^6$ K for $^6$Li to $T \approx 4-5 \times 10^6$ K for boron isotopes). Therefore, their observed surface abundances are determined by the rates of nuclear burnings as well as by the convective envelope extension [270]. At temperatures around few millions of Kelvin the (p,α) channel dominates the total proton-capture cross section. Together with direct measurements which at those energies are hindered by the low Coulomb barrier penetration probability, for charged-particle-induced reaction cross section, indirect methods were developed. Several of them have been suggested to access the cross sections relevant for astrophysics without extrapolations. The THM is one of the most powerful and useful and gives the possibility to measure the bare-nucleus cross section of a binary reaction of interest for astrophysics at
<table><caption>**Table 6** Tables with priorities and feasibility as addressed in the working group</caption><thead><tr><th>Tag</th><th>Description</th><th>Reaction</th><th>Phase</th></tr></thead><tbody><tr><td>LNS-NA-EXN-a0</td><td><sup>26</sup>Al<sub>gs</sub> Nucleosynthesis</td><td><sup>26</sup>Al(n,α)<sup>23</sup>Na</td><td>A</td></tr><tr><td>LNS-NA-EXN-a1</td><td>Novae nucleosynthesis</td><td><sup>31</sup>P(p,α)<sup>28</sup>Si</td><td>A</td></tr><tr><td>LNS-NA-NAI-a0</td><td>Advanced burning—AGB</td><td><sup>23</sup>Na(p,α)<sup>20</sup>Ne, <sup>23</sup>Na(p, γ)<sup>24</sup>Mg</td><td>A</td></tr><tr><td>LNS-NA-NAI-a1</td><td>He and C burning</td><td><sup>16</sup>O + <sup>12</sup>C, Hoyle state studies</td><td>A</td></tr><tr><td>LNS-NA-NIN-a0</td><td>Neutron poison reaction</td><td><sup>25</sup>Mg (n, γ)<sup>26</sup>Mg, <sup>22</sup>Ne (n, γ)<sup>23</sup>Ne</td><td>A/B</td></tr><tr><td>LNS-NA-NIN-a1</td><td>Half-life/branching in stellar plasma (PANDORA)</td><td><sup>134, 135</sup>Cs(β<sup>-</sup>)<sup>134, 135</sup>Ba<br><sup>176</sup>Lu(β<sup>-</sup>)<sup>176</sup>Hf<br><sup>85</sup>Kr(β<sup>-</sup>)<sup>85</sup>Rb</td><td>A/B</td></tr><tr><td>LNS-NA-NIN-b0</td><td>Plasma opacity measurement (PANDORA)</td><td>Se, Sr, Nb elements</td><td>B</td></tr><tr><td>LNS-NA-NAI-b0</td><td>Light elements depletion</td><td>LiBeB with NESTOR/i-LUCE)</td><td>B/C</td></tr><tr><td>LNS-NA-EXN-b0</td><td>Multimodal BBN</td><td>BBN network, <sup>7</sup>Be decay)</td><td>B/C</td></tr><tr><td>LNS-NA-NAI-c0</td><td>O burning</td><td><sup>16</sup>O + <sup>16</sup>O</td><td>C</td></tr><tr><td>LNS-NA-NAI-c1</td><td><sup>7</sup>Be decay in stellar plasma (PANDORA)</td><td><sup>7</sup>Be(e<sup>-</sup>,γ)<sup>7</sup>Li</td><td>C</td></tr><tr><td>LNS-NA-NAI-c2</td><td>Spectroscopy of medium mass</td><td><sup>34</sup>S(p,γ)<sup>35</sup>Cl</td><td>C</td></tr><tr><td>LNS-NA-EXN-c0</td><td>X-Ray Bursts</td><td><sup>14</sup>O(p,α)<sup>17</sup>O, <sup>18</sup>Ne (α, p)<sup>21</sup>Na</td><td>C</td></tr><tr><td>LNS-NA-NIN-c0</td><td>Neutron source reactions</td><td><sup>22</sup>Ne (α, n)<sup>26</sup>Mg</td><td>C</td></tr><tr><td>LNS-NA-NIN-c1</td><td>R-process investigations with POLYFEMO</td><td>β-delayed neutron decay</td><td>C</td></tr><tr><td>LNS-NA-NIN-c3</td><td>Continuous and pulsed neutron sources<br>Driven by laser and ion beams</td><td><sup>140</sup>Ce (n, γ)<sup>141</sup>Ce and <sup>94</sup>Zr (n, γ)<sup>95</sup>Zr</td><td>C</td></tr></tbody></table>

extensively discussed in Sect. 5.3.3. Neutron-induced reactions are also important for understanding the role of neutron-poison reactions in stellar environment (tag LNS-NA-NIN-a0 in Table 6) as discussed in Sect. 5.3. In this framework an important role can be played by lasers for driving continuous and pulsed neutron sources as reported in Sect. 5.3.2 (tag LNS-NA-NIN-c3 in Table 6). Naturally also for n-producing reactions like the <sup>22</sup>Ne(α,n)<sup>25</sup>Mg, astrophysical studies will benefit from LNS facilities as for Ne-implantation from NESTOR or experiments using MAGNEX (tag LNS-NA-NIN-c0 in Table 6) as explained in details in Sect. 5.3.1. The FraISe facility will also offer relevant possibilities of studying the nucleosynthesis connected to r-process using the POLYFEMO neutron detector as it is reported in Sect. 5.3.4 (see tag LNS-NA-NIN-c1 in Table 6).

We believe that the synergistic efforts of the nuclear and astrophysical or theoretical communities, as well as the building up of a *common foundation* for new generations of investigators, will lead to a stronger nuclear astrophysical community which may be one of the keys to a better understanding of the physical processes taking place in the Universe. The planned activities have been organized into 3 phases, from phase 1 (experiments which can be performed as soon as machines will be restarted) to phase 3 (experiments where a longer R & D is required). This is synthesized in Fig. 36.

## 5.1 Nuclear and atomic inputs for quiescent stellar evolution

Most of stellar evolution proceeds via quiescent burnings which produce the largest part of the energy released by a stellar object in its lifetime. Moreover, a large part of nuclides production is strongly related to it, especially in the light elements regime (A ≤ 56). In those processes, nuclear and atomic inputs determine many aspects of the overall stellar evolution [269].

### 5.1.1 Light elements depletion

Important information ranging from the primordial nucleosynthesis to the still-on-going galactic cosmic ray (GCR) and stellar nucleosynthesis are retrieved from the study of lithium, beryllium and boron (hereafter LiBeB) abundances. Those light elements are destroyed during stellar evolution via nuclear processes at temperatures around few $10^6$ K ($T \approx 2 \times 10^6$ K for $^6$Li to $T \approx 4-5 \times 10^6$ K for boron isotopes). Therefore, their observed surface abundances are determined by the rates of nuclear burnings as well as by the convective envelope extension [270]. At temperatures around few millions of Kelvin the (p,α) channel dominates the total proton-capture cross section. Together with direct measurements which at those energies are hindered by the low Coulomb barrier penetration probability, for charged-particle-induced reaction cross section, indirect methods were developed. Several of them have been suggested to access the cross sections relevant for astrophysics without extrapolations. The THM is one of the most powerful and useful and gives the possibility to measure the bare-nucleus cross section of a binary reaction of interest for astrophysics at
<figure><img src="image_35.png" /><figcaption>Fig. 36 Phase plot of the different nuclear astrophysics activities discussed in the text</figcaption></figure>

Gamow energies without the influence of Coulomb suppression or electron screening phenomena [271, 272]. Several of the processes involving LiBeB, as discussed above, were already studied at LNS [273–276].

The comparison of these indirect methods results with the direct ones may shed light on the electron screening effect that is far from being understood, despite long-standing efforts. Moreover, this phenomenon has been studied in recent years in a series of experiments [277]; such results may be compared with direct and THM measurements in order to better investigate the phenomenon.

Taking advantage of the new noble gases source (NESTOR), reactions involving light elements like $ ^7Li(p,\alpha) ^4He $ or $ ^6Li(p,\alpha) ^3He $ or $ ^{11}B(p,\alpha) ^8Be $ can be studied via THM applied to the $ ^3He $ breakup (i.e., using the 3-body reaction $ ^7Li(^3He, \alpha\alpha) ^2H $ for the first process) not only to measure the cross section at Gamow energies but also to further check the “spectator invariance” [278, 279]. The same reactions may be studied in a synergistic effort by using the I-LUCE laser facility which will be soon available at LNS and by applying the Coulomb Explosion technique which has already been successfully applied to $ ^2H(d,p) ^3H $ reaction in [280].

### 5.1.2 $ ^7Be $ half-life in strongly ionized stellar environments studied with PANDORA

The weak decay of $ ^7Be $ via electron capture (EC) into $ ^7Li $ is of relevant interest for both primordial nucleosynthesis models, concerning the cosmological lithium problem, and for the stellar interior structure models which relies on the neutrino flux yields. In particular $ ^7Be $ leads to one of the several reaction channels for studying the solar neutrino flux [281] and the neutrino oscillations. The EC decay probability of $ ^7Be $ [282] is a crucial parameter for estimating its abundances in spite of the branching ratio (BR) of other destruction channels (i.e., $ ^7Be(p,\gamma) ^8B $). Terrestrial decay into $ ^7Li(\frac{3}{2}^{-}) $ ground state (BR 89.7 %) or first $ ^7Li $ excited state (BR 10.3 %) occurs with a half-life of 53 days. This is no longer true for strongly ionized environments [283, 284]. Several theoretical works in the last decade tried to catch the fundamental impact of the atomic environment on the nuclear decay [285]. Models based on single-particle mean-field, with the aim to catch atomic influence—of hot plasma composed of $ ^7Be $ atoms surrounded by protons/electrons as degenerate quantum Fermi gas—on the weak interaction, have recently shown strong variation of $ ^7Be $ half-life as a function of plasma density, temperature and charge state distribution (CSD) [284]. The experimental verification of these theoretical predictions would be highly desired. In this context, PANDORA, as a multidisciplinary facility and compact plasma trap, can suit with the experimental requirements [27]. Magneto-plasmas conceived in the facility allow to confine ions of radioisotopes in a microwave-sustained plasma, with electron density up to $ 10^{13} \text{ cm}^{-3} $ and energy up to tens of keV. The facility is thought for first-of-its-kind nuclear decay measurements in plasmas resembling stellar conditions, especially in terms of temperature and CSD. The study of the $ ^7Be $ case decay can be afforded via $ \gamma $-tagging of 477.6 keV $ \gamma $-rays emission from first-excited $ ^7Li $ state using a dedicated high-efficiency and low-resolution hyper-purity germanium (HPGe) detector array [286]. A technological solution for studying such short-living (≈ 60 days) radioisotopes will be provided by the construction of an in-flight injection line of radioactive ion beams (RIBs) into the plasma trap. A feasibility study to produce $ ^7Be $ nuclei has been performed, considering a SC proton beam hitting a boron nitride compound; fragmentation reaction will produce the isotope from boron. Then, effusing nuclei will be extracted at +1 charge state, and subsequently injected into a radio-frequency quadrupole cooler to optimize the beam envelope properties, longitudinal matching and energy, before entering the plasma potential and penetrate in the plasma core. The line is thought to optimize the capture efficiency in plasma of the RIB and to breed the charge state of nuclei, according to the well-known principles of the charge breeding technique.
<figure><img src="image_35.png" /><figcaption>Fig. 36 Phase plot of the different nuclear astrophysics activities discussed in the text</figcaption></figure>

Gamow energies without the influence of Coulomb suppression or electron screening phenomena [271, 272]. Several of the processes involving LiBeB, as discussed above, were already studied at LNS [273–276].

The comparison of these indirect methods results with the direct ones may shed light on the electron screening effect that is far from being understood, despite long-standing efforts. Moreover, this phenomenon has been studied in recent years in a series of experiments [277]; such results may be compared with direct and THM measurements in order to better investigate the phenomenon.

Taking advantage of the new noble gases source (NESTOR), reactions involving light elements like $ ^7Li(p,\alpha) ^4He $ or $ ^6Li(p,\alpha) ^3He $ or $ ^{11}B(p,\alpha) ^8Be $ can be studied via THM applied to the $ ^3He $ breakup (i.e., using the 3-body reaction $ ^7Li(^3He, \alpha\alpha) ^2H $ for the first process) not only to measure the cross section at Gamow energies but also to further check the “spectator invariance” [278, 279]. The same reactions may be studied in a synergistic effort by using the I-LUCE laser facility which will be soon available at LNS and by applying the Coulomb Explosion technique which has already been successfully applied to $ ^2H(d,p) ^3H $ reaction in [280].

### 5.1.2 $ ^7Be $ half-life in strongly ionized stellar environments studied with PANDORA

The weak decay of $ ^7Be $ via electron capture (EC) into $ ^7Li $ is of relevant interest for both primordial nucleosynthesis models, concerning the cosmological lithium problem, and for the stellar interior structure models which relies on the neutrino flux yields. In particular $ ^7Be $ leads to one of the several reaction channels for studying the solar neutrino flux [281] and the neutrino oscillations. The EC decay probability of $ ^7Be $ [282] is a crucial parameter for estimating its abundances in spite of the branching ratio (BR) of other destruction channels (i.e., $ ^7Be(p,\gamma) ^8B $). Terrestrial decay into $ ^7Li(\frac{3}{2}^{-}) $ ground state (BR 89.7 %) or first $ ^7Li $ excited state (BR 10.3 %) occurs with a half-life of 53 days. This is no longer true for strongly ionized environments [283, 284]. Several theoretical works in the last decade tried to catch the fundamental impact of the atomic environment on the nuclear decay [285]. Models based on single-particle mean-field, with the aim to catch atomic influence—of hot plasma composed of $ ^7Be $ atoms surrounded by protons/electrons as degenerate quantum Fermi gas—on the weak interaction, have recently shown strong variation of $ ^7Be $ half-life as a function of plasma density, temperature and charge state distribution (CSD) [284]. The experimental verification of these theoretical predictions would be highly desired. In this context, PANDORA, as a multidisciplinary facility and compact plasma trap, can suit with the experimental requirements [27]. Magneto-plasmas conceived in the facility allow to confine ions of radioisotopes in a microwave-sustained plasma, with electron density up to $ 10^{13} \text{ cm}^{-3} $ and energy up to tens of keV. The facility is thought for first-of-its-kind nuclear decay measurements in plasmas resembling stellar conditions, especially in terms of temperature and CSD. The study of the $ ^7Be $ case decay can be afforded via $ \gamma $-tagging of 477.6 keV $ \gamma $-rays emission from first-excited $ ^7Li $ state using a dedicated high-efficiency and low-resolution hyper-purity germanium (HPGe) detector array [286]. A technological solution for studying such short-living (≈ 60 days) radioisotopes will be provided by the construction of an in-flight injection line of radioactive ion beams (RIBs) into the plasma trap. A feasibility study to produce $ ^7Be $ nuclei has been performed, considering a SC proton beam hitting a boron nitride compound; fragmentation reaction will produce the isotope from boron. Then, effusing nuclei will be extracted at +1 charge state, and subsequently injected into a radio-frequency quadrupole cooler to optimize the beam envelope properties, longitudinal matching and energy, before entering the plasma potential and penetrate in the plasma core. The line is thought to optimize the capture efficiency in plasma of the RIB and to breed the charge state of nuclei, according to the well-known principles of the charge breeding technique.
<figure><img src="image_36.png" /><figcaption>**Fig. 37** $^{12}$C + $^{12}$C fusion reactions cross section as measured by the THM in [14]</figcaption></figure>

### 5.1.3 Helium, carbon and oxygen burning

Helium, carbon and oxygen burning influences the fate of massive stars (exceeding eight solar masses), especially their late evolutionary stages. The main processes are the triple-$\alpha$ capture, which involves the so-called Hoyle state, the $^{12}$C + $^{12}$C fusion reaction, which is efficient at temperatures greater than $0.4 \times 10^9$ K, or the $^{16}$O + $^{16}$O or $^{16}$O + $^{12}$C fusion, which determines the fate of SN progenitors and the related nucleosynthesis.

THM has provided in the recent years an important measurement of the $^{12}$C + $^{12}$C reactions both in the $\alpha$ as well as in the p emitting channel. The pioneering experiment performed at the LNS Tandem [14], and the measured cross section represent a cornerstone for future application for THM reactions involving heavier nuclei (see Fig. 37). This new reaction rate impacts heavily on the stellar structure and evolution as it was already pointed out by Chieffi et al. [287]. In perspective, the same methodology will be applied to other crucial reactions such as the $^{16}$O + $^{16}$O (tag LNS-NA-NAI-c0 in Table 6) or $^{16}$O + $^{12}$C. They will be studied taking advantage of the $^{20}$Ne beam which will be produced by NESTOR and accelerated by the Tandem. Indeed, the use of $^{20}$Ne as a possible Trojan Horse nucleus was already proved in [288] and reference therein. The possibility to study those three reactions involving C and O can provide ultimate information for stellar evolutionary models for massive stars and help to reduce the huge uncertainties which are present in stellar reaction rates, thus enriching the overall comprehension of several astrophysical problems like the C/O ratio in final evolutionary stages, depth of convective zone, and reducing the uncertainties in $M_{up}$.

Another crucial phase for massive star evolution is the helium burning via the 3-$\alpha$ interaction. This was recently studied at LNS in two different experiments [289] and in [123]. Using the same methodology as in [123] with an improved energy resolution provided by the use of advanced detector array [2], sounder experimental data on the Hoyle state may be conveyed to the astrophysical community as well as possible experimental evidences of the presence of an Efimov state [290].

### 5.1.4 Advanced cycles: NeNaAl cycle

The NeNa and MgAl cycles are typical of high-temperature ($T_9(10^9$K) ~ 0.05) H-burning reaction networks of evolved stars [269]. Because of the higher Coulomb barriers involved, those cycles are not as relevant as the CNO one for the energy production in stars, but play an important role in the nucleosynthesis of elements heavier than Ne. Recently, the development of $^{23}$Na and $^{27}$Al beams at LNS has allowed to study such reactions at the Tandem by using the THM. Some studies have already shown the feasibility of such measurements using innovative experimental devices, as reported in [15] for the $^{27}$Al(p,$\alpha$)$^{24}$Mg reaction which is the process that drives the destruction of $^{27}$Al, the production of $^{24}$Mg, and closes the MgAl cycle when its rate exceeds the one of the competing (p,$\gamma$) reaction. Asymptotic Giant Branch (AGB) stars have the right values of temperature and density to efficiently host CNO, NeNa and MgAl cycles: all of these play an important role in both Quiescent and Hot Bottom Burning and are relevant for the production of both $^{20}$Ne and $^{27}$Al via the $^{23}$Na(p,$\alpha$)$^{20}$Ne and $^{23}$Na(p,$\gamma$)$^{24}$Mg, respectively. Nevertheless, the cross section of both processes is largely unknown at low energies, and extrapolations are affected by large errors (more than one order of magnitude) [291]. On the other side of the NeNa cycle, $^{20}$Ne can be destroyed via the $^{20}$Ne(p,$\gamma$)$^{21}$Na: its cross section is also largely unknown [292], leaving many questions regarding the NeNa cycle still opened.

In future, three different experiments may be performed using indirect methods at LNS. The $^{23}$Na(p,$\alpha$)$^{20}$Ne will be studied using THM at the Tandem accelerator using the available $^{23}$Na ($E_{beam}$ = 58 MeV) on CD$_2$, using the deuterium as TH nucleus
<figure><img src="image_36.png" /><figcaption>**Fig. 37** $^{12}$C + $^{12}$C fusion reactions cross section as measured by the THM in [14]</figcaption></figure>

### 5.1.3 Helium, carbon and oxygen burning

Helium, carbon and oxygen burning influences the fate of massive stars (exceeding eight solar masses), especially their late evolutionary stages. The main processes are the triple-$\alpha$ capture, which involves the so-called Hoyle state, the $^{12}$C + $^{12}$C fusion reaction, which is efficient at temperatures greater than $0.4 \times 10^9$ K, or the $^{16}$O + $^{16}$O or $^{16}$O + $^{12}$C fusion, which determines the fate of SN progenitors and the related nucleosynthesis.

THM has provided in the recent years an important measurement of the $^{12}$C + $^{12}$C reactions both in the $\alpha$ as well as in the p emitting channel. The pioneering experiment performed at the LNS Tandem [14], and the measured cross section represent a cornerstone for future application for THM reactions involving heavier nuclei (see Fig. 37). This new reaction rate impacts heavily on the stellar structure and evolution as it was already pointed out by Chieffi et al. [287]. In perspective, the same methodology will be applied to other crucial reactions such as the $^{16}$O + $^{16}$O (tag LNS-NA-NAI-c0 in Table 6) or $^{16}$O + $^{12}$C. They will be studied taking advantage of the $^{20}$Ne beam which will be produced by NESTOR and accelerated by the Tandem. Indeed, the use of $^{20}$Ne as a possible Trojan Horse nucleus was already proved in [288] and reference therein. The possibility to study those three reactions involving C and O can provide ultimate information for stellar evolutionary models for massive stars and help to reduce the huge uncertainties which are present in stellar reaction rates, thus enriching the overall comprehension of several astrophysical problems like the C/O ration in final evolutionary stages, depth of convective zone, and reducing the uncertainties in $M_{up}$.

Another crucial phase for massive star evolution is the helium burning via the 3-$\alpha$ interaction. This was recently studied at LNS in two different experiments [289] and in [123]. Using the same methodology as in [123] with an improved energy resolution provided by the use of advanced detector array [2], sounder experimental data on the Hoyle state may be conveyed to the astrophysical community as well as possible experimental evidences of the presence of an Efimov state [290].

### 5.1.4 Advanced cycles: NeNaAl cycle

The NeNa and MgAl cycles are typical of high-temperature ($T_9(10^9$K) ~ 0.05) H-burning reaction networks of evolved stars [269]. Because of the higher Coulomb barriers involved, those cycles are not as relevant as the CNO one for the energy production in stars, but play an important role in the nucleosynthesis of elements heavier than Ne. Recently, the development of $^{23}$Na and $^{27}$Al beams at LNS has allowed to study such reactions at the Tandem by using the THM. Some studies have already shown the feasibility of such measurements using innovative experimental devices, as reported in [15] for the $^{27}$Al(p,$\alpha$)$^{24}$Mg reaction which is the process that drives the destruction of $^{27}$Al, the production of $^{24}$Mg, and closes the MgAl cycle when its rate exceeds the one of the competing (p,$\gamma$) reaction. Asymptotic Giant Branch (AGB) stars have the right values of temperature and density to efficiently host CNO, NeNa and MgAl cycles: all of these play an important role in both Quiescent and Hot Bottom Burning and are relevant for the production of both $^{20}$Ne and $^{27}$Al via the $^{23}$Na(p,$\alpha$)$^{20}$Ne and $^{23}$Na(p,$\gamma$)$^{24}$Mg, respectively. Nevertheless, the cross section of both processes is largely unknown at low energies, and extrapolations are affected by large errors (more than one order of magnitude) [291]. On the other side of the NeNa cycle, $^{20}$Ne can be destroyed via the $^{20}$Ne(p,$\gamma$)$^{21}$Na: its cross section is also largely unknown [292], leaving many questions regarding the NeNa cycle still opened.

In future, three different experiments may be performed using indirect methods at LNS. The $^{23}$Na(p,$\alpha$)$^{20}$Ne will be studied using THM at the Tandem accelerator using the available $^{23}$Na ($E_{beam}$ = 58 MeV) on CD$_2$, using the deuterium as TH nucleus
to trigger the $ ^2H(^{23}Na, ^{20}Ne\alpha) $n three-body process. The direct part of the two $(p,\gamma)$ reactions will be investigated by studying the $ ^{23}Na(^{3}He,d)^{24}Mg $ and $ ^{20}Ne(^{3}He,d)^{21}Na $ proton transfer reactions: in both cases, the experiments will be performed using the NESTOR source. The latter will also need a gaseous target, while for the former we plan to use a NaF solid one. In the context of the transfer reactions of interest for $(p,\gamma)$ reactions in p-layer of AGB stars, the possibility to use the OSCAR array (hOdoscope of Silicons for Correlations and Analysis of Reactions) [132, 138] for particle identification, with a good angular coverage/resolution and energy resolution, will allow to perform nuclear spectroscopy of medium mass nuclei. This is relevant both for checking shell models predictions for moderately p-rich and n-rich nuclei, and to determine the resonance strengths of low-energy states involved in transfer reactions. A proposed measurement is about the $ ^{34}S(p,\gamma)^{35}Cl $ via the reaction $ ^{34}S(^{3}He,d)^{35}Cl $, using the NESTOR noble gas beam.

## 5.2 The explosive universe: BBN and explosive nucleosynthesis

Quiescent nuclear burning is characterized by processes such as the pp-chains, the CNO cycles and the He- and C-burning sequences that occur when a star is in Main Sequence or in a most advanced phases as RGB or AGB. Chemical element nucleosynthesis and energy production take place also in explosive conditions. Such conditions can be found in completely different astrophysical scenarios, that is, the Big Bang and final phases of stellar evolution such as Novae, X-Ray Bursts and Supernovae. In particular, in this second explosive environment, where extremes of temperature and density are met, nuclear reactions are often much faster than the timescales for $ \beta $-decay, consequently nuclear reactions can occur far from $ \beta $-stability involving unstable nuclei. Several input came from the scientific community about possible experimental studies of nuclear reactions involved in explosive astrophysical environments to be performed at LNS taking advantage of the long-standing expertise in experimental nuclear astrophysics and of the new research facilities which will be available at LNS in the next years.

### 5.2.1 Big Bang Nucleosynthesis

The Big Bang Nucleosynthesis (BBN) occurred roughly during the first 20 min after the Bang, when the temperature fell down to $ 10^9 - 10^8 $ K. Together with the cosmic microwave background radiation (CMB) and the Hubble expansion rate, BBN is one of the three main evidences of the Big Bang Model and allows to probe the universe at the earliest time. In particular, the BBN provides an evaluation of the primordial abundances of light elements, mainly deuterium, $ ^3He, ^4He, $ and lithium as a function of the only free parameter $ \eta = n_b/n_\gamma $, that is, the baryon-to-photon ratio, once the neutron lifetime, the number of neutrino families, and the nuclear reaction network of 12 reactions are fixed [293, 294]. BBN success relies on the agreement between the predicted primordial abundances and the abundances evaluated from astronomical observations. Moreover, the $ \eta $ parameter inferred considering observations and BBN predictions is in agreement with its independent estimation from CMB measurement [294, 295]. Nevertheless, there is still an unsolved issue referred to as the cosmological lithium problem (CLiP), that is, the discrepancy of about a factor 3 between the predicted $ ^7Li $ abundances by BBN [294] and the abundances derived from metal-poor halo-star observations [296].

Nuclear processes involved in the BBN network can be tackled at LNS in the next future from three different sides:

* with the laser facility I-LUCE, to measure nuclear cross sections under plasma conditions;

* with “conventional” accelerators, to measure nuclear cross sections via indirect techniques, such as the THM;

* with the PANDORA plasma trap, to study $ ^7Be $ decay under plasma conditions (see Sect. 5.1.2).

The implementation of I-LUCE, a sub-picosecond laser with intensities up to $ 10^{19}-10^{21} $ W/cm$^2$, will open a new scenario for research in nuclear astrophysics, providing novel experimental approaches. Several physical cases can be studied (see Sect. 5.1.1) such as the nuclear reactions involved in the BBN as $ d(d,n)^3He, d(d,p)t, ^3He(d,p)^4He, t(d,n)\alpha, ^7Li(p,\alpha)^4He $. The main advantage of some of these new experimental paradigms regards the possibility to study nuclear reactions in a controlled laboratory plasma with a thermodynamic status not too different from typical astrophysical scenarios. Moreover, a new evaluation of the electron screening effect will arise from the comparison of the cross section obtained in laboratory plasma conditions with the bare-nucleus cross section obtained from THM measurements, as it has been found for instance in [297].

Different experimental techniques can be used to study nuclear reactions with a high-power, high-intensity laser with decent repetition rate (such as I-LUCE). The Coulomb explosion (CE) of cryogenically cooled gas mixtures allows the generation of a multi-keV plasma with a Maxwell-Boltzmann distribution inducing nuclear reaction at astrophysical energies (Gamow-like window). The CE is based on the interaction of ultrashort high-intensity laser pulse $ 10^{16}-10^{18} $W/cm$^2$ with an expanding gas cluster mixture delivered by a nozzle at proper conditions in terms of temperature and pressure, in order to maximize the laser absorption. The laser pulse energy is absorbed by electrons via heating mechanisms such as rapid collisions causing the full strip of the electrons of the gas. The sudden onset of a positive space charge triggers the Coulomb dissociation of the clusters resulting in multi-keV ion acceleration with a nearly isotropic emission. The accelerated ions interact in the surrounding plasma and nuclear reactions take place. By measuring the ion energy distribution and detecting the reaction products, one can infer information to obtain the cross section of the selected nuclear reactions. The first CE experiments that can be performed once that the laser facility will be available will be dedicated to the d-d, d-$ ^3He, $ and t+d (as secondary process) using a $ D_2-$ $ ^3He $ gas mixture. The feasibility of the proposed
to trigger the $ ^2H(^{23}Na, ^{20}Ne\alpha) $n three-body process. The direct part of the two (p,γ) reactions will be investigated by studying the $ ^{23}Na(^{3}He,d)^{24}Mg $ and $ ^{20}Ne(^{3}He,d)^{21}Na $ proton transfer reactions: in both cases, the experiments will be performed using the NESTOR source. The latter will also need a gaseous target, while for the former we plan to use a NaF solid one. In the context of the transfer reactions of interest for (p,γ) reactions in p-layer of AGB stars, the possibility to use the OSCAR array (hOdoscope of Silicons for Correlations and Analysis of Reactions) [132, 138] for particle identification, with a good angular coverage/resolution and energy resolution, will allow to perform nuclear spectroscopy of medium mass nuclei. This is relevant both for checking shell models predictions for moderately p-rich and n-rich nuclei, and to determine the resonance strengths of low-energy states involved in transfer reactions. A proposed measurement is about the $ ^{34}S(p,\gamma)^{35}Cl $ via the reaction $ ^{34}S(^{3}He,d)^{35}Cl $, using the NESTOR noble gas beam.

## 5.2 The explosive universe: BBN and explosive nucleosynthesis

Quiescent nuclear burning is characterized by processes such as the pp-chains, the CNO cycles and the He- and C-burning sequences that occur when a star is in Main Sequence or in a most advanced phases as RGB or AGB. Chemical element nucleosynthesis and energy production take place also in explosive conditions. Such conditions can be found in completely different astrophysical scenarios, that is, the Big Bang and final phases of stellar evolution such as Novae, X-Ray Bursts and Supernovae. In particular, in this second explosive environment, where extremes of temperature and density are met, nuclear reactions are often much faster than the timescales for β-decay, consequently nuclear reactions can occur far from β-stability involving unstable nuclei. Several input came from the scientific community about possible experimental studies of nuclear reactions involved in explosive astrophysical environments to be performed at LNS taking advantage of the long-standing expertise in experimental nuclear astrophysics and of the new research facilities which will be available at LNS in the next years.

### 5.2.1 Big Bang Nucleosynthesis

The Big Bang Nucleosynthesis (BBN) occurred roughly during the first 20 min after the Bang, when the temperature fell down to $10^9 - 10^8$ K. Together with the cosmic microwave background radiation (CMB) and the Hubble expansion rate, BBN is one of the three main evidences of the Big Bang Model and allows to probe the universe at the earliest time. In particular, the BBN provides an evaluation of the primordial abundances of light elements, mainly deuterium, $ ^3He, ^4He, $ and lithium as a function of the only free parameter $ \eta = n_b/n_\gamma $, that is, the baryon-to-photon ratio, once the neutron lifetime, the number of neutrino families, and the nuclear reaction network of 12 reactions are fixed [293, 294]. BBN success relies on the agreement between the predicted primordial abundances and the abundances evaluated from astronomical observations. Moreover, the $ \eta $ parameter inferred considering observations and BBN predictions is in agreement with its independent estimation from CMB measurement [294, 295]. Nevertheless, there is still an unsolved issue referred to as the cosmological lithium problem (CLiP), that is, the discrepancy of about a factor 3 between the predicted $ ^7Li $ abundances by BBN [294] and the abundances derived from metal-poor halo-star observations [296].

Nuclear processes involved in the BBN network can be tackled at LNS in the next future from three different sides:

* with the laser facility I-LUCE, to measure nuclear cross sections under plasma conditions;

* with "conventional" accelerators, to measure nuclear cross sections via indirect techniques, such as the THM;

* with the PANDORA plasma trap, to study $ ^7Be $ decay under plasma conditions (see Sect. 5.1.2).

The implementation of I-LUCE, a sub-picosecond laser with intensities up to $10^{19}-10^{21} W/cm^2$, will open a new scenario for research in nuclear astrophysics, providing novel experimental approaches. Several physical cases can be studied (see Sect. 5.1.1) such as the nuclear reactions involved in the BBN as $d(d,n)^3He, d(d,p)t, ^3He(d,p)^4He, t(d,n)\alpha, ^7Li(p,\alpha)^4He$. The main advantage of some of these new experimental paradigms regards the possibility to study nuclear reactions in a controlled laboratory plasma with a thermodynamic status not too different from typical astrophysical scenarios. Moreover, a new evaluation of the electron screening effect will arise from the comparison of the cross section obtained in laboratory plasma conditions with the bare-nucleus cross section obtained from THM measurements, as it has been found for instance in [297].

Different experimental techniques can be used to study nuclear reactions with a high-power, high-intensity laser with decent repetition rate (such as I-LUCE). The Coulomb explosion (CE) of cryogenically cooled gas mixtures allows the generation of a multi-keV plasma with a Maxwell-Boltzmann distribution inducing nuclear reaction at astrophysical energies (Gamow-like window). The CE is based on the interaction of ultrashort high-intensity laser pulse $10^{16}-10^{18} W/cm^2$ with an expanding gas cluster mixture delivered by a nozzle at proper conditions in terms of temperature and pressure, in order to maximize the laser absorption. The laser pulse energy is absorbed by electrons via heating mechanisms such as rapid collisions causing the full strip of the electrons of the gas. The sudden onset of a positive space charge triggers the Coulomb dissociation of the clusters resulting in multi-keV ion acceleration with a nearly isotropic emission. The accelerated ions interact in the surrounding plasma and nuclear reactions take place. By measuring the ion energy distribution and detecting the reaction products, one can infer information to obtain the cross section of the selected nuclear reactions. The first CE experiments that can be performed once that the laser facility will be available will be dedicated to the d-d, d-$^3$He, and t+d (as secondary process) using a $D_2$-$^3$He gas mixture. The feasibility of the proposed
measurement is supported by previous experiments performed with the same technique [280]. I-LUCE will allow to extend the explored energy range covering the full range of interest for the BBN. Another possible experimental technique to study nuclear reactions with laser exploits the interaction between an ion beam from standard accelerator (or for an ion source) delivered on a laser-induced plasma target. This will allow in-plasma measurement, with the advantages of a beam from accelerators (low-energy spread and high intensity). The aforementioned technique requires solid feasibility studies, mostly related to the synchronization of the accelerated ion beam with the short plasma lifetimes. Nevertheless, at the present time LNS holds a nearly unique position providing the possibility to perform this kind of research in the next future.

Regarding the study of nuclear reactions of interest for BBN with "conventional" accelerators, the first physical case is the measurement of the $ ^7Li(d,n) ^8Be $ reaction cross section. This process of interest for the CLiP contributes to the $ ^7Li $ destruction, affecting the prediction of $ ^7Li $ abundance. However, large uncertainties still exist in current $ ^7Li(d,n) ^8Be $ reaction rates widely used in BBN models. Existing experimental cross section data for this reaction are very limited and the most majority of them are not in the BBN energy range. Among them, only two sets of data are located in the energy region of BBN interest, but show huge differences [298]. Therefore, new experimental measurements of this reaction in the BBN energy region are needed. This reaction can be studied for the first time with THM applied to the $ ^7Li(^3He,n ^8Be)H $ three-body reaction taking advantage of the $ ^3He $ beam (the TH nucleus) that will be provided by the new NESTOR ion source and accelerated by the Tandem.

The opportunity to have a $ ^3He $ beam from NESTOR source triggered also the idea to perform a new THM study of the $ ^7Li(p,\alpha) ^4He $ reaction of interest for the CLiP as well as for the stellar lithium depletion (see Sect. 5.1.1).

The $ ^3H(d,n) ^4He $ reaction is one of the twelve fundamental reactions of the BBN network and it is the most promising for future fusion energy plants. Sensitivity studies underline that a change on $ ^3H(d,n) ^4He $ reaction rate has an impact of the $ ^7Li $ abundance [299]. The reaction can be studied for the first time with THM applied to the $ ^7Li(d, n \alpha) \text{ three-body reaction, where the } ^7Li(t+\alpha) $ is the TH nucleus. This would be the first THM measurement involving a TH nucleus with inter-cluster motion in p-wave. For this reason preliminary studies dedicated to the experimental measurement of the $ ^7Li $ momentum distribution are required. The same reactions will be studied, in a synergistic effort, also using the I-LUCE laser with the CE technique allowing for a new evaluation of the electron screening effects.

BBN can be tackled also by means of the PANDORA plasma trap. The expected variation (increasing) of the $ ^7Be $ half-life could have a relevant impact on the CLiP [281, 284]. The experimental measurement of $ ^7Be $ decay in plasma, requires a devoted upgrade of the PANDORA facility (as described in Sec. 5.1.2), but sensitivity studies will be performed soon to evaluate the impact of a change in the $ ^7Be $ constant decay on $ ^7Li $ abundance.

### 5.2.2 Nucleosynthesis in Novae, X-Ray Bursts and Supenovae

Classical novae consist in stellar explosions that occur in close binary systems, where H-rich matter is transferred from a low-mass main sequence star (or sometimes a red giant) to the surface of a white dwarf (CO or ONe). On the other hand, X-Ray Bursts are thermonuclear explosions that take place in binary systems where the compact object is a neutron star. Understanding X-Ray bursts is important not only for investigating their properties but also to probe neutron stars. Others dramatic explosive events in galactic history are supernovae, either Thermonuclear (exploding white dwarfs in close binary systems) or Core-Collapse (CCSN whose progenitors are massive stars at the end of their evolution, triggering the birth of neutron stars or black holes).

Nuclear inputs play a crucial role in the physics of the explosion, for all the above mentioned astrophysical scenarios. Many of the reactions involved in these explosive astrophysical scenarios are induced by short-lived unstable nuclei which should be studied by means of RIBs. The expertise obtained at LNS on the production of long-lived RIBS in batch mode and the subsequent availability of FraiSe gives us the opportunity to improve the nuclear physics inputs required in the detailed modeling of these stellar events.

$ ^{26}\text{Al}$ is of outstanding importance in astrophysics. Observations, by space-borne telescopes, of the $ \gamma $-rays from the decay of $ ^{26}\text{Al} $ to $ ^{26}\text{Mg} $ in the interstellar medium confirmed that nucleosynthesis is ongoing in the Galaxy. The distribution of $ ^{26}\text{Al} $ across the Galaxy confirmed that massive stars dominate the production of this isotope [300]. $ ^{26}\text{Al} $ abundance inferred from $ \gamma $-ray astronomy allows to constrain the neutron star formation rate in our Galaxy [300], which is a key parameter in the field of multimessenger astronomy [301]. Moreover, the study of the aluminum isotopic ratio in some meteoritic inclusions (calcium–aluminum-rich inclusions) also provides information about the solar system birth and on the CCSN that maybe triggered its formation [302, 303].

As highlighted by sensitivity studies [304] at temperatures higher than 1 GK, achieved during the pre-supernova stage and the subsequent explosion (CCSN), the $ ^{26}\text{Al} $ abundances are strongly dependent on the $ ^{26}\text{Al}(n,p) ^{26}\text{Mg} $ and $ ^{26}\text{Al}(n,\alpha) ^{23}\text{Na} $ reactions responsible for the $ ^{26}\text{Al} $ destruction. Both reaction channels have been recently studied at n-TOF facility [305, 306], reducing the uncertainty on the reaction rates. Nevertheless, the measured energy range did not allow to reach the temperature range of interest for massive stars (pre-supernova and CCSN). This energy region can be however explored by means of a THM measurement. The neutron-induced $ ^{26}\text{Al}^{gs} $ destruction channels (n,p) and (n,α), with $ ^{26}\text{Al} $ at the ground state, will be investigated applying the THM to the $ ^{2}\text{H}( ^{26}\text{Al}^{gs}, p ^{26}\text{Mg})p $ and $ ^{2}\text{H}( ^{26}\text{Al}^{gs}, \alpha ^{23}\text{Na})p $ three-body reactions, where the deuteron is the virtual neutron source [307]. THM has been successfully applied to the study of nuclear reactions of astrophysical interest involving unstable nuclei [308–310] and induced by neutrons on RIBs [311].

These measurements require the production of the long-lived $ ^{26}\text{Al}^{gs} $ RIB in batch mode at the Tandem. The feasibility of these studies relies on: the possibility to have $ ^{26}\text{Al} $ cathodes, to be used in the LNS Tandem sputter source, provided by Paul Scherrer
measurement is supported by previous experiments performed with the same technique [280]. I-LUCE will allow to extend the explored energy range covering the full range of interest for the BBN. Another possible experimental technique to study nuclear reactions with laser exploits the interaction between an ion beam from standard accelerator (or for an ion source) delivered on a laser-induced plasma target. This will allow in-plasma measurement, with the advantages of a beam from accelerators (low-energy spread and high intensity). The aforementioned technique requires solid feasibility studies, mostly related to the synchronization of the accelerated ion beam with the short plasma lifetimes. Nevertheless, at the present time LNS holds a nearly unique position providing the possibility to perform this kind of research in the next future.

Regarding the study of nuclear reactions of interest for BBN with "conventional" accelerators, the first physical case is the measurement of the $ ^7Li(d,n) ^8Be $ reaction cross section. This process of interest for the CLiP contributes to the $ ^7Li $ destruction, affecting the prediction of $ ^7Li $ abundance. However, large uncertainties still exist in current $ ^7Li(d,n) ^8Be $ reaction rates widely used in BBN models. Existing experimental cross section data for this reaction are very limited and the most majority of them are not in the BBN energy range. Among them, only two sets of data are located in the energy region of BBN interest, but show huge differences [298]. Therefore, new experimental measurements of this reaction in the BBN energy region are needed. This reaction can be studied for the first time with THM applied to the $ ^7Li(^3He,n ^8Be)H $ three-body reaction taking advantage of the $ ^3He $ beam (the TH nucleus) that will be provided by the new NESTOR ion source and accelerated by the Tandem.

The opportunity to have a $ ^3He $ beam from NESTOR source triggered also the idea to perform a new THM study of the $ ^7Li(p,\alpha) ^4He $ reaction of interest for the CLiP as well as for the stellar lithium depletion (see Sect. 5.1.1).

The $ ^3H(d,n) ^4He $ reaction is one of the twelve fundamental reactions of the BBN network and it is the most promising for future fusion energy plants. Sensitivity studies underline that a change on $ ^3H(d,n) ^4He $ reaction rate has an impact of the $ ^7Li $ abundance [299]. The reaction can be studied for the first time with THM applied to the $ ^7Li(d, n \alpha) \text{ three-body reaction, where the } ^7Li(t+\alpha) $ is the TH nucleus. This would be the first THM measurement involving a TH nucleus with inter-cluster motion in p-wave. For this reason preliminary studies dedicated to the experimental measurement of the $ ^7Li $ momentum distribution are required. The same reactions will be studied, in a synergistic effort, also using the I-LUCE laser with the CE technique allowing for a new evaluation of the electron screening effects.

BBN can be tackled also by means of the PANDORA plasma trap. The expected variation (increasing) of the $ ^7Be $ half-life could have a relevant impact on the CLiP [281, 284]. The experimental measurement of $ ^7Be $ decay in plasma, requires a devoted upgrade of the PANDORA facility (as described in Sec. 5.1.2), but sensitivity studies will be performed soon to evaluate the impact of a change in the $ ^7Be $ constant decay on $ ^7Li $ abundance.

### 5.2.2 Nucleosynthesis in Novae, X-Ray Bursts and Supenovae

Classical novae consist in stellar explosions that occur in close binary systems, where H-rich matter is transferred from a low-mass main sequence star (or sometimes a red giant) to the surface of a white dwarf (CO or ONe). On the other hand, X-Ray Bursts are thermonuclear explosions that take place in binary systems where the compact object is a neutron star. Understanding X-Ray bursts is important not only for investigating their properties but also to probe neutron stars. Others dramatic explosive events in galactic history are supernovae, either Thermonuclear (exploding white dwarfs in close binary systems) or Core-Collapse (CCSN whose progenitors are massive stars at the end of their evolution, triggering the birth of neutron stars or black holes).

Nuclear inputs play a crucial role in the physics of the explosion, for all the above mentioned astrophysical scenarios. Many of the reactions involved in these explosive astrophysical scenarios are induced by short-lived unstable nuclei which should be studied by means of RIBs. The expertise obtained at LNS on the production of long-lived RIBS in batch mode and the subsequent availability of FraiSe gives us the opportunity to improve the nuclear physics inputs required in the detailed modeling of these stellar events.

$ ^{26}\text{Al}$ is of outstanding importance in astrophysics. Observations, by space-borne telescopes, of the $ \gamma $-rays from the decay of $ ^{26}\text{Al} $ to $ ^{26}\text{Mg} $ in the interstellar medium confirmed that nucleosynthesis is ongoing in the Galaxy. The distribution of $ ^{26}\text{Al} $ across the Galaxy confirmed that massive stars dominate the production of this isotope [300]. $ ^{26}\text{Al} $ abundance inferred from $ \gamma $-ray astronomy allows to constrain the neutron star formation rate in our Galaxy [300], which is a key parameter in the field of multimessenger astronomy [301]. Moreover, the study of the aluminum isotopic ratio in some meteoritic inclusions (calcium–aluminum-rich inclusions) also provides information about the solar system birth and on the CCSN that maybe triggered its formation [302, 303].

As highlighted by sensitivity studies [304] at temperatures higher than 1 GK, achieved during the pre-supernova stage and the subsequent explosion (CCSN), the $ ^{26}\text{Al} $ abundances are strongly dependent on the $ ^{26}\text{Al}(n,p)^{26}\text{Mg} $ and $ ^{26}\text{Al}(n,\alpha)^{23}\text{Na} $ reactions responsible for the $ ^{26}\text{Al} $ destruction. Both reaction channels have been recently studied at n-TOF facility [305, 306], reducing the uncertainty on the reaction rates. Nevertheless, the measured energy range did not allow to reach the temperature range of interest for massive stars (pre-supernova and CCSN). This energy region can be however explored by means of a THM measurement. The neutron-induced $ ^{26}\text{Al}^{gs} $ destruction channels (n,p) and (n,α), with $ ^{26}\text{Al} $ at the ground state, will be investigated applying the THM to the $ ^{2}\text{H}(^{26}\text{Al}^{gs}, p^{26}\text{Mg})p $ and $ ^{2}\text{H}(^{26}\text{Al}^{gs}, \alpha^{23}\text{Na})p $ three-body reactions, where the deuteron is the virtual neutron source [307]. THM has been successfully applied to the study of nuclear reactions of astrophysical interest involving unstable nuclei [308–310] and induced by neutrons on RIBs [311].

These measurements require the production of the long-lived $ ^{26}\text{Al}^{gs} $ RIB in batch mode at the Tandem. The feasibility of these studies relies on: the possibility to have $ ^{26}\text{Al} $ cathodes, to be used in the LNS Tandem sputter source, provided by Paul Scherrer
**Fig. 38** Typical experimental apparatus for RIBs-induced THM experiment. In particular, the double array of telescopes made up of double-sided silicon strip detectors (DSSSD), which is place inside the scattering chamber

<figure><img src="image_37.png" /></figure>

Institute (PSI); the experience gained in the production of $^{27}$Al beam that allowed to understand the proper chemical composition for the $^{26}$Al cathode; the successful production of $^{10}$Be ($t_{1/2} = 1.4\ 10^6\ y$) the first RIB beam produced in batch mode at LNS [128] (see Sect. 3.2.1).

In order to perform the THM measurement, the $^{26}$Mg and $^{23}$Na heavy fragments will be detected in coincidence with the corresponding lighter products, p and $\alpha$, while the low-energy proton spectator will not be detected. The detection system consisting of several telescopes made up of double-sided silicon strip detectors (DSSSD) will allow to cover a wide angular range since in inverse kinematics the heavy fragments are emitted at very forward angles while the light ones span a very large range of emission angles. A picture of a typical detection setup is shown in Fig. 38.

The availability of a $^{26}$Al$^{gs}$ beam will also allow the study of the $^{26}$Al$^{gs}$(p,γ)$^{27}$Si that contributes to the $^{26}$Al destruction in Novae and AGB stars having an important impact on $^{26}$Al abundance [312]. The reaction will be studied using the ANC indirect method [313] to gain information on the direct capture contribution to the $^{26}$Al$^{gs}$(p,γ)$^{27}$Si reaction cross section and to get information on the $^{27}$Si resonant states above the proton threshold. The ANC will be extracted from the measurement of a transfer reaction $^{3}$He($^{26}$Al$^{gs}$,d)$^{27}$Si with a $^{26}$Al$^{gs}$ beam at 3–5 AMeV delivered on a $^{3}$He gas target.

In studying nuclear reactions responsible for the $^{26}$Al destruction the ground (gs) and the isomeric (m) state at 228 keV must be taken into account. Indeed, the significant angular momentum difference between ground and isomeric states gives rise to a very small γ-ray decay constant, while $^{26}$Al$^m\ \beta$-decays to the ground state of $^{26}$Mg with a half-life of $T_{1/2} = 6.35$ s. Therefore, at the low temperatures that characterize many astrophysical scenarios, $T < 400$ MK, the $^{26}$Al ground and isomeric states do not reach thermal equilibrium and must be treated as two separate isotopes. While the reactions with $^{26}$Al at the ground state will be studied at LNS, reactions with $^{26}$Al at the isomeric state will be investigated at LNL where the $^{26}$Al$^m$ beam will be provided by SPES in a framework of complementarity between LNS and LNL research activities.

The availability of a $^{10}$Be beam at LNS (see Sect. 3.2.1) allows the possibility to study the $^{10}$Be($\alpha$,n)$^{13}$C reaction. The $^{10}$Be abundance in early solar system, inferred from $^{10}$B excesses in a range of meteoritic samples, can provide a constraint on the mass value of the CCSN responsible for the formation of our solar system [303]. $^{10}$Be($\alpha$,n)$^{13}$C is the main destruction channel of $^{10}$Be, but the adopted reaction rate is obtained from theoretical calculations since no experimental measurements are available in the literature [303]. The $^{10}$Be($\alpha$,n)$^{13}$C reaction cross section can be measured via THM with a $^{10}$Be beam delivered to the TH nucleus (a possible candidate being $^{6}$Li) to transfer the $\alpha$ particle.

Another very important long-lived nucleus for CCSN is $^{44}$Ti, since it allows a direct diagnostic of the CCSN explosion energy and timescale [314]. The $^{44}$Ti abundance is strongly affected by the $^{44}$Ti($\alpha$,p)$^{47}$V reaction, the main $^{44}$Ti destruction channel. Very few direct data are available in the literature, in particular, only an upper limit has been provided at energies of astrophysical interest [315]. A possible experimental approach to measure the $^{44}$Ti($\alpha$,p)$^{47}$V cross section at the energies typical of the CCSN environment could be by means of the THM with a $^{44}$Ti beam produced in batch mode at the Tandem accelerator. Given the technical difficulties related to $^{44}$Ti beam production, in particular due to radio safety issues, preliminary feasibility studies must be performed.

Regarding X-Ray Bursts nucleosynthesis, $^{14}$O($\alpha$,p)$^{44}$F and $^{18}$Ne($\alpha$,p)$^{21}$Na have been proposed as possible physical cases that have an influence on the X-Ray Bursts light curve [299]. Moreover, $^{18}$Ne($\alpha$,p)$^{21}$Na reaction leads to CNO breakout while powering a strong rp-process, responsible for the synthesis of A ~ 60 nuclei. These reactions can be studied applying the THM and taking advantage of the short-lived RIBs $^{14}$O and $^{18}$Ne provided by FraISe and of the new scattering chamber GIRA (see Sect. 2.3) with a degrading and focusing system to produce RIBs at energies useful for the THM application. Another possible solution might be the coupling between the Tandem accelerator and the FraISe separator. It is clear that important feasibility tests as well as improvements in the experimental setup are required, thus increasing experimental opportunities at LNS over a longer time range.

Nova nucleosynthesis includes the production of some intermediate-mass nuclei. The $^{31}$P($p,\alpha$)$^{28}$Si and $^{35}$Cl($p,\alpha$)$^{32}$S reactions are of particular interest in the synthesis of elements in the SiCl mass region. Variation of their reaction rates may affect production of several elements from Si to Ar [316]. The availability of few experimental data reinforces the need to study such reactions via THM with $^{31}$P and $^{35}$Cl provided by the Tandem accelerator.
**Fig. 38** Typical experimental apparatus for RIBs-induced THM experiment. In particular, the double array of telescopes made up of double-sided silicon strip detectors (DSSSD), which is place inside the scattering chamber

<figure><img src="image_37.png" /></figure>

Institute (PSI); the experience gained in the production of $^{27}$Al beam that allowed to understand the proper chemical composition for the $^{26}$Al cathode; the successful production of $^{10}$Be ($t_{1/2} = 1.4\ 10^6\ y$) the first RIB beam produced in batch mode at LNS [128] (see Sect. 3.2.1).

In order to perform the THM measurement, the $^{26}$Mg and $^{23}$Na heavy fragments will be detected in coincidence with the corresponding lighter products, p and $\alpha$, while the low-energy proton spectator will not be detected. The detection system consisting of several telescopes made up of double-sided silicon strip detectors (DSSSD) will allow to cover a wide angular range since in inverse kinematics the heavy fragments are emitted at very forward angles while the light ones span a very large range of emission angles. A picture of a typical detection setup is shown in Fig. 38.

The availability of a $^{26}$Al$^{gs}$ beam will also allow the study of the $^{26}$Al$^{gs}$(p,γ)$^{27}$Si that contributes to the $^{26}$Al destruction in Novae and AGB stars having an important impact on $^{26}$Al abundance [312]. The reaction will be studied using the ANC indirect method [313] to gain information on the direct capture contribution to the $^{26}$Al$^{gs}$(p,γ)$^{27}$Si reaction cross section and to get information on the $^{27}$Si resonant states above the proton threshold. The ANC will be extracted from the measurement of a transfer reaction $^{3}$He($^{26}$Al$^{gs}$,d)$^{27}$Si with a $^{26}$Al$^{gs}$ beam at 3–5 AMeV delivered on a $^{3}$He gas target.

In studying nuclear reactions responsible for the $^{26}$Al destruction the ground (gs) and the isomeric (m) state at 228 keV must be taken into account. Indeed, the significant angular momentum difference between ground and isomeric states gives rise to a very small γ-ray decay constant, while $^{26}$Al$^m\ \beta$-decays to the ground state of $^{26}$Mg with a half-life of $T_{1/2} = 6.35$ s. Therefore, at the low temperatures that characterize many astrophysical scenarios, $T < 400$ MK, the $^{26}$Al ground and isomeric states do not reach thermal equilibrium and must be treated as two separate isotopes. While the reactions with $^{26}$Al at the ground state will be studied at LNS, reactions with $^{26}$Al at the isomeric state will be investigated at LNL where the $^{26}$Al$^m$ beam will be provided by SPES in a framework of complementarity between LNS and LNL research activities.

The availability of a $^{10}$Be beam at LNS (see Sect. 3.2.1) allows the possibility to study the $^{10}$Be($\alpha$,n)$^{13}$C reaction. The $^{10}$Be abundance in early solar system, inferred from $^{10}$B excesses in a range of meteoritic samples, can provide a constraint on the mass value of the CCSN responsible for the formation of our solar system [303]. $^{10}$Be($\alpha$,n)$^{13}$C is the main destruction channel of $^{10}$Be, but the adopted reaction rate is obtained from theoretical calculations since no experimental measurements are available in the literature [303]. The $^{10}$Be($\alpha$,n)$^{13}$C reaction cross section can be measured via THM with a $^{10}$Be beam delivered to the TH nucleus (a possible candidate being $^{6}$Li) to transfer the $\alpha$ particle.

Another very important long-lived nucleus for CCSN is $^{44}$Ti, since it allows a direct diagnostic of the CCSN explosion energy and timescale [314]. The $^{44}$Ti abundance is strongly affected by the $^{44}$Ti($\alpha$,p)$^{47}$V reaction, the main $^{44}$Ti destruction channel. Very few direct data are available in the literature, in particular, only an upper limit has been provided at energies of astrophysical interest [315]. A possible experimental approach to measure the $^{44}$Ti($\alpha$,p)$^{47}$V cross section at the energies typical of the CCSN environment could be by means of the THM with a $^{44}$Ti beam produced in batch mode at the Tandem accelerator. Given the technical difficulties related to $^{44}$Ti beam production, in particular due to radio safety issues, preliminary feasibility studies must be performed.

Regarding X-Ray Bursts nucleosynthesis, $^{14}$O($\alpha$,p)$^{44}$F and $^{18}$Ne($\alpha$,p)$^{21}$Na have been proposed as possible physical cases that have an influence on the X-Ray Bursts light curve [299]. Moreover, $^{18}$Ne($\alpha$,p)$^{21}$Na reaction leads to CNO breakout while powering a strong rp-process, responsible for the synthesis of A ~ 60 nuclei. These reactions can be studied applying the THM and taking advantage of the short-lived RIBs $^{14}$O and $^{18}$Ne provided by FraISe and of the new scattering chamber GIRA (see Sect. 2.3) with a degrading and focusing system to produce RIBs at energies useful for the THM application. Another possible solution might be the coupling between the Tandem accelerator and the FraISe separator. It is clear that important feasibility tests as well as improvements in the experimental setup are required, thus increasing experimental opportunities at LNS over a longer time range.

Nova nucleosynthesis includes the production of some intermediate-mass nuclei. The $^{31}$P($p,\alpha$)$^{28}$Si and $^{35}$Cl($p,\alpha$)$^{32}$S reactions are of particular interest in the synthesis of elements in the SiCl mass region. Variation of their reaction rates may affect production of several elements from Si to Ar [316]. The availability of few experimental data reinforces the need to study such reactions via THM with $^{31}$P and $^{35}$Cl provided by the Tandem accelerator.
## 5.3 s- and r-process

Neutron-capture nucleosynthesis allows for the production of elements with masses beyond $A \approx 60$ through two different processes, namely the s(slow)-process and the r(rapid)-process, during which β-unstable nuclei can be also produced [269]. The slow neutron-capture process (s-process) produces heavy elements via a series of neutron captures occurring at timescales $\tau_{n\gamma}$ much longer than the β-decay lifetimes $\tau_{\beta}$ of radioactive species ($\tau_{n\gamma} \gg \tau_{\beta}$). This will allow for the production of stable nuclei close to the stability valley. On the contrary, the rapid neutron-capture process (r-process) defines those series of neutron-capture reactions occurring at shorter timescales, if compared to typical β-decay lifetimes ($\tau_n \ll \tau_{\beta}$), thus allowing for the production of neutron-rich (radioactive) species, far from the stability valley [269].

### 5.3.1 The s-process nucleosynthesis

The s-process nucleosynthesis is responsible for most of the elements between iron and strontium ($60 \le A \le 90$) through the so-called weak component of the s-process occurring in massive stars, being the needed neutrons mainly produced by the neutron reaction source $^{22}$Ne($\alpha$,n)$^{25}$Mg [317, 318]. Furthermore, the so-called main component of the s-process, allowing for the production of $A \ge 90$ nuclei is mostly related to asymptotic giant branch (AGB) stars where the $^{13}$C($\alpha$,n)$^{16}$O reaction acts as the main neutron source [319, 320].

Besides the role played by stellar models and mixing phenomena [318, 320], several experimental nuclear physics investigations have been made in the recent years for studying either the two main neutron sources [321, 322], as well as the processes removing neutrons for the next stages of nucleosynthesis (the so-called neutron-poison reactions) and recycling processes [307, 323, 324].

Thanks to the new or freshly upgraded facilities at LNS, some of the most important studies can be performed for reducing the still present experimental uncertainties on s-process nucleosynthesis. In particular, the reactions which plays the role of a major stellar neutron source, i.e., $^{22}$Ne($\alpha$,n)$^{25}$Mg, can be investigated by applying the THM [325] on Ne-implanted solid targets thanks to the NESTOR ECR ion source which can allow accelerating noble gas, as neon and helium. A possible complementary study involves the implantation of $^{22}$Ne in a heavy metal (e.g., tungsten or tantalum) using the NESTOR source, followed by measurements of the $^{22}$Ne($^{6}$Li,d)$^{26}$Mg or $^{22}$Ne($^{7}$Li,t)$^{26}$Mg reactions in order to extract $\alpha$ particle widths of $^{22}$Ne+$\alpha$ resonances. In fact, there is a significant disagreement about the energy and the character of these resonances, thus measurements to clarify if these resonances exist are vital. The MAGNEX large acceptance magnetic spectrometer is the ideal device for these types of measurements, since it offers a large angular range combined with a high resolution.

The corresponding neutron-poison reactions, i.e., $^{25}$Mg(n,γ)$^{26}$Mg and $^{22}$Ne(n,γ)$^{23}$Ne, can be also investigated via the ANC method where the $^{22}$Ne+n process could benefit from the new NESTOR noble gas coupled with the Tandem accelerator.

With particular attention to the main component, the neutron-poison reaction $^{16}$O(n,γ)$^{17}$O can be investigated by applying the ANC method [313], while the recycling $^{17}$O($\alpha$,n)$^{20}$Ne can be studied by coupling THM with nuclei having strong $\alpha$-cluster structure or by investigating the reverse $^{20}$Ne(n,α)$^{17}$O process by using the foreseen $^{20}$Ne Tandem beam provided by the NESTOR source. Moreover, the measurement of the $^{21}$Ne(p,p')$^{21}$Ne inelastic scattering cross section can be decisive to constrain the resonance information in $^{21}$Ne. At present, there is a lack of clarity about the number and location of levels in the $^{21}$Ne compound nucleus and the $^{21}$Ne(p,p')$^{21}$Ne measurement will help to clarify this information as it has been done in a number of previous experimental studies [326].

The nucleosynthesis of the elements heavier than Fe is the tarnish of neutron processes. Among these, the s-process is considered the best known, although its understanding is still affected by a lack of data. In particular, those about β-decay and electron capture rates in stellar conditions, which could be soon investigated experimentally for the first time at LNS thanks to the PANDORA experiment [27, 286]. Measuring lifetimes of unstable isotopes in plasma conditions, along with measuring with high accuracy the cross sections for their (n,γ) reactions as the up to date RIBS facilities are allowing, will shed light on the branching of the s-nucleosynthesis path. The recent sensitivity study of the s-process to β-decay and neutron-capture rates reported in [320] has shown how using different nuclear data set (e.g., cross sections, from the online compilation KADONIS 0.3 and 1.0 [327]) the predicted abundances (from nucleosynthesis computations in AGB stars of different mass and metallicity) for the solar system and meteorite grains can be very different, addressing or not the observational constraints. In particular, the authors focused their attention on the branching points around $N = 50$ and $N = 82$ affecting the Kr-Rb nucleosynthesis and the production of Ba isotopes. However, a further inspection of the branching and related nuclear physics inputs is needed also at higher atomic mass, where several complexities are induced by the presence of short-lived isomeric states of otherwise stable isotopes. Those make the s-process network poorly defined around key nuclei such as the pairs of cosmochronometers: $^{176}$Lu-$^{176}$Hf and $^{187}$Os-$^{187}$Re processes.

### 5.3.2 Continuous and pulsed neutron sources driven by laser and ion beams for nuclear astrophysics

The availability of intense and pulsed neutron sources driven by ion beams, could open new perspectives for research at LNS thus allowing for the investigation of neutron-capture processes of astrophysical relevance. Well-established techniques are currently being adopted in several laboratories to produce neutron beams, that meet the specific requirements of many scientific fields
## 5.3 s- and r-process

Neutron-capture nucleosynthesis allows for the production of elements with masses beyond $A \approx 60$ through two different processes, namely the s(slow)-process and the r(rapid)-process, during which β-unstable nuclei can be also produced [269]. The slow neutron-capture process (s-process) produces heavy elements via a series of neutron captures occurring at timescales $\tau_{n\gamma}$ much longer than the β-decay lifetimes $\tau_{\beta}$ of radioactive species ($\tau_{n\gamma} \gg \tau_{\beta}$). This will allow for the production of stable nuclei close to the stability valley. On the contrary, the rapid neutron-capture process (r-process) defines those series of neutron-capture reactions occurring at shorter timescales, if compared to typical β-decay lifetimes ($\tau_n \ll \tau_{\beta}$), thus allowing for the production of neutron-rich (radioactive) species, far from the stability valley [269].

### 5.3.1 The s-process nucleosynthesis

The s-process nucleosynthesis is responsible for most of the elements between iron and strontium ($60 \le A \le 90$) through the so-called weak component of the s-process occurring in massive stars, being the needed neutrons mainly produced by the neutron reaction source $^{22}$Ne($\alpha$,n)$^{25}$Mg [317, 318]. Furthermore, the so-called main component of the s-process, allowing for the production of $A \ge 90$ nuclei is mostly related to asymptotic giant branch (AGB) stars where the $^{13}$C($\alpha$,n)$^{16}$O reaction acts as the main neutron source [319, 320].

Besides the role played by stellar models and mixing phenomena [318, 320], several experimental nuclear physics investigations have been made in the recent years for studying either the two main neutron sources [321, 322], as well as the processes removing neutrons for the next stages of nucleosynthesis (the so-called neutron-poison reactions) and recycling processes [307, 323, 324].

Thanks to the new or freshly upgraded facilities at LNS, some of the most important studies can be performed for reducing the still present experimental uncertainties on s-process nucleosynthesis. In particular, the reactions which plays the role of a major stellar neutron source, i.e., $^{22}$Ne($\alpha$,n)$^{25}$Mg, can be investigated by applying the THM [325] on Ne-implanted solid targets thanks to the NESTOR ECR ion source which can allow accelerating noble gas, as neon and helium. A possible complementary study involves the implantation of $^{22}$Ne in a heavy metal (e.g., tungsten or tantalum) using the NESTOR source, followed by measurements of the $^{22}$Ne($^{6}$Li,d)$^{26}$Mg or $^{22}$Ne($^{7}$Li,t)$^{26}$Mg reactions in order to extract $\alpha$ particle widths of $^{22}$Ne+$\alpha$ resonances. In fact, there is a significant disagreement about the energy and the character of these resonances, thus measurements to clarify if these resonances exist are vital. The MAGNEX large acceptance magnetic spectrometer is the ideal device for these types of measurements, since it offers a large angular range combined with a high resolution.

The corresponding neutron-poison reactions, i.e., $^{25}$Mg(n,γ)$^{26}$Mg and $^{22}$Ne(n,γ)$^{23}$Ne, can be also investigated via the ANC method where the $^{22}$Ne+n process could benefit from the new NESTOR noble gas coupled with the Tandem accelerator.

With particular attention to the main component, the neutron-poison reaction $^{16}$O(n,γ)$^{17}$O can be investigated by applying the ANC method [313], while the recycling $^{17}$O($\alpha$,n)$^{20}$Ne can be studied by coupling THM with nuclei having strong $\alpha$-cluster structure or by investigating the reverse $^{20}$Ne(n,α)$^{17}$O process by using the foreseen $^{20}$Ne Tandem beam provided by the NESTOR source. Moreover, the measurement of the $^{21}$Ne(p,p')$^{21}$Ne inelastic scattering cross section can be decisive to constrain the resonance information in $^{21}$Ne. At present, there is a lack of clarity about the number and location of levels in the $^{21}$Ne compound nucleus and the $^{21}$Ne(p,p')$^{21}$Ne measurement will help to clarify this information as it has been done in a number of previous experimental studies [326].

The nucleosynthesis of the elements heavier than Fe is the tarnish of neutron processes. Among these, the s-process is considered the best known, although its understanding is still affected by a lack of data. In particular, those about β-decay and electron capture rates in stellar conditions, which could be soon investigated experimentally for the first time at LNS thanks to the PANDORA experiment [27, 286]. Measuring lifetimes of unstable isotopes in plasma conditions, along with measuring with high accuracy the cross sections for their (n,γ) reactions as the up to date RIBS facilities are allowing, will shed light on the branching of the s-nucleosynthesis path. The recent sensitivity study of the s-process to β-decay and neutron-capture rates reported in [320] has shown how using different nuclear data set (e.g., cross sections, from the online compilation KADONIS 0.3 and 1.0 [327]) the predicted abundances (from nucleosynthesis computations in AGB stars of different mass and metallicity) for the solar system and meteorite grains can be very different, addressing or not the observational constraints. In particular, the authors focused their attention on the branching points around $N = 50$ and $N = 82$ affecting the Kr-Rb nucleosynthesis and the production of Ba isotopes. However, a further inspection of the branching and related nuclear physics inputs is needed also at higher atomic mass, where several complexities are induced by the presence of short-lived isomeric states of otherwise stable isotopes. Those make the s-process network poorly defined around key nuclei such as the pairs of cosmochronometers: $^{176}$Lu-$^{176}$Hf and $^{187}$Os-$^{187}$Re processes.

### 5.3.2 Continuous and pulsed neutron sources driven by laser and ion beams for nuclear astrophysics

The availability of intense and pulsed neutron sources driven by ion beams, could open new perspectives for research at LNS thus allowing for the investigation of neutron-capture processes of astrophysical relevance. Well-established techniques are currently being adopted in several laboratories to produce neutron beams, that meet the specific requirements of many scientific fields
[328–332]. The LNS accelerators could exploit conversion reactions such as (p,n), (d,n), and (α,n) to produce neutron beams. The flux, angular, and the energy distribution of the neutrons depend on the adopted conversion reaction and on properties of the ion beam, which can be varied within the operational limits of the accelerators and of any radiation protection constraints. As an example of practical application, an accurate setup including, if necessary, a neutron moderator, may allow to produce neutrons with energy distributions well approximated by the Maxwell–Boltzmann distributions at energies of astrophysical interest [329]. These neutrons may be suitable for measurements of Maxwellian Averaged Cross Sections (MACS) for nuclear reactions involved in nucleosynthesis processes, exploiting the well-established technique of neutron activation [330]. Depending on the measurement to be performed and the available neutron fluxes, the driver beams can be either continuous or pulsed, the latter to provide neutron bunches with adjustable duty cycle and repetition rate. In those cases where it is necessary to measure the neutrons time of flight, a flight path of about 5 m should be sufficient to discriminate the neutron energy up to a few tens of MeV. A further important opportunity is represented by the 250 TW laser I-LUCE, that will be available in the next few years at LNS. The production of huge quantities of light particles (such as protons and deuterons) with energy up to a few tens of MeV, in combination with suitable conversion targets, can lead to provide very short (<1ns) neutron bunches with flux around $10^5–10^6$ neutron/sr/shot, with angular distribution strongly peaked in the forward angles [331]. A careful selection of the targets, respectively, for the laser beam and for the neutron conversion, combined with a well-designed setup (based for example on the so-called pitcher–catcher setup), can represent a valid solution to produce neutron bunches with high fluxes and high time resolution. The flexibility of a laser-based approach may allow for the irradiation of relatively short-lived elements, which can be produced by the fragmentation of the projectile using Tandem and cyclotron beams, by implanting into a target placed close to the laser-driven neutron source. This technique allows for the measurement of radioactive isotopes that typically need to be rapidly transported from the production site to the experimental site. With respect to the *s*-process nucleosynthesis, two possible applications of the described technique are 1) the measurement of the $^{140}$Ce(n,γ)$^{141}$Ce ( $^{141}$Ce T$_{1/2}$ = 32.5 days) that represents a bottleneck for the *s*-process nucleosynthesis and determines to a large extent the cerium abundance in stars, and 2) the measurement of $^{94}$Zr(n,γ)$^{95}$Zr ( $^{95}$Zr t$_{1/2}$ = 64 days) that is crucial in the modeling of *s*-process nucleosynthesis in AGB stars because Zr is situated at a crucial point, where the two *s*-components (weak and main) match. These measurements will be two complementary studies to activation and TOF measurements already existing in the literature [333, 334].

### 5.3.3 The *r*-process nucleosynthesis

The *r*-process nucleosynthesis is called for to explain the production of the stable (and some long-lived radioactive) neutron-rich nuclides heavier than iron that are observed in stars of various metallicities (i.e., in the solar system), as it extensively discussed in [335]. Nowadays, several sites for *r*-process have been suggested, such as CCSN, neutrino-induced processes in the outer shells of massive stars, ejecta from compact binary mergers, and the so-called magnetohydrodynamic MHD-jet supernovae (having fast rotation, high magnetic fields and neutron eject along the poles) [335]. Recently, the discovery of neutron star mergers (NSM) [336] events strongly confirms the occurrence of such processes responsible for the production the elements beyond lead and bismuth. Besides the production of gravitational waves and γ-ray Bursts, NSM produces also transient optical–near-infrared source powered by the synthesis of large amounts of very heavy elements via the *r*-process. Such brilliant electromagnetic signals are known as kilonovae (KN) [336] from which, in principle, the *r*-process element abundances could be derived via the inspection of the transient light curves. Because of the composition complexity, relying on both freshly synthesized light and heavy *r*-process elements, the matter opacity ($\kappa$) is an intricate feature, varying from relatively low to high values depending on the ejecta dynamics, thermodynamic parameters, and *r*-process nucleosynthesis yield [337–340].

A complete understanding of such phenomena, i.e., the reproduction of the *r*-elements abundances in the cosmos via devoted nucleosynthesis codes, passes through focused studies in astrophysics, nuclear physics, atomic physics, and plasma physics. The EoS of hot and dense nuclear matter is of highest importance for modeling the astrophysical environments expected to be the sites for rapid neutron-capture process, providing the pressure response during the dynamic phases and the particle composition [341]. Simulations of core-collapse supernova and neutron-star mergers are, therefore, very sensitive to the adopted EoS and in particular to its stiffness and its isovector part (i.e., symmetry energy).

An important uncertainty factor, which complicates the theoretical interpretations, arises from the limited knowledge about KN ejecta opacity data in typical conditions. However, the new possibilities given by radioactive beam facilities will allow the production of several neutron-rich nuclei, improving the present understanding of the *r*-process. Experiments, in particular, will allow to predict the elemental abundance of such elements and to link the observed abundances with the KN features as well as with the astrophysical conditions and constraints on the nucleosynthesis sites.

Experimental measurements of opacities at electron densities and temperatures typical of astrophysical sites will be boosted by trapped magneto-plasmas conceived in PANDORA [27], thus paving the way to further developments such as shedding light on *r*-process generated metallic species at specific time stages of KN diffusion [342]. To this aim, a feasibility study has been recently performed.

In particular, astrophysical models for KN ejecta in the post-merging phase bound plasma conditions, typical of ECR plasma, to a time stage between few hours and few days after the merging, which corresponds to the blue-KN stage (low opacity, light *r* element component, KN light curve peak in the optical range) has been considered. The numerical calculations of expected opacities for the
[328–332]. The LNS accelerators could exploit conversion reactions such as (p,n), (d,n), and (α,n) to produce neutron beams. The flux, angular, and the energy distribution of the neutrons depend on the adopted conversion reaction and on properties of the ion beam, which can be varied within the operational limits of the accelerators and of any radiation protection constraints. As an example of practical application, an accurate setup including, if necessary, a neutron moderator, may allow to produce neutrons with energy distributions well approximated by the Maxwell-Boltzmann distributions at energies of astrophysical interest [329]. These neutrons may be suitable for measurements of Maxwellian Averaged Cross Sections (MACS) for nuclear reactions involved in nucleosynthesis processes, exploiting the well-established technique of neutron activation [330]. Depending on the measurement to be performed and the available neutron fluxes, the driver beams can be either continuous or pulsed, the latter to provide neutron bunches with adjustable duty cycle and repetition rate. In those cases where it is necessary to measure the neutrons time of flight, a flight path of about 5 m should be sufficient to discriminate the neutron energy up to a few tens of MeV. A further important opportunity is represented by the 250 TW laser I-LUCE, that will be available in the next few years at LNS. The production of huge quantities of light particles (such as protons and deuterons) with energy up to a few tens of MeV, in combination with suitable conversion targets, can lead to provide very short (<1ns) neutron bunches with flux around $10^5–10^6$ neutron/sr/shot, with angular distribution strongly peaked in the forward angles [331]. A careful selection of the targets, respectively, for the laser beam and for the neutron conversion, combined with a well-designed setup (based for example on the so-called pitcher-catcher setup), can represent a valid solution to produce neutron bunches with high fluxes and high time resolution. The flexibility of a laser-based approach may allow for the irradiation of relatively short-lived elements, which can be produced by the fragmentation of the projectile using Tandem and cyclotron beams, by implanting into a target placed close to the laser-driven neutron source. This technique allows for the measurement of radioactive isotopes that typically need to be rapidly transported from the production site to the experimental site. With respect to the *s*-process nucleosynthesis, two possible applications of the described technique are 1) the measurement of the $^{140}$Ce(n,γ)$^{141}$Ce ( $^{141}$Ce T$_{1/2}$ = 32.5 days) that represents a bottleneck for the *s*-process nucleosynthesis and determines to a large extent the cerium abundance in stars, and 2) the measurement of $^{94}$Zr(n,γ)$^{95}$Zr ( $^{95}$Zr t$_{1/2}$ = 64 days) that is crucial in the modeling of *s*-process nucleosynthesis in AGB stars because Zr is situated at a crucial point, where the two *s*-components (weak and main) match. These measurements will be two complementary studies to activation and TOF measurements already existing in the literature [333, 334].

### 5.3.3 The *r*-process nucleosynthesis

The *r*-process nucleosynthesis is called for to explain the production of the stable (and some long-lived radioactive) neutron-rich nuclides heavier than iron that are observed in stars of various metallicities (i.e., in the solar system), as it extensively discussed in [335]. Nowadays, several sites for *r*-process have been suggested, such as CCSN, neutrino-induced processes in the outer shells of massive stars, ejecta from compact binary mergers, and the so-called magnetohydrodynamic MHD-jet supernovae (having fast rotation, high magnetic fields and neutron eject along the poles) [335]. Recently, the discovery of neutron star mergers (NSM) [336] events strongly confirms the occurrence of such processes responsible for the production the elements beyond lead and bismuth. Besides the production of gravitational waves and γ-ray Bursts, NSM produces also transient optical-near-infrared source powered by the synthesis of large amounts of very heavy elements via the *r*-process. Such brilliant electromagnetic signals are known as kilonovae (KN) [336] from which, in principle, the *r*-process element abundances could be derived via the inspection of the transient light curves. Because of the composition complexity, relying on both freshly synthesized light and heavy *r*-process elements, the matter opacity ($\kappa$) is an intricate feature, varying from relatively low to high values depending on the ejecta dynamics, thermodynamic parameters, and *r*-process nucleosynthesis yield [337–340].

A complete understanding of such phenomena, i.e., the reproduction of the *r*-elements abundances in the cosmos via devoted nucleosynthesis codes, passes through focused studies in astrophysics, nuclear physics, atomic physics, and plasma physics. The EoS of hot and dense nuclear matter is of highest importance for modeling the astrophysical environments expected to be the sites for rapid neutron-capture process, providing the pressure response during the dynamic phases and the particle composition [341]. Simulations of core-collapse supernova and neutron-star mergers are, therefore, very sensitive to the adopted EoS and in particular to its stiffness and its isovector part (i.e., symmetry energy).

An important uncertainty factor, which complicates the theoretical interpretations, arises from the limited knowledge about KN ejecta opacity data in typical conditions. However, the new possibilities given by radioactive beam facilities will allow the production of several neutron-rich nuclei, improving the present understanding of the *r*-process. Experiments, in particular, will allow to predict the elemental abundance of such elements and to link the observed abundances with the KN features as well as with the astrophysical conditions and constraints on the nucleosynthesis sites.

Experimental measurements of opacities at electron densities and temperatures typical of astrophysical sites will be boosted by trapped magneto-plasmas conceived in PANDORA [27], thus paving the way to further developments such as shedding light on *r*-process generated metallic species at specific time stages of KN diffusion [342]. To this aim, a feasibility study has been recently performed.

In particular, astrophysical models for KN ejecta in the post-merging phase bound plasma conditions, typical of ECR plasma, to a time stage between few hours and few days after the merging, which corresponds to the blue-KN stage (low opacity, light *r* element component, KN light curve peak in the optical range) has been considered. The numerical calculations of expected opacities for the
<figure><img src="image_38.png" /><figcaption>**Fig. 39 a** Weighted mean opacity ($\alpha$) for r-process element abundances (elements vs. neutron richness) at $k_B T = 0.65$ eV and density $10^{18}~m^{-3}$. The weighting was performed [342] by using relative abundances of species as resulting from SKYNET [344] nuclear network calculations of r-process nucleosynthesis yields as a function of $Y_e$. **b** Grid of experimental values for electron density $\rho$ [$m^{-3}$]—temperature (in terms of $k_B T$ [eV]) from optical emission spectroscopy measurements on the Flexible Plasma Trap, with the experimental uncertainties range ($\delta\rho, \delta k_B T$)</figcaption></figure>

most relevant physics cases (in terms of nucleosynthesis abundances at that stage) have been performed, reporting on mean opacities for some relevant r-process elements as expected at different electron fractions $Y_e$. The design of experimental setup and measurements have been started using the operative Flexible Plasma Trap (FPT) available at the LNS, characterizing on a smaller scale, with respect to the under-construction PANDORA trap, plasma parameters to provide sounder experimental conditions to resemble astrophysical conditions of the blue-KN stage (~eV, ~$10^{11}~cm^{-3}$) [343]. First experimental results have been recently collected on gaseous plasmas (Ar, H) to closely reproduce Kilonovae conditions, posing the bases for the envisaged future plasma opacity measurements on light r-process elements to be performed in the PANDORA trap. Preliminary numerical results on mean opacity for r-process elements abundances and plasma experimental conditions that can be reached in the plasma trap are shown in Fig. 39.

### 5.3.4 β-delayed neutron emission probability $P_n$ measurements at LNS

Since the r-process occurs far from the nuclear stability valley, it leads to very neutron-rich nuclei that then decay toward the line of stability. Most of these nuclei are $\beta_n$ emitters. The initial abundance distribution is shaped by the decay half-life $t_{1/2}$, but the neutron emission affects the final abundances in two ways: on the one hand it shifts the decay path to lower masses, and on the other hand it provides a source of neutrons for late captures that will shift it in the opposite way. Thus, a good knowledge of the β-delayed neutron emission probability $P_n$ and $t_{1/2}$ values of the nuclei between the line of stability and the r-process path is needed for a correct understanding of the observed abundances [146]. In this sense, at the LNS, $P_n$ measurements for many neutron emitters such as $^{66}\text{Co}$ ($t_{1/2} \sim 0.2$ s) or $^{72}\text{Ni}$ ($t_{1/2} \sim 0.2$ s) could be performed by using the FraISe facility for RIBs production coupled with the high-efficiency neutron counter (polycube) POLYFEMO successfully used in the past for $^{8}\text{Li}(\alpha,n)^{11}\text{B}$ cross section measurements [345].

### 5.3.5 Low-mass r-process nucleosynthesis

In neutrino-driven winds above nascent neutron stars or after the merging of two neutron stars low-mass r-process elements may be formed at high temperatures in a very short timescale of the order of milliseconds. After the explosion, the abundances are in nuclear statistical equilibrium due to the high temperature, but as matter expands, the temperature and the density decrease and protons and $\alpha$ particles start to build up heavier nuclei by, e.g., ($\alpha$,xn), and (p,xn) reactions. In this so-called weak r-process nucleosynthesis scenario, isotopes between Sr and Ag may be formed [346–349].

The study of the synthesis of these low-mass r-isotopes requires the use of a large reaction network involving a few thousand, mostly unstable nuclei. The necessary reaction rates are calculated from the cross sections computed with the Hauser-Feshbach statistical model which relies on different nuclear physics parameter sets. Recently, a series of sensitivity calculations were performed to evaluate the theoretical uncertainty of these cross section calculations [350–352]. These works identified the $\alpha$+nucleus optical potential parameter sets ($\alpha$OMP's) as the main source of uncertainty.

The difference between the cross section based on various $\alpha$OMP's can exceed even an order of magnitude [350, 352]. Therefore, experiments are critical to determine the parameters of the $\alpha$OMP, to reduce the uncertainties of the ($\alpha$,n) rates and to increase the reliability of the astrophysical calculations. The direct measurement of the $\alpha$-induced reaction cross sections on unstable isotopes are extraordinarily challenging. However, the parameters of the $\alpha$OMP can be derived experimentally from the analysis of the angular distributions and excitation functions of elastically scattered $\alpha$ particles. In the last decade several elastic $\alpha$ scattering experiments were performed worldwide to constrain the parameters of the $\alpha$OMP [353, 354] (and references therein). However, the systematic measurement of $\alpha$ elastic scattering angular distributions along isotopic and isotopic chains showed that there is no parametric solution able to describe the variation of the scattering cross sections as a function of the neutron/proton numbers [355,
<figure><img src="image_38.png" /><figcaption>**Fig. 39 a** Weighted mean opacity ($\alpha$) for r-process element abundances (elements vs. neutron richness) at $k_B T = 0.65$ eV and density $10^{18} \text{ m}^{-3}$. The weighting was performed [342] by using relative abundances of species as resulting from SKYNET [344] nuclear network calculations of r-process nucleosynthesis yields as a function of $Y_e$. **b** Grid of experimental values for electron density $\rho$ [$\text{m}^{-3}$]—temperature (in terms of $k_B T$ [eV]) from optical emission spectroscopy measurements on the Flexible Plasma Trap, with the experimental uncertainties range ($\delta\rho, \delta k_B T$)</figcaption></figure>

most relevant physics cases (in terms of nucleosynthesis abundances at that stage) have been performed, reporting on mean opacities for some relevant r-process elements as expected at different electron fractions $Y_e$. The design of experimental setup and measurements have been started using the operative Flexible Plasma Trap (FPT) available at the LNS, characterizing on a smaller scale, with respect to the under-construction PANDORA trap, plasma parameters to provide sounder experimental conditions to resemble astrophysical conditions of the blue-KN stage (~eV, ~$10^{11} \text{ cm}^{-3}$) [343]. First experimental results have been recently collected on gaseous plasmas (Ar, H) to closely reproduce Kilonovae conditions, posing the bases for the envisaged future plasma opacity measurements on light r-process elements to be performed in the PANDORA trap. Preliminary numerical results on mean opacity for r-process elements abundances and plasma experimental conditions that can be reached in the plasma trap are shown in Fig. 39.

### 5.3.4 β-delayed neutron emission probability $P_n$ measurements at LNS

Since the r-process occurs far from the nuclear stability valley, it leads to very neutron-rich nuclei that then decay toward the line of stability. Most of these nuclei are $\beta_n$ emitters. The initial abundance distribution is shaped by the decay half-life $t_{1/2}$, but the neutron emission affects the final abundances in two ways: on the one hand it shifts the decay path to lower masses, and on the other hand it provides a source of neutrons for late captures that will shift it in the opposite way. Thus, a good knowledge of the β-delayed neutron emission probability $P_n$ and $t_{1/2}$ values of the nuclei between the line of stability and the r-process path is needed for a correct understanding of the observed abundances [146]. In this sense, at the LNS, $P_n$ measurements for many neutron emitters such as $^{66}\text{Co}$ ($t_{1/2} \sim 0.2$ s) or $^{72}\text{Ni}$ ($t_{1/2} \sim 0.2$ s) could be performed by using the FraISe facility for RIBs production coupled with the high-efficiency neutron counter (polycube) POLYFEMO successfully used in the past for $^{8}\text{Li}(\alpha,n)^{11}\text{B}$ cross section measurements [345].

### 5.3.5 Low-mass r-process nucleosynthesis

In neutrino-driven winds above nascent neutron stars or after the merging of two neutron stars low-mass r-process elements may be formed at high temperatures in a very short timescale of the order of milliseconds. After the explosion, the abundances are in nuclear statistical equilibrium due to the high temperature, but as matter expands, the temperature and the density decrease and protons and $\alpha$ particles start to build up heavier nuclei by, e.g., ($\alpha$,xn), and (p,xn) reactions. In this so-called weak r-process nucleosynthesis scenario, isotopes between Sr and Ag may be formed [346–349].

The study of the synthesis of these low-mass r-isotopes requires the use of a large reaction network involving a few thousand, mostly unstable nuclei. The necessary reaction rates are calculated from the cross sections computed with the Hauser-Feshbach statistical model which relies on different nuclear physics parameter sets. Recently, a series of sensitivity calculations were performed to evaluate the theoretical uncertainty of these cross section calculations [350–352]. These works identified the $\alpha$+nucleus optical potential parameter sets ($\alpha$OMP's) as the main source of uncertainty.

The difference between the cross section based on various $\alpha$OMP's can exceed even an order of magnitude [350, 352]. Therefore, experiments are critical to determine the parameters of the $\alpha$OMP, to reduce the uncertainties of the ($\alpha$,n) rates and to increase the reliability of the astrophysical calculations. The direct measurement of the $\alpha$-induced reaction cross sections on unstable isotopes are extraordinarily challenging. However, the parameters of the $\alpha$OMP can be derived experimentally from the analysis of the angular distributions and excitation functions of elastically scattered $\alpha$ particles. In the last decade several elastic $\alpha$ scattering experiments were performed worldwide to constrain the parameters of the $\alpha$OMP [353, 354] (and references therein). However, the systematic measurement of $\alpha$ elastic scattering angular distributions along isotopic and isotopic chains showed that there is no parametric solution able to describe the variation of the scattering cross sections as a function of the neutron/proton numbers [355,
356]. Thus, the extrapolation of the potential parameters toward the region of unstable nuclei is questionable. Furthermore, there are no experimental elastic $\alpha$ scattering data on unstable nuclei, and accordingly the parametric system used in the astrophysical calculations remained untested to this day.

According to the above discussed arguments, the neutron-rich RIBs available at LNS can be useful to study the $\alpha$OMP parameterizations by inverse elastic scattering experiments, for example $^{63}\text{Co}(\alpha,\alpha)^{63}\text{Co}$, $^{67}\text{Cu}(\alpha,\alpha)^{67}\text{Cu}$ or $^{59}\text{Fe}(\alpha,\alpha)^{59}\text{Fe}$.

It's worth mentioning that inverse elastic $\alpha$ scattering experiments were already performed at LNS—using stable Sn beams—thus the experimental approach is certainly feasible.

# 6 Nuclear physics applications

Nuclear physics applications span a very broad range of topics. In this section, the perspectives at the LNS-INFN for the coming years on this subject will be discussed. Three major scientific topics can be identified: (i) medical, (ii) laser and (iii) plasma traps applications.

(i) Activities related to Medical applications (Sect. 6.1) are well consolidated, starting from the 2000s with the construction of the CATANA facility for hadrontherapy. Future study programs in this area are still focused on the availability of stable LNS beams, covering hot topics such as the Flash radiotherapy (LNS-A-MA-a0) and Flash BNCT (boron-neutron-capture therapy, LNS-A-MA-b0) or the more recent perspective of the possible use of multiple beams to perform more efficient treatment plans. The huge variety of ion beams available at LNS opens up study perspectives also in the field of space science; in particular the investigation of not well-known cross sections useful for the radiation risk model evaluation applied to cosmonauts during space missions (LNS-A-MA-b1). All these topics will be explored in details in Sect. 6.1.1. A new and interesting outlook will be raised from the future availability of radioactive ion beams (RIBs) and high-intensity beams (HIBs) (Sect. 6.1.2). In particular, RIBs opportunity can trigger new approach for innovation on treatment methods that could be coupled with online contemporary diagnostic tools, to perform innovative treatment plans (LNS-A-MA-c0) while HIBs (HIBs) open to investigation on cross sections studies for new exotic radioisotopes and radiopharmaceutical (LNS-A-MA-c1).

(ii) The near future of LNS research activities also involves the new high-power laser facility and the almost unique possibility to have, in the same experimental area, intense laser-accelerated and conventional ion beams. This will open unprecedented possibilities of investigations of nuclear and plasma physics. All the new acceleration schemes developed in the recent years even by LNS users, triggered ideas and proposals for the development of new and compact laser-driven secondary sources (Sect. 6.2.1) useful for several applications (electrons and ions LNS-A-LA-a0, neutrons LNS-A-LA-b1, positrons and photons LNS-A-LA-c1). High-intensity lasers interacting with solids produce non-equilibrium plasma having high equivalent temperatures and high ion energies. Under these conditions, different nuclear reactions can be induced (LNS-A-LA-a1). New and interesting perspectives for applications in the field of health LNS-A-LA-c0 and energy can come out from these studies (Sect. 6.2.1). Fundamental aspects like ion energy loss and the stopping power in plasmas (LNS-A-LA-b0) should be mentioned because they have strong impact on energy production from fusion power. A novel approach to the direct production of pure H2 (LNS-A-LA-c2) from liquid water using femtosecond laser-induced plasma has been also proposed in Sect. 6.2.2. This topic provides the basis for exploring further concepts of hydrogen production.

(iii) Magnetic confinement is one of major topics of fusion energy research. The plasma trap PANDORA will be the new LNS facility designed for multidisciplinary studies in the fields of nuclear and plasma physics, astrophysics, etc., including applicative issues like fusion power. In the section dedicated to plasma traps, Sect. 6.3, most of the potential applications deriving from the developments related to the PANDORA facility are highlighted. The section is divided essentially into three main topics: (i) magnetic Plasmas and related issues (ions heating, charge breeding, stopping power, etc.; (ii) physics and technology aspects for fusion plasmas; (iii) innovative plasma chambers and resonators for compact reactors development. Ion beam plasma interaction is a relevant topic in several fields of plasma physics, from fusion devices to modern ion source and Sect. 6.3.1 is dedicated to the several R & D studies proposed on this subject (LNS-A-PT-a0). Section 6.3.2 deals with the R & D on plasma diagnostics and wave propagation/absorption; detection, collimation and active shuttering methods for soft X and hard X spectroscopy and tomography or innovative heating and energy transport mechanisms for increasing confinement and reaction rates (LNS-A-PT-b0). In Sect. 6.3.3, new plasma chambers and resonators ensuring better radiation-plasma coupling, stability, control and confinement are proposed (LNS-A-PT-b1).

The midterm timescale has been divided into three phases, from the phase A (which includes the activities which can be performed as soon as the facilities will be ready) to phase C (where a more longer R & D work will be requested). Time schedules and priority codes of the previous discussed research topics are synthetically reported in Fig. 40 and in Table 7.

## 6.1 Medical applications

The possibility to have, in the next future, proton and ion beams of high intensity (up to hundreds or even thousands of Grays per second) and in a wide energy range (30–100 AMeV) will pave the way toward new applications and investigations in the field of
356]. Thus, the extrapolation of the potential parameters toward the region of unstable nuclei is questionable. Furthermore, there are no experimental elastic $\alpha$ scattering data on unstable nuclei, and accordingly the parametric system used in the astrophysical calculations remained untested to this day.

According to the above discussed arguments, the neutron-rich RIBs available at LNS can be useful to study the $\alpha$OMP parameterizations by inverse elastic scattering experiments, for example $^{63}\text{Co}(\alpha,\alpha)^{63}\text{Co}$, $^{67}\text{Cu}(\alpha,\alpha)^{67}\text{Cu}$ or $^{59}\text{Fe}(\alpha,\alpha)^{59}\text{Fe}$.

It's worth mentioning that inverse elastic $\alpha$ scattering experiments were already performed at LNS—using stable Sn beams—thus the experimental approach is certainly feasible.

# 6 Nuclear physics applications

Nuclear physics applications span a very broad range of topics. In this section, the perspectives at the LNS-INFN for the coming years on this subject will be discussed. Three major scientific topics can be identified: (i) medical, (ii) laser and (iii) plasma traps applications.

(i) Activities related to Medical applications (Sect. 6.1) are well consolidated, starting from the 2000s with the construction of the CATANA facility for hadrontherapy. Future study programs in this area are still focused on the availability of stable LNS beams, covering hot topics such as the Flash radiotherapy (LNS-A-MA-a0) and Flash BNCT (boron-neutron-capture therapy, LNS-A-MA-b0) or the more recent perspective of the possible use of multiple beams to perform more efficient treatment plans. The huge variety of ion beams available at LNS opens up study perspectives also in the field of space science; in particular the investigation of not well-known cross sections useful for the radiation risk model evaluation applied to cosmonauts during space missions (LNS-A-MA-b1). All these topics will be explored in details in Sect. 6.1.1. A new and interesting outlook will be raised from the future availability of radioactive ion beams (RIBs) and high-intensity beams (HIBs) (Sect. 6.1.2). In particular, RIBs opportunity can trigger new approach for innovation on treatment methods that could be coupled with online contemporary diagnostic tools, to perform innovative treatment plans (LNS-A-MA-c0) while HIBs (HIBs) open to investigation on cross sections studies for new exotic radioisotopes and radiopharmaceutical (LNS-A-MA-c1).

(ii) The near future of LNS research activities also involves the new high-power laser facility and the almost unique possibility to have, in the same experimental area, intense laser-accelerated and conventional ion beams. This will open unprecedented possibilities of investigations of nuclear and plasma physics. All the new acceleration schemes developed in the recent years even by LNS users, triggered ideas and proposals for the development of new and compact laser-driven secondary sources (Sect. 6.2.1) useful for several applications (electrons and ions LNS-A-LA-a0, neutrons LNS-A-LA-b1, positrons and photons LNS-A-LA-c1). High-intensity lasers interacting with solids produce non-equilibrium plasma having high equivalent temperatures and high ion energies. Under these conditions, different nuclear reactions can be induced (LNS-A-LA-a1). New and interesting perspectives for applications in the field of health LNS-A-LA-c0 and energy can come out from these studies (Sect. 6.2.1). Fundamental aspects like ion energy loss and the stopping power in plasmas (LNS-A-LA-b0) should be mentioned because they have strong impact on energy production from fusion power. A novel approach to the direct production of pure H2 (LNS-A-LA-c2) from liquid water using femtosecond laser-induced plasma has been also proposed in Sect. 6.2.2. This topic provides the basis for exploring further concepts of hydrogen production.

(iii) Magnetic confinement is one of major topics of fusion energy research. The plasma trap PANDORA will be the new LNS facility designed for multidisciplinary studies in the fields of nuclear and plasma physics, astrophysics, etc., including applicative issues like fusion power. In the section dedicated to plasma traps, Sect. 6.3, most of the potential applications deriving from the developments related to the PANDORA facility are highlighted. The section is divided essentially into three main topics: (i) magnetic Plasmas and related issues (ions heating, charge breeding, stopping power, etc.; (ii) physics and technology aspects for fusion plasmas; (iii) innovative plasma chambers and resonators for compact reactors development. Ion beam plasma interaction is a relevant topic in several fields of plasma physics, from fusion devices to modern ion source and Sect. 6.3.1 is dedicated to the several R & D studies proposed on this subject (LNS-A-PT-a0). Section 6.3.2 deals with the R & D on plasma diagnostics and wave propagation/absorption; detection, collimation and active shuttering methods for soft X and hard X spectroscopy and tomography or innovative heating and energy transport mechanisms for increasing confinement and reaction rates (LNS-A-PT-b0). In Sect. 6.3.3, new plasma chambers and resonators ensuring better radiation-plasma coupling, stability, control and confinement are proposed (LNS-A-PT-b1).

The midterm timescale has been divided into three phases, from the phase A (which includes the activities which can be performed as soon as the facilities will be ready) to phase C (where a more longer R & D work will be requested). Time schedules and priority codes of the previous discussed research topics are synthetically reported in Fig. 40 and in Table 7.

## 6.1 Medical applications

The possibility to have, in the next future, proton and ion beams of high intensity (up to hundreds or even thousands of Grays per second) and in a wide energy range (30–100 AMeV) will pave the way toward new applications and investigations in the field of
<figure><img src="image_39.png" /><figcaption>**Fig. 40 Timeline organization of the future activities in the field of nuclear applications at LNS**</figcaption></figure>

<table><caption>**Table 7 Tables with priorities and feasibility as addressed in the working group**</caption><thead><tr><td>Tag</td><td>Description</td><td>Facilities</td><td>Phase</td></tr></thead><tbody><tr><td>LNS-A-MA-a0</td><td>Flash radiotherapy</td><td>Cyclotron+GIRA</td><td>A</td></tr><tr><td>LNS-A-MA-b0</td><td>Flash BNCT</td><td>LASER</td><td>B</td></tr><tr><td>LNS-A-MA-b1</td><td>Space applications</td><td>Cyclotron+CHIMERA</td><td>B</td></tr><tr><td>LNS-A-MA-c0</td><td>RIBs for beam PET</td><td>Cyclotron+Zero° line</td><td>C</td></tr><tr><td>LNS-A-MA-c1</td><td>HIBs for exotic radioisotopes</td><td>Cyclotron+GIRA</td><td>C</td></tr><tr><td>LNS-A-LA-a0</td><td>Laser-driven secondary sources (e, Ions)</td><td>High-power laser</td><td>A</td></tr><tr><td>LNS-A-LA-a1</td><td>Laser-driven nuclear reactions</td><td>High-power laser</td><td>A</td></tr><tr><td>LNS-A-LA-b0</td><td>Stopping power in plasma</td><td>High-power laser + Tandem</td><td>B</td></tr><tr><td>LNS-A-LA-b1</td><td>Laser-driven secondary sources (neutrons)</td><td>High-power laser</td><td>B</td></tr><tr><td>LNS-A-LA-c0</td><td>Laser-driven radioisotopes productions</td><td>High-power laser + Tandem</td><td>C</td></tr><tr><td>LNS-A-LA-c1</td><td>Laser-driven secondary sources (positrons, gamma)</td><td>High-power laser</td><td>C</td></tr><tr><td>LNS-A-LA-c2</td><td>Laser-driven pure H2</td><td>High-power laser</td><td>C</td></tr><tr><td>LNS-A-PT-a0</td><td>Charge breeding and ion heating</td><td>INFN-PIC, PANDORA + Tandem</td><td>A</td></tr><tr><td>LNS-A-PT-b0</td><td>Fusion plasmas (wave propagation/absorption and diagnostics)</td><td>FTP + PANDORA</td><td>B</td></tr><tr><td>LNS-A-PT-b1</td><td>Compact reactors (innovative chambers, resonators, fuels)</td><td>PANDORA</td><td>B</td></tr></tbody></table>

Medical Physics. Stable and, if needed, intense ion beams can be used to study the projectile and target fragmentation with higher accuracy, to investigate the frontier of the multiple-ion approach also in the 'FLASH' regime, to better quantify the effects of the cosmic radiation on humans, especially for space radioprotection applications and, finally, to explore the possibility of production of exotic radioisotopes. The concurrent opportunity of radioactive beams will moreover give the chance to perform and study advanced imaging techniques as the case of the *in-beam positron emission tomography* (in-beam PET) that is, nowadays, a new and almost non-explored functional imaging technique.

### 6.1.1 Stable proton and ions beams

The quality and variety (in terms of ion species, energy and dose rate) of the ion beams available at INFN-LNS will open the possibility to investigate many advanced and pioneering research topics connected to the Medical physics applications. Among these, we can certainly consider advanced studies for a better quantification of the projectile and target fragmentation in hadrontherapy, the
<figure><img src="image_39.png" /><figcaption>**Fig. 40 Timeline organization of the future activities in the field of nuclear applications at LNS**</figcaption></figure>

<table><caption>**Table 7 Tables with priorities and feasibility as addressed in the working group**</caption><thead><tr><td>Tag</td><td>Description</td><td>Facilities</td><td>Phase</td></tr></thead><tbody><tr><td>LNS-A-MA-a0</td><td>Flash radiotherapy</td><td>Cyclotron+GIRA</td><td>A</td></tr><tr><td>LNS-A-MA-b0</td><td>Flash BNCT</td><td>LASER</td><td>B</td></tr><tr><td>LNS-A-MA-b1</td><td>Space applications</td><td>Cyclotron+CHIMERA</td><td>B</td></tr><tr><td>LNS-A-MA-c0</td><td>RIBs for beam PET</td><td>Cyclotron+Zero° line</td><td>C</td></tr><tr><td>LNS-A-MA-c1</td><td>HIBs for exotic radioisotopes</td><td>Cyclotron+GIRA</td><td>C</td></tr><tr><td>LNS-A-LA-a0</td><td>Laser-driven secondary sources (e, Ions)</td><td>High-power laser</td><td>A</td></tr><tr><td>LNS-A-LA-a1</td><td>Laser-driven nuclear reactions</td><td>High-power laser</td><td>A</td></tr><tr><td>LNS-A-LA-b0</td><td>Stopping power in plasma</td><td>High-power laser + Tandem</td><td>B</td></tr><tr><td>LNS-A-LA-b1</td><td>Laser-driven secondary sources (neutrons)</td><td>High-power laser</td><td>B</td></tr><tr><td>LNS-A-LA-c0</td><td>Laser-driven radioisotopes productions</td><td>High-power laser + Tandem</td><td>C</td></tr><tr><td>LNS-A-LA-c1</td><td>Laser-driven secondary sources (positrons, gamma)</td><td>High-power laser</td><td>C</td></tr><tr><td>LNS-A-LA-c2</td><td>Laser-driven pure H2</td><td>High-power laser</td><td>C</td></tr><tr><td>LNS-A-PT-a0</td><td>Charge breeding and ion heating</td><td>INFN-PIC, PANDORA + Tandem</td><td>A</td></tr><tr><td>LNS-A-PT-b0</td><td>Fusion plasmas (wave propagation/absorption and diagnostics)</td><td>FTP + PANDORA</td><td>B</td></tr><tr><td>LNS-A-PT-b1</td><td>Compact reactors (innovative chambers, resonators, fuels)</td><td>PANDORA</td><td>B</td></tr></tbody></table>

Medical Physics. Stable and, if needed, intense ion beams can be used to study the projectile and target fragmentation with higher accuracy, to investigate the frontier of the multiple-ion approach also in the 'FLASH' regime, to better quantify the effects of the cosmic radiation on humans, especially for space radioprotection applications and, finally, to explore the possibility of production of exotic radioisotopes. The concurrent opportunity of radioactive beams will moreover give the chance to perform and study advanced imaging techniques as the case of the *in-beam positron emission tomography* (in-beam PET) that is, nowadays, a new and almost non-explored functional imaging technique.

### 6.1.1 Stable proton and ions beams

The quality and variety (in terms of ion species, energy and dose rate) of the ion beams available at INFN-LNS will open the possibility to investigate many advanced and pioneering research topics connected to the Medical physics applications. Among these, we can certainly consider advanced studies for a better quantification of the projectile and target fragmentation in hadrontherapy, the
<figure><img src="image_40.png" /><figcaption>**Fig. 41** General layout of the FOOT apparatus</figcaption></figure>

possibility to study the multi-ion approach in radiotherapy and the chance to investigate the “FLASH” effects also with charged particles heavier than protons.

### *Projectile and target fragmentation*

Protons and heavier ions entering in the tissues when used for radiotherapy purposes generate target and projectile fragmentation in a way depending on the incident energy, material constitution and projectile type. In particle therapy, proton or ¹²C ion beams are used to treat deep-seated solid tumors exploiting the advantageous characteristics of charged particles energy deposition in matter and a larger relative biological effectiveness (RBE). He ions are currently not exploited in clinics and would provide a reduced lateral scattering and an improved RBE with respect to proton, while decreasing the fragmentation tail with respect to C ions. For Z > 1 ions, fragmentation of projectiles needs to be carefully taken into account when planning a treatment. The fragmentation cross section for He, C and O ions at energy of interest for particle therapy (roughly between 60 and 250 MeV/u) is not known with sufficient accuracy and Monte Carlo models are scarcely reliable. For all these reasons the FOOT experiment [357] has been designed to measure the fragmentation cross section relevant for particle therapy applications with a movable setup, capable to fit the experimental rooms of different facilities. We propose to exploit He, C and O beams, available at INFN-LNS, whose energy is compliant for particle therapy application, to study the fragmentation with the FOOT apparatus Fig. 41.

FOOT is a table-top setup, with a lever arm of about 2 m. It includes a ToF system, composed of two detectors made of plastic scintillator for ToF and dE/dx measurement, a drift chamber as a beam monitor, a magnetic spectrometer formed of three different silicon detectors for the momentum measurements and a BGO calorimeter to obtain the kinetic energy, thus the mass of the fragment. FOOT is able to evaluate cross section value with errors within the 10%.

The full FOOT apparatus was completed in 2022 and experimental campaign at GSI (D) and (CNAO hadrontherapy facility, I) have been already performed with the aim of characterize the ion beams and measure the relevant cross section of Oxygen (200 AMeV - 400 AMeV) and Carbon (at 200 AMeV). The FOOT group is proposing to perform a set of experimental data taking campaign at INFN-LNS, in order to measure the ⁴He, ¹²C and ¹⁶O fragmentation cross sections at energy below 80 AMeV.

The new *multi-ion* radiotherapy (MIRT) approach theoretically provides an higher optimization in terms of LET (Linear Energy Transfer) distributions. In such scenario, ⁴He offers a decreased lateral scatter effect versus proton with less fragmentation tail dose versus carbon. The energy available at LNS (80 AMeV) is compliant for possible particle therapy application. Moreover, the knowledge of fragmentation cross sections of ¹²C and ¹⁶O ion beams at such energies allow for the investigation the fragmentation reactions in the entrance channel, where the phenomenon is clinically important for the presence of the health tissues.

### *Multiple-ion radiotherapy*

Treatment design and delivery techniques for particle radiotherapy are becoming more sophisticated: from passive scattering (broad beam), that was the first implemented transport approach, to active scanning (spot/raster-scanning) widely used today in almost any new facility. On the other side, the treatment approach always make use of a single ion species: protons, helium, carbon, oxygen or neon ions are employed in patient treatment in an exclusively way. Conversely, a new approach known as multi-ion therapy (MIT) is emerging as potential new treatment concept that involves mixing ion species into a single treatment fraction. By mixing low (p, He) and high (C, O, Ne) LET particles, MIT offers additional degrees of freedom in treatment design, planning and optimization otherwise not attainable with the use of a single radiation quality. MIT dedicated treatment planning and optimization systems must handle the mixed radiation field of multiple primary particle beams to accurately predict effective dose. Accuracy of these systems relies on precise and detailed measurement and modeling of nuclear interactions of ion beams. MIT approach is nowadays studied at the Hidelberg Ion Therapy center or HIT (D), at the National Institute of Radiological Sciences or NIRS (J)
<figure><img src="image_40.png" /><figcaption>**Fig. 41** General layout of the FOOT apparatus</figcaption></figure>

possibility to study the multi-ion approach in radiotherapy and the chance to investigate the “FLASH” effects also with charged particles heavier than protons.

### *Projectile and target fragmentation*

Protons and heavier ions entering in the tissues when used for radiotherapy purposes generate target and projectile fragmentation in a way depending on the incident energy, material constitution and projectile type. In particle therapy, proton or ¹²C ion beams are used to treat deep-seated solid tumors exploiting the advantageous characteristics of charged particles energy deposition in matter and a larger relative biological effectiveness (RBE). He ions are currently not exploited in clinics and would provide a reduced lateral scattering and an improved RBE with respect to proton, while decreasing the fragmentation tail with respect to C ions. For Z > 1 ions, fragmentation of projectiles needs to be carefully taken into account when planning a treatment. The fragmentation cross section for He, C and O ions at energy of interest for particle therapy (roughly between 60 and 250 MeV/u) is not known with sufficient accuracy and Monte Carlo models are scarcely reliable. For all these reasons the FOOT experiment [357] has been designed to measure the fragmentation cross section relevant for particle therapy applications with a movable setup, capable to fit the experimental rooms of different facilities. We propose to exploit He, C and O beams, available at INFN-LNS, whose energy is compliant for particle therapy application, to study the fragmentation with the FOOT apparatus Fig. 41.

FOOT is a table-top setup, with a lever arm of about 2 m. It includes a ToF system, composed of two detectors made of plastic scintillator for ToF and dE/dx measurement, a drift chamber as a beam monitor, a magnetic spectrometer formed of three different silicon detectors for the momentum measurements and a BGO calorimeter to obtain the kinetic energy, thus the mass of the fragment. FOOT is able to evaluate cross section value with errors within the 10%.

The full FOOT apparatus was completed in 2022 and experimental campaign at GSI (D) and (CNAO hadrontherapy facility, I) have been already performed with the aim of characterize the ion beams and measure the relevant cross section of Oxygen (200 AMeV - 400 AMeV) and Carbon (at 200 AMeV). The FOOT group is proposing to perform a set of experimental data taking campaign at INFN-LNS, in order to measure the ⁴He, ¹²C and ¹⁶O fragmentation cross sections at energy below 80 AMeV.

The new *multi-ion* radiotherapy (MIRT) approach theoretically provides an higher optimization in terms of LET (Linear Energy Transfer) distributions. In such scenario, ⁴He offers a decreased lateral scatter effect versus proton with less fragmentation tail dose versus carbon. The energy available at LNS (80 AMeV) is compliant for possible particle therapy application. Moreover, the knowledge of fragmentation cross sections of ¹²C and ¹⁶O ion beams at such energies allow for the investigation the fragmentation reactions in the entrance channel, where the phenomenon is clinically important for the presence of the health tissues.

### *Multiple-ion radiotherapy*

Treatment design and delivery techniques for particle radiotherapy are becoming more sophisticated: from passive scattering (broad beam), that was the first implemented transport approach, to active scanning (spot/raster-scanning) widely used today in almost any new facility. On the other side, the treatment approach always make use of a single ion species: protons, helium, carbon, oxygen or neon ions are employed in patient treatment in an exclusively way. Conversely, a new approach known as multi-ion therapy (MIT) is emerging as potential new treatment concept that involves mixing ion species into a single treatment fraction. By mixing low (p, He) and high (C, O, Ne) LET particles, MIT offers additional degrees of freedom in treatment design, planning and optimization otherwise not attainable with the use of a single radiation quality. MIT dedicated treatment planning and optimization systems must handle the mixed radiation field of multiple primary particle beams to accurately predict effective dose. Accuracy of these systems relies on precise and detailed measurement and modeling of nuclear interactions of ion beams. MIT approach is nowadays studied at the Hidelberg Ion Therapy center or HIT (D), at the National Institute of Radiological Sciences or NIRS (J)
<figure><img src="image_41.png" /><figcaption>**Fig. 42** Multiple-ion concepts as studied at the GSI, where oxygen and helium ions are used to optimize the biological dose distribution of tumors with radioresistant sections</figcaption></figure>

and at GSI Helmholtzzentrum für Schwerionenforschung (D) where different aspects of this new modality are studied. Figure 42 [358, 359] shows the study conducted at GSI, where MIT is used to overcome the hypoxia related tumor radio-resistance using a combination of ¹⁶O and ⁴He ions that is also called *multi-ion kill painting*.

INFN-LNS beams (that include all the aforementioned beams) will be an ideal candidate to study either from a physics (fragmentation cross sections) and from a radiobiology point of view, the capability of a multi-ion approach. Even if, in fact, the maximum available energies per nucleon cannot be used for clinical treatments, they are ideal for studying the most basic effects of ions being the low-energy region (below 100 AMeV), in fact the most critical and unknown region from a radiotherapy point of view.

*Heavy-ion cross section measurements for therapy and space applications*

The reliability of particle transport codes, widely used for medical and space radiation applications, strongly depends on nuclear cross section models. A recent cross section data base [360] pointed out that for several important systems either no or only limited total reaction cross section data can be found in literature and sometimes not consistent values are reported. The same is true for single and double differential cross section systems and neutron production cross sections [361]. Future measurements at the LNS cyclotron facility could help to close some of these gaps, in particular for the intermediate to low energy range. Interesting systems to study are combinations of elements largely present in the space radiation environment (e.g., helium, carbon, nitrogen, oxygen, silicon, iron) with the constituents of relevant shielding materials (e.g., lithium, carbon, aluminum, silicon, oxygen). In the cases where either the projectile is not available or the target material is of difficult production or handling, inverse kinematic approaches could be very efficient to overcome these difficulties.

The research infrastructure for the proposed cross section measurements is the LNS Cyclotron Facility where total reaction and double differential cross sections for neutron and light ion fragments can be measured exploiting the power of the CHIMERA facility. Here the following nuclear reactions, in the energy range of the incident particle of 40–80 MeV/u, can be considered: ⁴He, ¹⁴Ne, ²⁸Si, ⁵⁶Fe + ⁷Li, ¹²C, ²⁷Al → n, ¹,²,³H, ³,⁴He + X

### 6.1.2 Radioactive ions beams (RIBs) and high-intensity beams (HIBs)

**RIBs-Advanced imaging techniques: in-beam PET** “In-beam PET” is a PET (positron emission tomography) where $\beta^+$ are produced from unstable ($^{15}$O, $^{11}$C, $^{10}$C mainly) isotopes generated by the interaction of the irradiation beam with human tissues beam and the generated gamma pairs are measured online during the irradiation. Figure 43 shows the dose (dashed lines) profile of a $^{12}$C beam (left) and proton (right) beam. The corresponding activity profiles, of the induced radionuclides, are reported with the continuous black lines. Data are reproduced, with permission, from Parodi [362].

In case of stable ion beams with a sufficient energy to generate an appreciable PET signal, the possibility to have high beam currents might be beneficial not only for tests in relation to radiation hardness and suppression/exploitation of radiation background, but also for generating special delivery regimes like FLASH or mini-beams, as well as secondary radioactive beams.

**HIBs-FLASH radiotherapy** Delivery of current particle radiotherapy treatments lasts order of a few minutes using conventional dose rates (≈ 0.1 Gy/s). However, recent experimental evidences suggest that sub-second treatment at ultrahigh dose rates (uHDR, > 40
<figure><img src="image_41.png" /><figcaption>**Fig. 42** Multiple-ion concepts as studied at the GSI, where oxygen and helium ions are used to optimize the biological dose distribution of tumors with radioresistant sections</figcaption></figure>

and at GSI Helmholtzzentrum für Schwerionenforschung (D) where different aspects of this new modality are studied. Figure 42 [358, 359] shows the study conducted at GSI, where MIT is used to overcome the hypoxia related tumor radio-resistance using a combination of ¹⁶O and ⁴He ions that is also called *multi-ion kill painting*.

INFN-LNS beams (that include all the aforementioned beams) will be an ideal candidate to study either from a physics (fragmentation cross sections) and from a radiobiology point of view, the capability of a multi-ion approach. Even if, in fact, the maximum available energies per nucleon cannot be used for clinical treatments, they are ideal for studying the most basic effects of ions being the low-energy region (below 100 AMeV), in fact the most critical and unknown region from a radiotherapy point of view.

*Heavy-ion cross section measurements for therapy and space applications*

The reliability of particle transport codes, widely used for medical and space radiation applications, strongly depends on nuclear cross section models. A recent cross section data base [360] pointed out that for several important systems either no or only limited total reaction cross section data can be found in literature and sometimes not consistent values are reported. The same is true for single and double differential cross section systems and neutron production cross sections [361]. Future measurements at the LNS cyclotron facility could help to close some of these gaps, in particular for the intermediate to low energy range. Interesting systems to study are combinations of elements largely present in the space radiation environment (e.g., helium, carbon, nitrogen, oxygen, silicon, iron) with the constituents of relevant shielding materials (e.g., lithium, carbon, aluminum, silicon, oxygen). In the cases where either the projectile is not available or the target material is of difficult production or handling, inverse kinematic approaches could be very efficient to overcome these difficulties.

The research infrastructure for the proposed cross section measurements is the LNS Cyclotron Facility where total reaction and double differential cross sections for neutron and light ion fragments can be measured exploiting the power of the CHIMERA facility. Here the following nuclear reactions, in the energy range of the incident particle of 40–80 MeV/u, can be considered: ⁴He, ¹⁴Ne, ²⁸Si, ⁵⁶Fe + ⁷Li, ¹²C, ²⁷Al → n, ¹,²,³H, ³,⁴He + X

### 6.1.2 Radioactive ions beams (RIBs) and high-intensity beams (HIBs)

**RIBs-Advanced imaging techniques: in-beam PET** “In-beam PET” is a PET (positron emission tomography) where $\beta^+$ are produced from unstable ($^{15}$O, $^{11}$C, $^{10}$C mainly) isotopes generated by the interaction of the irradiation beam with human tissues beam and the generated gamma pairs are measured online during the irradiation. Figure 43 shows the dose (dashed lines) profile of a $^{12}$C beam (left) and proton (right) beam. The corresponding activity profiles, of the induced radionuclides, are reported with the continuous black lines. Data are reproduced, with permission, from Parodi [362].

In case of stable ion beams with a sufficient energy to generate an appreciable PET signal, the possibility to have high beam currents might be beneficial not only for tests in relation to radiation hardness and suppression/exploitation of radiation background, but also for generating special delivery regimes like FLASH or mini-beams, as well as secondary radioactive beams.

**HIBs-FLASH radiotherapy** Delivery of current particle radiotherapy treatments lasts order of a few minutes using conventional dose rates (≈ 0.1 Gy/s). However, recent experimental evidences suggest that sub-second treatment at ultrahigh dose rates (uHDR, > 40
**Fig. 43** Activity and dose profiles generated by some of the most abundant radioisotopes produced in the interaction of ¹²C (left) and proton (right) beams in a PMMA target. The most common radioisotopes generated are reported in the cyan rectangle. Figure from Parodi [362]

<figure><img src="image_42.png" /></figure>

**Fig. 44** The combined use of the same (or different) radioisotopes that can be used for imaging and tumor treatment forms the so-called theranostic approach

<figure><img src="image_43.png" /></figure>

$$ \text{THERAPY (+ DIAGNOSTIC) = THERANOSTIC} $$

Gy/s for a delivered dose > 10 Gy) may provide several clinical advantages. Aside from increasing clinical efficiency and reducing uncertainties of intra-fraction organ-motion, the so-called FLASH effect has been observed experimentally, which elicits a potential differential sparing between surrounding healthy tissue and the tumor. To understand clinical potential of several ion species (proton [p], helium [He], carbon [C], oxygen [O] or neon [Ne] ions), dose rate dependencies on biological effect (in vitro and in vivo) must be measured across a broad range of dose and linear energy transfer (LET) levels in various tissue types. Subsequently, these data will guide future clinical practice via treatment design and modeling during planning to predict biological effect as a function of the major endpoints for FLASH (dose, LET and dose rate) for the mixed radiation spectra produced by therapeutic ion beams. A major limitation of performing such experiments at existing clinical facilities (e.g., clinical cyclotron- or synchrotron-based) is the inability to achieve “FLASH” conditions (>> 40 Gy/s at 10 Gy) for experimentally and clinically relevant volumes (> 1 cm²), as shown in previous work for proton and helium ions [363, 364] for high dose levels in both low and high LET regions. In this work, comprehensive radiobiological investigations will be made possible via delivery using the high-intensity cyclotron present at the facility. All these studies will be potentially possible at the INFN-LNS thanks to the high-intense ions beams that will be available.

*HIBs-innovative radioisotopes*

The new frontier of nuclear medicine is the “theranostic approach”, where radionuclides that combine imaging and radiotherapy properties (e.g., local tumors treatment) are employed by using a single radiopharmaceutical product as described in Fig. 44. The most important theranostic radionuclides nowadays known, i.e., having a nuclear decay pattern suitable for both applications, are ⁶⁷Cu, ⁶⁴Cu, ⁴⁷Sc and ⁶⁷Ga.

The *theranostic* approach may be also obtained with “theranostic pair,” i.e., isotopic radionuclides, one specific for imaging, while the other one for therapy. The most known pairs belonging to this group are ⁶¹⁻⁶⁴Cu/⁶⁷Cu, ⁴³⁻⁴⁴Sc/⁴⁷Sc, ⁶⁸Ga/⁶⁷Ga, ¹⁴⁹⁻¹⁵²Tb/¹⁵⁵⁻¹⁶¹Tb.

Most of the radionuclides nowadays used in nuclear medicine are massively produced by using nuclear reactors (e.g., ⁹⁹Mo/⁹⁹mTc generators, the most used radionuclide worldwide). On the other side, particles accelerators (accelerating p, d, alpha, etc.) as cyclotrons/linacs (or e-linacs producing a γ-source) are becoming the alternative supplying route of choice (in some cases, the only way), not only for the already established radionuclides, but also for the new emerging ones. Of course, to select the optimal radionuclides’ production pathway, it is mandatory to investigate all the possible nuclear reaction routes (cross sections measurements) and determine the full map of isotopic contaminants. For most of them, optimal production routes still need to be clarified and investigated and exploring reaction routes by using heavier (Z > 2) ions hitting particles may be certainly of interest.
**Fig. 43** Activity and dose profiles generated by some of the most abundant radioisotopes produced in the interaction of ¹²C (left) and proton (right) beams in a PMMA target. The most common radioisotopes generated are reported in the cyan rectangle. Figure from Parodi [362]

<figure><img src="image_42.png" /></figure>

**Fig. 44** The combined use of the same (or different) radioisotopes that can be used for imaging and tumor treatment forms the so-called theranostic approach

<figure><img src="image_43.png" /></figure>

$$ \text{THERAPY (+ DIAGNOSTIC) = THERANOSTIC} $$

Gy/s for a delivered dose > 10 Gy) may provide several clinical advantages. Aside from increasing clinical efficiency and reducing uncertainties of intra-fraction organ-motion, the so-called FLASH effect has been observed experimentally, which elicits a potential differential sparing between surrounding healthy tissue and the tumor. To understand clinical potential of several ion species (proton [p], helium [He], carbon [C], oxygen [O] or neon [Ne] ions), dose rate dependencies on biological effect (in vitro and in vivo) must be measured across a broad range of dose and linear energy transfer (LET) levels in various tissue types. Subsequently, these data will guide future clinical practice via treatment design and modeling during planning to predict biological effect as a function of the major endpoints for FLASH (dose, LET and dose rate) for the mixed radiation spectra produced by therapeutic ion beams. A major limitation of performing such experiments at existing clinical facilities (e.g., clinical cyclotron- or synchrotron-based) is the inability to achieve “FLASH” conditions (>> 40 Gy/s at 10 Gy) for experimentally and clinically relevant volumes (> 1 cm²), as shown in previous work for proton and helium ions [363, 364] for high dose levels in both low and high LET regions. In this work, comprehensive radiobiological investigations will be made possible via delivery using the high-intensity cyclotron present at the facility. All these studies will be potentially possible at the INFN-LNS thanks to the high-intense ions beams that will be available.

*HIBs-innovative radioisotopes*

The new frontier of nuclear medicine is the “theranostic approach”, where radionuclides that combine imaging and radiotherapy properties (e.g., local tumors treatment) are employed by using a single radiopharmaceutical product as described in Fig. 44. The most important theranostic radionuclides nowadays known, i.e., having a nuclear decay pattern suitable for both applications, are ⁶⁷Cu, ⁶⁴Cu, ⁴⁷Sc and ⁶⁷Ga.

The theranostic approach may be also obtained with “theranostic pair,” i.e., isotopic radionuclides, one specific for imaging, while the other one for therapy. The most known pairs belonging to this group are ⁶¹⁻⁶⁴Cu/⁶⁷Cu, ⁴³⁻⁴⁴Sc/⁴⁷Sc, ⁶⁸Ga/⁶⁷Ga, ¹⁴⁹⁻¹⁵²Tb/¹⁵⁵⁻¹⁶¹Tb.

Most of the radionuclides nowadays used in nuclear medicine are massively produced by using nuclear reactors (e.g., ⁹⁹Mo/⁹⁹mTc generators, the most used radionuclide worldwide). On the other side, particles accelerators (accelerating p, d, alpha, etc.) as cyclotrons/linacs (or e-linacs producing a γ-source) are becoming the alternative supplying route of choice (in some cases, the only way), not only for the already established radionuclides, but also for the new emerging ones. Of course, to select the optimal radionuclides’ production pathway, it is mandatory to investigate all the possible nuclear reaction routes (cross sections measurements) and determine the full map of isotopic contaminants. For most of them, optimal production routes still need to be clarified and investigated and exploring reaction routes by using heavier (Z > 2) ions hitting particles may be certainly of interest.
<figure><img src="image_44.png" /><figcaption>**Fig. 45** The BEST BCSI 70p (35–70 MeV, 750 μA max) cyclotron, SPES/LARAMED facility, Italy</figcaption></figure>

While the most accelerator-based radionuclides are nowadays, produced by public/private facilities using large network of low-energy medical cyclotrons (Ep < 20 MeV), some mid-energy p,d,α cyclotrons (i.e., Ep 20–35 MeV), a few high-energy p,d,α cyclotrons (i.e., Ep > 35 MeV) as the machine installed at ARRONAX (F), ZEVACOR (US), LARAMED (I), see Fig. 45.

With the planned upgrade of the acceleration machines, currently underway, the INFN-LNS will have:

* A K-800 superconducting cyclotron with an improved beam intensities which will be available for low-mid Z ion species with respect to the past.

* A Tandem accelerator with the availability of noble gasses.

Considering this, a dedicated (and very-well characterized) beamline for high quality nuclear cross sections measurements may be envisaged. On the other hand, new p, d, α and heavier ion-driven nuclear reaction routes may be explored in order to produce specific and emerging radionuclides for imaging/therapy/theranostic applications.

It would be desirable that this the proposed facility (and the related research activities) shall be coordinated between LNS and LNL laboratories, where the LARAMED facility is under construction, in order to avoid overlaps. The LARAMED facility will have a dedicated beamline to carry out nuclear cross sections measurements but based upon the SPES cyclotron that will accelerate (at least in the initial years) only protons.

## 6.2 Laser applications

The perspective to install an high-power (TW-PW scale), ultrashort (fs order) laser system to generate extremely dense plasmas by its interaction with matter and the almost unique possibility to have, in the same environment, the availability of accelerated (4–80 AMeV energy range) and intense ion beams from conventional accelerators will open unprecedented possibilities to study the physics of the plasma acceleration and of the Warm Dense Matter at the INFN-LNS laboratory (Catania, I). The perspectives of the use and applications (in medical, energetic and multidisciplinary fields) of radiation generated in laser-matter interaction processes are analyzed and briefly discussed in this Section.

### 6.2.1 Laser-driven secondary sources

In the past few decades, researchers have continued to explore the extent to which extreme laser-plasma environments, abruptly created at a target site by pulsed laser irradiation of very high intensity, can generate energetic particle and associated radiation emission. In the case of proton/ion acceleration, this has been especially true since 2000 [365].

For electrons, laser systems with peak powers of hundreds of terawatts (TW) can accelerate bunches to GeV energy levels with charges of 0.1 nano-Coulombs or more and for an intrinsically ultrashort ‘at-source’ duration. Higher laser powers are typically needed for laser-driven ion acceleration, but the highest kinetic energies remain sub-relativistic to date. For example, hundreds of terawatts of peak laser power can accelerate proton bunches to tens of MeV energies (the recently published maximum energies approach 100 MeV [366] with nano-Coulomb charge levels and with an intrinsically ultrashort ‘at-source’ duration.

These proton energies are therefore adequate also for generating energetic neutrons in nuclear reactions. In general, we may look to laser-driven particle acceleration as an innovative optical component of accelerator science advancement.

Laser-driven particle sources offer a unique set of parameters in a relatively compact and versatile setup. Their intrinsic short duration (as short as a few femtoseconds) opens up novel applications and allows to study the response of materials and biological samples in unprecedented regimes.

**Protons and electrons acceleration** Laser-matter interaction mechanisms represent one of the most innovative and promising approaches for particle acceleration and radiation generation. Among the different radiations, the generation, optimization and use of laser-driven electrons and protons are, nowadays, the most investigated; the production and use of neutrons, positrons and
<figure><img src="image_44.png" /><figcaption>**Fig. 45** The BEST BCSI 70p (35–70 MeV, 750 μA max) cyclotron, SPES/LARAMED facility, Italy</figcaption></figure>

While the most accelerator-based radionuclides are nowadays, produced by public/private facilities using large network of low-energy medical cyclotrons (Ep < 20 MeV), some mid-energy p,d,α cyclotrons (i.e., Ep 20–35 MeV), a few high-energy p,d,α cyclotrons (i.e., Ep > 35 MeV) as the machine installed at ARRONAX (F), ZEVACOR (US), LARAMED (I), see Fig. 45.

With the planned upgrade of the acceleration machines, currently underway, the INFN-LNS will have:

* A K-800 superconducting cyclotron with an improved beam intensities which will be available for low-mid Z ion species with respect to the past.

* A Tandem accelerator with the availability of noble gasses.

Considering this, a dedicated (and very-well characterized) beamline for high quality nuclear cross sections measurements may be envisaged. On the other hand, new p, d, α and heavier ion-driven nuclear reaction routes may be explored in order to produce specific and emerging radionuclides for imaging/therapy/theranostic applications.

It would be desirable that this the proposed facility (and the related research activities) shall be coordinated between LNS and LNL laboratories, where the LARAMED facility is under construction, in order to avoid overlaps. The LARAMED facility will have a dedicated beamline to carry out nuclear cross sections measurements but based upon the SPES cyclotron that will accelerate (at least in the initial years) only protons.

## 6.2 Laser applications

The perspective to install an high-power (TW-PW scale), ultrashort (fs order) laser system to generate extremely dense plasmas by its interaction with matter and the almost unique possibility to have, in the same environment, the availability of accelerated (4–80 AMeV energy range) and intense ion beams from conventional accelerators will open unprecedented possibilities to study the physics of the plasma acceleration and of the Warm Dense Matter at the INFN-LNS laboratory (Catania, I). The perspectives of the use and applications (in medical, energetic and multidisciplinary fields) of radiation generated in laser-matter interaction processes are analyzed and briefly discussed in this Section.

### 6.2.1 Laser-driven secondary sources

In the past few decades, researchers have continued to explore the extent to which extreme laser-plasma environments, abruptly created at a target site by pulsed laser irradiation of very high intensity, can generate energetic particle and associated radiation emission. In the case of proton/ion acceleration, this has been especially true since 2000 [365].

For electrons, laser systems with peak powers of hundreds of terawatts (TW) can accelerate bunches to GeV energy levels with charges of 0.1 nano-Coulombs or more and for an intrinsically ultrashort ‘at-source’ duration. Higher laser powers are typically needed for laser-driven ion acceleration, but the highest kinetic energies remain sub-relativistic to date. For example, hundreds of terawatts of peak laser power can accelerate proton bunches to tens of MeV energies (the recently published maximum energies approach 100 MeV [366] with nano-Coulomb charge levels and with an intrinsically ultrashort ‘at-source’ duration.

These proton energies are therefore adequate also for generating energetic neutrons in nuclear reactions. In general, we may look to laser-driven particle acceleration as an innovative optical component of accelerator science advancement.

Laser-driven particle sources offer a unique set of parameters in a relatively compact and versatile setup. Their intrinsic short duration (as short as a few femtoseconds) opens up novel applications and allows to study the response of materials and biological samples in unprecedented regimes.

**Protons and electrons acceleration** Laser-matter interaction mechanisms represent one of the most innovative and promising approaches for particle acceleration and radiation generation. Among the different radiations, the generation, optimization and use of laser-driven electrons and protons are, nowadays, the most investigated; the production and use of neutrons, positrons and
<figure><img src="image_45.png" /><figcaption>**Fig. 46** Target Normal Sheath Acceleration-TNSA. A thin target foil is irradiated by an intense laser pulse. The laser pre-pulse creates a pre-plasma on the target's front side. The main pulse interacts with the plasma and accelerates MeV energy electrons mainly in the forward direction. The electrons propagate through the target, where collisions with the background material can increase the divergence of the electron current. The electrons leave the rear side, resulting in a dense sheath. An electric field due to charge separation is created. The field is on the order of the laser electric field (TV/m), which ionizes atoms at the surface. The ions are then accelerated in this sheath field, pointing in the target normal direction</figcaption></figure>

<figure><img src="image_46.png" /><figcaption>**Fig. 47** Schematics of the peeler scheme. A femtosecond laser (red and blue) is incident on the edge of a microscale tape (gray). The micron-thick tape is infinitely long across the laser focus and is a few tens of microns wide along the laser propagation direction. Abundant electrons are continuously dragged out and accelerated forward by the intense laser. When these energetic electrons arrive at the rear edge of the tape, a longitudinal bunching field is established (yellow). Protons (green dots) are simultaneously accelerated and bunched by this field, leading to a highly mono-energetic proton beam. From [368]</figcaption></figure>

electromagnetic radiation are also considered by many research groups and it represents a frontier in radiation generation, as it will be discussed in Sect. 6.2.1.

The most established laser-based ion acceleration mechanism is Target Normal Sheath Acceleration [367], where energized electrons create a strong sheath field at the rear surface of a laser-irradiated foil (see Fig. 46), accelerating contaminant protons in a diverging, broadband beam (with cutoff energies up to 60–85 MeV depending on laser pulse duration).

Acceleration of heavier ions (e.g., carbon) from the bulk of a foil is possible through a different mechanism, Radiation Pressure Acceleration (or RPA), which leads to a spectral peak, so far in the 20–30 MeV/nucleon range.

Current work involves the use of miniature structures for collimating TNSA protons, as well as techniques for optimizing and upscaling carbon acceleration. Researchers are also working on more efficient schemes where sheath acceleration is driven by a different electron population accelerated from laser-excited surface plasma waves (see Fig. 47 [368]), as well as coupling collimation technique to RPA for delivery of high-flux carbon ion beamlets. These techniques promise proton and ion acceleration at energies higher than those today reached with the TNSA approach.

Electron acceleration by laser is based on the so-called laser wake field acceleration (LWFA) process in a plasma [369] allowing the generation of electron bunches with typical energy up to hundreds of MeV level to be produced, using 100-TW-scale, ultrashort laser systems. The typical electron charge per laser shot is up to 100 pC this opening the possibility to use high-energy electron beams for future radiotherapy protocols including the FLASH and the very high-energy electron approaches [370].

*Positrons and photons generation* High-power lasers also offer a unique degree of versatility, where not only the particle parameters can be seamlessly tuned to suit the desired application, but even the type of generated particle (e.g., electrons, positrons, and $\gamma$) can be selected with minor adjustments in the setup. Some of these generation mechanisms have been pioneered and developed by the plasma Group of the Queen's University in Belfast (UK) and by the INO-CNR laboratory in Pisa (I), where the production
<figure><img src="image_45.png" /><figcaption>**Fig. 46** Target Normal Sheath Acceleration-TNSA. A thin target foil is irradiated by an intense laser pulse. The laser pre-pulse creates a pre-plasma on the target's front side. The main pulse interacts with the plasma and accelerates MeV energy electrons mainly in the forward direction. The electrons propagate through the target, where collisions with the background material can increase the divergence of the electron current. The electrons leave the rear side, resulting in a dense sheath. An electric field due to charge separation is created. The field is on the order of the laser electric field (TV/m), which ionizes atoms at the surface. The ions are then accelerated in this sheath field, pointing in the target normal direction</figcaption></figure>

<figure><img src="image_46.png" /><figcaption>**Fig. 47** Schematics of the peeler scheme. A femtosecond laser (red and blue) is incident on the edge of a microscale tape (gray). The micron-thick tape is infinitely long across the laser focus and is a few tens of microns wide along the laser propagation direction. Abundant electrons are continuously dragged out and accelerated forward by the intense laser. When these energetic electrons arrive at the rear edge of the tape, a longitudinal bunching field is established (yellow). Protons (green dots) are simultaneously accelerated and bunched by this field, leading to a highly mono-energetic proton beam. From [368]</figcaption></figure>

electromagnetic radiation are also considered by many research groups and it represents a frontier in radiation generation, as it will be discussed in Sect. 6.2.1.

The most established laser-based ion acceleration mechanism is Target Normal Sheath Acceleration [367], where energized electrons create a strong sheath field at the rear surface of a laser-irradiated foil (see Fig. 46), accelerating contaminant protons in a diverging, broadband beam (with cutoff energies up to 60–85 MeV depending on laser pulse duration).

Acceleration of heavier ions (e.g., carbon) from the bulk of a foil is possible through a different mechanism, Radiation Pressure Acceleration (or RPA), which leads to a spectral peak, so far in the 20–30 MeV/nucleon range.

Current work involves the use of miniature structures for collimating TNSA protons, as well as techniques for optimizing and upscaling carbon acceleration. Researchers are also working on more efficient schemes where sheath acceleration is driven by a different electron population accelerated from laser-excited surface plasma waves (see Fig. 47 [368]), as well as coupling collimation technique to RPA for delivery of high-flux carbon ion beamlets. These techniques promise proton and ion acceleration at energies higher than those today reached with the TNSA approach.

Electron acceleration by laser is based on the so-called laser wake field acceleration (LWFA) process in a plasma [369] allowing the generation of electron bunches with typical energy up to hundreds of MeV level to be produced, using 100-TW-scale, ultrashort laser systems. The typical electron charge per laser shot is up to 100 pC this opening the possibility to use high-energy electron beams for future radiotherapy protocols including the FLASH and the very high-energy electron approaches [370].

*Positrons and photons generation* High-power lasers also offer a unique degree of versatility, where not only the particle parameters can be seamlessly tuned to suit the desired application, but even the type of generated particle (e.g., electrons, positrons, and $\gamma$) can be selected with minor adjustments in the setup. Some of these generation mechanisms have been pioneered and developed by the plasma Group of the Queen's University in Belfast (UK) and by the INO-CNR laboratory in Pisa (I), where the production