DREB Conference 2024

Single-nucleon knockout reactions at intermediate energies with $^9$Be and $^{12}$C targets have proven of great value to extract spectroscopic information from exotic atomic nuclei. In the early 2000s, a trend was noticed [1] in the so-called ``quenching'' factors (the ratio between experimental and theoretical cross sections) for these reactions, in which the knockout of the deficient species in an asymmetric nucleus presented significantly more reduction than the knockout of the abundant species. This trend has not been observed in transfer or removal reactions with proton targets $(p,pN)$ [2], as would be expected if it originated in the description of the structure of the nuclei. This prompts a revision of the description of the knockout reactions, to explore how it affects this dependence on the isospin asymmetry of the nuclei.

In this work, we study the interaction of the core (the residual nucleus after the removal of the nucleon) due to its final-state interaction with the knocked-out nucleon after it has been removed from the projectile. This interaction can lead to the core being excited to energies above its breakup threshold, which leads to its destruction and therefore, a reduction in the knockout cross section, which requires the survival of the core. We describe these effects via an eikonal description of the reaction, where the destruction of the core is modelled via an effective density, which is reduced in the nuclear interior, so that deeply-bound nucleons are more affected by core destruction. We find a significant reduction in the isospin-asymmetry dependence of the ``quenching'' factors [3] when considering the core destruction effect, which points to this reaction mechanism being fundamental for the correct description of the single-nucleon knockout process.

Systematic studies of nuclei along isotopic chains have revealed unexpected trends that challenge our understanding of nuclear structure. For two decades, nuclear physicists have grappled with the asymmetry dependence of the ratio R between the spectroscopic factors extracted experiments and that predicted by the nuclear shell model. Surprisingly, the strong asymmetry dependence of these strengths and their extreme values for highly asymmetric nuclei inferred from knockout reaction measurements on a target nucleus are not consistent with what is extracted from electron-induced, transfer, and quasi-free reaction data [1]. In this talk, I will present the first consistent analysis of one-nucleon transfer and one-nucleon knockout data, in which theoretical uncertainties associated with the nucleon-nucleus effective interactions considered in the reaction models are quantified using a Bayesian analysis [2]. Our results demonstrate that, taking into account these uncertainties, (i) transfer and knockout reactions lead to a consistent picture for the removal of a loosely-bound nucleon and (ii) there is still some tension between the strengths extracted from transfer and knockout data on deeply-bound nuclei. The uncertainties obtained in this work represent a lower bound and are already significantly larger than the original estimates.
[1] Aumann et al. Prog. Part. Nucl. Phys. 118, 103847 (2021)
[2] Hebborn, Nunes, and Lovell, Phys. Rev. Lett. 131, 212503 (2023).
*This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under the FRIB Theory Alliance Award No. DE-SC0013617, under Work Proposals no. SCW0498 and DE-SC0021422. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and by Los Alamos National Laboratory under Contract 89233218CNA000001.

The dynamics of quantum few- and many-body systems is often modeled with local interaction models, mainly due to simplicity, though more microscopic or fundamental approaches yield nonlocal interactions. For few-cluster nuclear reactions the interactions usually are given in the local form of real binding and complex optical potentials. We made a two-fold extension of that standard dynamics by developing a new nonlocal form of binding and optical potentials and simultaneously including the excitation of the nuclear core. Exact three-body Faddeev-type equations in momentum-space are solved for the description of nucleon transfer reactions (d,p) and (p,d) and deuteron inelastic scattering (d,d'). Example results for 10Be and 24Mg nuclei demonstrate a good reproduction of the experimental data and an improved consistency between the two-body (elastic and inelastic nucleon-nucleus scattering) and three-body description [1,2].

The description is being extended to nucleon knockout reactions with simultaneous excitation of the core into states absent in the initial nucleus, and thereby beyond the reach of the DWIA. Examples are 12C(p,2p)11B reactions leading to high-spin 5/2- or 7/2- states of 11B.

1. A. Deltuva, D. Jurčiukonis, Physics Letters B 840, 137867 (2023).
2. A. Deltuva, D. Jurčiukonis, Phys. Rev. C 107, 064602 (2023).

The ISOLDE Solenoidal Spectrometer (ISS) specialises in the study of direct reactions in inverse kinematics. The ISS was fully commissioned in 2021 with a new silicon detector array and has since undergone three successful physics campaigns. This talk will give an overview of the technical capabilities of ISS, as well as present recent measurements taken using the device. These focus on the single-particle properties of a variety of nuclear systems probed using the single-neutron adding $(d,p)$ reaction. They include, but are not limited to, studies of the structure of neutron-rich Be isotopes; the evolution of single-particle states into the $N=20$ Island of Inversion in $^{31}$Mg; and trends in single-particle states along $Z=50$ in neutron-deficient Sn isotopes and along $N=127$ north of $^{208}$Pb.

Direct reactions are fundamental tools to investigate the structure of exotic nuclei. Studies of nuclei far away from stability are usually performed with secondary radioactive beams, that suffer from low intensities and need to be compensated with thick targets and high efficient detection systems to increase luminosity. Active targets are invaluable devices that, among other important features, allow to reconstruct the reaction in three dimensions without loss of resolution.

The ACtive TArget and Time Projection Chamber (ACTAR TPC) detector [1-3] has been developed at GANIL to cover a broad physics programme. The device was commissioned in 2018 showing an excellent performance of the detector [4]. Since then, several experiments have been performed at GANIL. In this talk, We will present the recent results from the first transfer campaign. The main goal of the experiment was the study of the spin-orbit splitting between the proton 0p3/2-0p1/2 orbitals. The reaction $^{20}$O(d,$^{3}$He) selectively populates single-particles states in $^{19}$N. Excitation energy and angular distributions will be shown. Results were compared to shell model calculations with state-of-the art interactions.

[1] T. Roger et al. Nucl. Instrum. Meth. Phys. Res. A 895, 126 (2018).
[2] J. Pancin et al. Nucl. Instrum. Meth. Phys. Res. A 735, 532 (2014).

[3] P. Konczykowski et al., Nucl. Instrum. Meth. Phys. Res. A 927, 125 (2019).
[4] B. Mauss et al. Nucl. Instrum. Meth. Phys. Res. A 940, 498 (2019).
[5] J. Lois-Fuentes Ph.D. USC (2023)

The exponential decay of unstable states is one of the most pervasive and most studied phenomena in microscopic physics, yet its quantum-mechanical theory remains obscure in many ways. The exponential decay is not a trivial consequence of quantum dynamics; rather, it emerges from a complex equilibrium involving a resonant state with a decaying amplitude and a rotating phase, balanced by the effects of outgoing radiation.

Crucial to our understanding are the early and late-time dynamics, particularly in the context of weakly bound nuclear states in exotic nuclei. Unlike their bound counterparts, these states retain a 'memory' of their formation and background components, a history that manifests in their non-exponential decay dynamics. This memory aspect opens a window into the nuanced transient stages between different decay regimes, often marked by interference among various contributions. These interferences manifest as oscillations in the decay curve and correlations in the decay products, offering rich insights into the decay process.

Our presentation will focus on the latest research efforts aimed at unraveling these complex phenomena. We will explore innovative methodologies and experimental approaches to observe and interpret these dynamics in nuclei. The insights gained promise to enhance our understanding of quantum decay dynamics and its application in nuclear physics.

Neutron-rich nuclei provide important insights to nuclear forces and to the nuclear equation of state. Advances in ab initio methods combined with new opportunities with rare isotope beams enable unique explorations of their properties based on nuclear forces applicable over the entire nuclear chart. In this Letter, we develop novel chiral low-resolution interactions that accurately describe bulk properties from $^{16}$O to $^{208}$Pb. With these, we investigate density distributions and neutron skins of neutron-rich nuclei. Our results show that neutron skins are narrowly predicted over all nuclei with interesting sensitivities for the most extreme, experimentally unexplored cases.

The direct reaction theory widely used to study single-particle spectroscopic strength in nucleon transfer experiments is based on a Hamiltonian with two-nucleon interactions only. We point out that in reactions where three-body effects are important, for example, such as $(d,p)$ and $(p,2p)$, an additional three-body force arises due to three-nucleon ($3N$) interaction between nucleons belonging to different fragments. We develop calculations of this $3N$-induced force for one-nucleon removal reactions thus making an essential step towards bringing together nuclear structure theory, where 3N force is routinely used, and nuclear direct reaction theory, based on two-nucleon interactions only.

We study the effects of the $3N$ force on nucleon transfer in $(d,p)$ and $(d,n)$ reactions on $^{56}$Ni, $^{48}$Ca, $^{26m}$Al and $^{24}$O targets at deuteron incident energies between 4 and 40 MeV/nucleon. Deuteron breakup is treated exactly within a continuum discretized coupled-channel approach. We found that an additional three-body force can noticeably alter the angular distributions at forward angles, with consequences for spectroscopic factors' studies. We also present the study of transfer to $2p$ continuum in the $^{25}$F$(p,2p)^{24}$O reaction, involving the same overlap function as in the $^{24}$O($d,n)^{25}$F case, quantifyng the differences in the spectroscopic factors due to additional $3N$-induced force.

Theory for knockout reactions

Knockout reactions with protons or light nuclei at intermediate energies have been used for many years as a tool to extract information of stable and exotic nuclei, e.g., single-particle structure, short-range correlations or cluster formation. They are often described theoretically in an eikonal approach that was applied rather successfully in the analysis. However, secondary processes might affect the cross sections, e.g., a knocked-out nucleon can destroy the core or target. There are different, but conflicting suggestions to include such effects, see, e.g., [1,2], and also the importance of the separation-energy is discussed [3]. In this contribution, the basic features of an alternative approach are presented that will be realized in a new reaction code. It relies on a statistical simulation of the reaction process that uses a modified eikonal approach in combination with single-particle wave functions from a mean-field model of the participating nuclei.

[1] C.A. Bertulani, Phys. Lett. B 846 (2023) 138250
[2] M. Gomez-Ramos, J. Gomez-Camacho, and A.M. Moro, Phys. Lett. B 847 (2023) 138284
[3] C. Hebborn and P. Capel, Phys. Lett. B 848 (2024) 138413

The development of radioactive-ion beams in the mid-80s has enabled the exploration of the nuclear chart far from stability. This technical breakthrough has led to the discovery of nuclear structures unobserved at the bottom of the valley of stability: shell inversion, halo nuclei etc. [1] At the heart of these discoveries are nuclear reactions used to probe the structure of short-lived nuclei. Breakup reactions, inclusive or exclusive, have been extensively used to study the single-particle structure of nuclei far from stability [2]. In particular, spectroscopic factors have been systematically inferred from knockout reactions on light targets, viz. $^9$Be or $^{12}$C. Unexpectedly, these values differ significantly from shell-model predictions [3]; they also do not agree with spectroscopic factors obtained from single-nucleon transfer measurements [4]. To try and understand these differences, we study systematically the sensitivity of nuclear-dominated breakup reactions to the projectile wave function [5,6,7,8]. Contrary to the common belief, these reactions remain quite peripheral, in the sense that they probe mostly the tail of the single-nucleon overlap wave function. More precisely, the knockout cross section scales very well with the rms radius of the projectile wave function, and not the square of its norm, i.e. the spectroscopic factor [8]. Since this is true for both loosely- and deeply-bound nucleons, this result may explain the systematic disagreement between various reaction probes. It also suggests a new method to infer the neutron radius of nuclei far from stability.

References:
[1] I. Tanihata, J. Phys. G, 22, 157 (1996).
[2] P.G. Hansen and J.A. Tostevin, Annu. Rev. Nucl. Part. Sci. 53, 219 (2003).
[3] A. Gade et al., Phys. Rev. C 77 (2008) 044306; Phys. Rev. C 103, 054610 (2021).
[4] J. Lee et al. Phys. Rev. Lett. 104, 112701 (2010).
[5] P. Capel and F.M. Nunes, Phys. Rev. C 75, 054609 (2007).
[6] C. Hebborn and P. Capel, Phys. Rev. C 100, 054607 (2019).
[7] C. Hebborn and P. Capel, Phys. Rev. C 104, 024616 (2021).
[8] C. Hebborn and P. Capel, Phys. Lett. B 848, 138413 (2024).

The Projected Generator Coordinate Method (PGCM) is a powerful and versatile many-body method that has been used for decades to study low-energy nuclear structure. In particular, the PGCM is particularly well suited to describe collective nuclear phenomena such as deformation or pairing. Also, a great strength of the method is the proper treatment of quantum numbers associated with the symmetries of the Hamiltonian that permits the unambiguous evaluation of the principal observables of interest in nuclear spectroscopy (spin and parity, electric quadrupole and magnetic dipole moments, reduced transition probabilities, $\ldots$). In the past, PGCM calculations have been mostly performed using phenomenological representations of the nuclear Hamiltonian. In recent years, however, we also developed numerical tools to perform advanced PGCM calculations based on microscopic Hamiltonians derived from Chiral Effective Field Theory (χEFT).

In this presentation, I will discuss the recent progress to anchor the PGCM in an ab initio philosophy and show new results on the spectroscopy of exotic light nuclei such as the neutron-rich isotope $^{16}$C. These calculations, based on modern χEFT interactions, demonstrate the power of the method to study the low-energy spectrum of short-lived nuclei produced in the new generation of radioactive ion beam (RIB) facilities. From a more general perspective, the development of more robust and predictive theoretical methods should prove helpful in the interpretation of new empirical data collected in future experiments performed with RIBs.

The proton-induced $\alpha$ knockout reaction, ($p,p\alpha$), is a powerful probe of the $\alpha$ formation in nuclei. It has been shown that a modern theoretical calculation of the $\alpha$ amplitude in the $^{20}$Ne ground state combined with the ($p,p\alpha$) reaction calculation by the distorted wave impulse approximation can quantitatively reproduce the experimental data [1]. On the other hand, quantitative reproductions of the $\alpha$ knockout cross section from medium to heavy nuclei are still challenging [2]. Stimulated by the theoretical prediction [3] and the $\alpha$ knockout reaction experiment of Sn isotopes [4], the universality of the $\alpha$ formation throughout the nuclear chart is also an interesting subject.
In this contribution, from a reaction theory point of view, I will present the recent progress in the $\alpha$ formation phenomena studied by the ($p,p\alpha$) reaction and our recent achievement which showed the possibility that the $\alpha$ knockout reaction may be a good probe for the $\alpha$ formation on the surface of the $\alpha$ decay nuclei [4]. I will also discuss the future perspectives of the $\alpha$ knockout reaction with regard to the ONOKORO project, which is being carried out mainly at RIKEN, RCNP and HIMAC in Japan.

[1] K. Yoshida et al., Phys. Rev. C 94, 044604 (2016) [arXiv:1603.00638].
[2] Yasutaka Taniguchi et al., Phys. Rev. C 103, L031305 (2021). [arXiv:2101.04820].
[3] S. Typel, Phys. Rev. C 89, 064321 (2014).
[4] Junki Tanaka et al., Science 371, 260 (2021).
[5] Kazuki Yoshida and Junki Tanaka, Phys. Rev. C 106, 014621 (2022). [arXiv:2111.07541]

While the independent particle picture that nucleons (protons and neutrons) move almost independently inside nuclei is well established, it is also known that several nucleons form a cluster and behave as a single entity in them. Nuclear clustering is a phenomenon that breaks the uniformity of nuclei and can be a key to elucidating the mechanism of alpha decay, determining the equation-of-state of neutron stars, etc. Therefore, experimental and theoretical studies have been intensively conducted [1] to answer such questions as ''What kind of clusters can exist?'' ''What kind of motion do they have in nuclei?'' ''Are they universal on the nuclear chart?'' and ''What mechanism does nuclear clustering realize?''

The proton-induced knockout reaction is one of the experimental methods to observe the presence of clusters and their motion in nuclei [2-9]. In this reaction, a proton collides with a nucleus at an energy of several hundred MeV per nucleon and knocks out a particle from the nucleus. The advantage of using this reaction is that because the incident energy is high, the proton does not perturb the nucleus very much, and we can approximately describe the reaction as the scattering of the proton and the cluster [10]. It allows us to extract information about the cluster in the nucleus with a relatively small uncertainty than other nuclear reactions.

From experimental data of knockout reactions, we can determine the orbital on which the cluster moved, i.e., the radial quantum number $n$, the orbital angular momentum $l$, and the total angular momentum $j$. One topic strongly related to the determination of $j$ is the Maris polarization [11, 12]. The Maris polarization is a phenomenon in which the sign of the analyzing power $A_y$ is reversed in a nucleon knockout reaction depending on whether the knocked-out nucleon moved on the $j=l+1/2$ or $j=l-1/2$ orbitals with the appropriate kinematic conditions (mainly the kinetic energies of the particles). The Maris polarization can also occur in cluster knockout reactions, but we can find only a few examples discussed except in nucleon knockout reactions. In this talk, I will introduce the Maris polarization and show how $A_y$ behaves for the three orbitals $j=l+1$, $l$, and $l-1$ when the spin is 1, using the deuteron knockout reaction as an example.

References:
[1] See, for example, T. Uesaka et al., Grants-in-Aid of Japan Society for the Promotion of Science, No. JP21H04975, https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-21H04975/.
[2] C. Samanta et al., Phys. Rev. C 26, 1379 (1982).
[3] K. Yoshida et al., Phys. Rev. C 94, 044604 (2016).
[4] K. Yoshida et al., Phys. Rev. C 98, 024614 (2018).
[5] K. Yoshida et al., Phys. Rev. C 100, 044601 (2019).
[6] J. Tanaka and Z. Yang et al., Science 371, 260 (2021).
[7] K. Yoshida et al., Phys. Rev. C 106, 014621 (2022).
[8] Y. Chazono et al., Phys. Rev. C 106, 064613 (2022).
[9] T. Edagawa et al., Phys. Rev. C 107, 054603 (2023).
[10] T. Wakasa et al., Prog. Part. Nucl. Phys. 96, 32 (2017), and references therein.
[11] Th. A. J. Maris, Nucl. Phys. 9, 577 (1958).
[12] G. Jacob et al., Phys. Lett. 45, 181 (1973).

The signature of the coexistence between single-particle, cluster and collective degrees of freedom of nuclei in reactions is a timely issue.
These rich aspects of the nuclear structure have been standardly described by simple shell models, cluster and collective structure models respectively.
Ultimately, the complexity associated to the coexistence traces back to the bare NN and NNN interactions which induce important NN correlations in nuclear medium, such as short ranged and tensor ones.
We shall reveal recent insights on aspects of many body degrees of freedom in the reaction mechanism for nucleon knockout from a stable/exotic projectile in the collision with a proton target.

We shall present a comprehensive analysis of (p,pN) reactions in inverse kinematics at around 400 MeV/A covering the mass range $\mathrm{A}\leq 12$ and including
Lithium, Beryllium, Carbon and Boron isotopes [1,2]. Total cross sections are calculated using
the many-body {\it ab initio} Quantum Monte Carlo fully correlated wave functions generated with the NN Argonne V18 and the NNN Urbana X (AV18+UX) potentials [3]
and merged into the Faddeev/Alt-Grassberger-Sandhas (F-AGS) [4] reaction formalism, which allows a consistent and simultaneous treatment of all channels, providing an exact solution of the three-body scattering problem for an assumed three-body Hamiltonian. A comparison with available data measured at GSI [5] will be shown.

Additionally, we shall present kinematically semi-inclusive and fully exclusive cross sections for {$^{12}\mathrm{C}(p,2p)$} in direct kinematics at 100 MeV/u, assuming a dynamical excitation of the $^{11}\mathrm{B}$ core during the scattering process
[6]. We use a generalized F-AGS with channel coupling,
where the fragment excited states are generated from a rotational model.
The results will be compared with available data measured at the IUCF
where the $^{11}\mathrm{B}$ final state can be in the ground and any of the low lying negative parity states
$\{3/2^{-},1/2^{-},5/2^{-},3/2_2^{-}\}$ [7]. These experiments show a strong population of the 4.44 MeV $(5/2^{-})$ state which cannot be understood from a dominant single-particle knockout with an inert core.

[1] R. Crespo, A.Arriaga, R. Wiringa, E. Cravo, A. Deltuva, A.Mecca, Phys Lett B 803, 135355 (2020).
[2] E. Cravo, R.B. Wiringa, R. Crespo, A. Deltuva, A. Arriaga, M.Piraulli, {\it Quenching of the quantum $p$- strength in light exotic nuclei}, to be submitted.
[3] R. B. Wiringa, et al.,Phys. Rev. C 89, 024305 (2014).
[4] E.~O. Alt, P. Grassberger, and W. Sandhas, Nucl.~Phys. {\bf B2}, 167 (1967).
[5] M. Holl et al., Phys. Lett. 795, 682, (2019).
[6] E. Cravo, R. Crespo, A. Deltuva, {\it Signature of single-particle and collective effects in kinematically exclusive observables for $^{12}$C(p,2p) at 100 MeV}, to be submitted
[7] D.W. Devins, et al. Aust. J. Phys, 32, 323 (1979).

The intrinsic view of quadrupole deformed nuclear rotors is
still prevalent in the community. In it, the shape is characterised by the
$\beta$ and $\gamma$ parameters. A lot of discussions have taken place
about the existence of "rigid" triaxial nuclei, i.e. having a well
defined value of $\gamma$. However, the only invariant quantities
that are physically relevant in the laboratory frame are the
Kumar invariants Q$^2$ and Q$^3$, from which $\beta$ and $\gamma$
can be deduced. We have been able to compute recently, without any
approximation, the higher order invariants (up to Q$^6$) that make it
possible to evaluate the variances of $\beta$ and $\gamma$. The conclusions
are that $\beta$ is softer that usually assumed, and that the $\gamma$ span at
1$\sigma$ is typically of 20-30º, at odds with the image of rigid triaxiallity.
I will touch upon as well some issues related to the extraction of these
shape parameters by means of ultra relativistic heavy ion collisions.

The $^{32}$Si(t,p)$^{34}$Si reaction was measured in inverse kinematics at a 6.3 MeV/u incident energy using the SOLARIS spectrometer at FRIB in order to study the structure of nuclei around the “island of inversion”. Outgoing protons were measured over an angular range of ~20-40 degrees (center-of-mass) and populated excited states of $^{34}$Si were identified at energies up to 7 MeV. Additionally, the $^{32}$Si($^{3}$He,d)$^{33}$P reaction was simultaneously measured, where populated excited states in $^{33}$P were identified at energies up to 5 MeV. Due to the nature of the data taken, several machine learning methods were utilized for event identification, including multi-class classification predictive modeling and anomaly detection. Analysis is ongoing; measured proton angular distributions from the (t,p) reaction for most states will be used in comparison with distorted wave Born approximations (DWBA) calculations to make tentative spin assignments, and the deduced spectroscopic amplitudes will be compared with occupation numbers from shell-model calculations. In addition, a complementary experiment, the $^{34}$S(t,p$\gamma$)$^{36}$S reaction to be carried out with the HELIOS spectrometer at the ATLAS facility at Argonne National Lab, will be discussed in terms of a more complete systematic study in the region.

This work was supported by the US Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357. This material is based upon work supported by NSF’s National Superconducting Cyclotron Laboratory which is a major facility fully funded by the National Science Foundation under award PHY-1565546; the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract Number DE-AC02-06CH11357 (Argonne) and under Award Number DE-SC0014552 (UConn); the Spanish Ministerio de Economia y Competitividad through the Programmes "Ramon y Cajal" with the grant number RYC2019-028438-I; the U.K. Science and Technology Facilities Council (Grant No. ST/P004423/1); and the International Technology Center Pacific (ITC-PAC) under Contract No. FA520919PA138. SOLARIS is funded by the DOE Office of Science under the FRIB Cooperative Agreement DE-SC0000661.

Since advent of the RIBF, the NaI(Tl) based scintillation array DALI2+ [1] has been the workhorse for in-beam $\gamma$-ray spectroscopy experiments with fast beams. Due to its modest energy resolution, caused by large opening angles and intrinsic energy resolution of NaI(Tl) scintillators, long absorption lengths of the scintillation material, as well as modest time resolution, the long-term potential is limited. Limited available budget makes low cost alternatives to 4$\pi$ Ge tracking arrays with superior features in terms of time resolution, full energy peak efficiency and peak-to-total, desirable. Consequently, a new-generation scintillator array for in-beam $\gamma$-ray experiments, the HYPATIA (HYbrid Photon detector Array To Investigate Atomic nuclei) project, has been launched in 2023. For HYPATIA, HR-GAGG and CeBr3 scintillators have been identified as the most promising crystals. Key advantages for the former include its high density, low radiation length, and that it's not hygroscopic and emits no self-activity, while the latter offers a better intrinsic resolution and extremely fast decay time.

HYPATIA is envisaged to be employed at different experimental stations of the upgraded RIBF and its magnetic spectrometers (ZeroDegree, SAMURAI, SHARAQ), each having different performance requirements and constraints. Key experiments to be carried out in the future at the RIBF at intermediate energies involve inelastic scattering on high-Z targets to induce Coulomb excitation, as well as inelastic scattering and quasi-free (p,2p) and (p,pn) reactions on liquid hydrogen.

In my presentation, I will provide an overview of the HYPATIA project, including how well its performance compares to other existing and planned $\gamma$-ray spectrometers, and examples of possible future experiments beyond spectroscopy
of the first excited 2$^+$ state.

[1] S. Takeuchi et al., NIMA 763, (596) 2014.

Halo nuclei have been a prolific field of Nuclear Physics since its discovery together with the dawn of radioactive beam facilities. The halo is formed by one or two weakly bound nucleons, usually neutrons, orbiting around the rest of nucleons that conforms a compact core. In the case of neutron halo, all the charge is inside core, and, so, a cornerstone in the study of neutron halo is the Dipole Electric Transition Probability, B(E1).

Such B(E1) distribution is usually obtained by performing Coulomb-dominated break-up reactions assuming that, under certain conditions, break-up is only due to dipole Coulomb excitation. Being also 11Be one of the most explored one-neutron halo and usually a benchmark for different models and theories, it is remarkable the fact that two different sets of 11Be on 208Pb data [1,2] led to apparently incompatible B(E1) distributions.

In this contribution we will show how an extension of the Continuum-Discretaized Coupled-Channels method, capable to introduce core excitations (XCDCC) can be used to study Coulomb break-up in order to extract the B(E1). We will discuss a recently proposed procedure which has been able to obtain compatible B(E1) from both data, giving an end to this long-standing discrepancy [3]. Finally, we will apply the same procedure to other cases of interest such us 15C and 19C.

[1] N. Fukuda, et al., Phys. Rev. C 70, 054606 (2004)
[2] R. Palit, et al., Phys. Rev. C 68, 034318 (2003)
[3] A.M.Moro, J.A.Lay, and J.Gómez Camacho, Phys. Lett. B 811, 135959 (2020)

T. Otsuka,1,2,3, Y. Tsunoda,4,5 N. Shimizu,4,5 Y. Utsuno,6,4 T. Abe,2 and H. Ueno2

1 Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
2 RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
3 KU Leuven, Instituut voor Kern- en Stralingsfysica, 3000 Leuven, Belgium
4 Center for Nuclear Study, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
5 Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577, Japan
6Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan

The shapes of heavy deformed nuclei have been believed, for seven decades, to be axially-symmetric as Bohr and Mottelson suggested from early days of nuclear physics1), providing textbook items. Very recent studies, however, demonstrate that this view may not be true, and that the nuclear shapes, if deformed, are triaxial more or less, not only in so-called gamma-soft nuclei but also in axially-symmetric deformed nuclei in the traditional scope. This feature is new, and was not reported even in our earlier work along the same line 2). Namely, recent advances have gone much beyond the outcome of the initial work 2). In fact, recent advanced studies with the state-of-the-art CI calculations by the QVSM (advanced version of MCSM) indicates that even a conventionally typical axially-symmetric prolate ground state of 154Sm is shown to be triaxial with gamma equal to 3.3 degrees. Such CI calculations successfully describe the structure of a number of heavy nuclei, with more developed triaxiality in other nuclei, for instance, 166Er. The driving forces for such triaxiality are two-fold from nuclear forces, making the triaxiality quite robust. One of them is the same monopole interaction producing the shell evolution in exotic nuclei, and is responsible for triaxiality with gamma equal to 7-10 degrees. The other is more universal, and makes the triaxial shape as equilibrium for virtually all nuclei, while the degree of triaxiality appears to be 3-5 degrees (but not zero). Gamma-soft nuclei, characterized by gamma being nearly 30 degrees, exist besides these nuclei. Because of the triaxiality, the so-called gamma band is shown not to be a gamma-phonon excitation a la Aage Bohr, but to be a K^P=2^+ band within the same triaxial members as the K^P=0^+ ground-band members. It is then of extreme interest to look for experimental approaches for possible verifications of this new picture. We will present some possible reactions from Relativistic Heavy-Ion Collisions (in LHC and RHIC), to multiple Coulomb excitations as a more conventional but powerful methodology. Besides them, direct excitations of the gamma band in nuclei, including those with small gamma angles like 154Sm, are of new interest. In such cases, the gamma band always exists, but may appear at higher excitation energy (> 2 MeV) with weaker but notable E2 strength, for smaller values of gamma. Thus, the search for possible signatures of a variety of the triaxiality will be discussed in this talk, as well as the new view of deformed shape itself. We will also ask the audience to think over possible other experimental approaches to such new perspectives of nuclear shapes and excitations.

References
1) Bohr, A. & Mottelson, B.R., Nuclear Structure (Benjamin, New York, 1975), Vol. II.
2) Otsuka, T., Tsunoda, Y., Abe, T., Shimizu, N., Van Duppen, P., Underlying Structure of Collective Bands and Self-Organization in Quantum Systems, Phys. Rev. Lett. 123, 222502 (2019).

In the nuclear chart the Nickel isotopic chain offers a unique opportunity to study the interplay between single-particle and collective excitations in atomic nuclei, for which important observables are the energy of the first 2$^+$ excited state in even-even nuclei and the reduced transition probability B(E2; 2$^+ \rightarrow 0^+$). The B(E2) can be indirectly measured via Coulomb Excitation (Coulex) and proton inelastic scattering. Coulex, being a purely electromagnetic probe under specific experimental conditions, is sensitive only to the proton contribution. Proton scattering, on the contrary, can assess the contribution of neutrons to the collectivity, and, more importantly, the ratio between the proton and neutron matrix elements.
In an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL) of the Michigan State University (MSU) we measured the ($p,p’$) inelastic scattering of the neutron-rich Ni isotopes $^{68,70,72}$Ni. Radioactive Ni beams impinged at 80-90 MeV/u on a liquid hydrogen target and the scattered beam particles were detected in the S800 spectrometer while the coincident $\gamma$ rays in the GRETINA $\gamma$-ray array. The high $\gamma$-ray energy resolution allowed to identify yrast and yrare states in these nuclei and, from the measurement of the inelastic scattering cross section, to deduce their deformation length $\delta$. Proton/neutron matrix elements have been extracted for the different coexisting shapes.
This experiment is complementary to a series of recent measurements in the region. The results, which will be presented at the conference, help drawing a more complete picture on the nuclear structure evolution along the $Z=28$ proton shell closure.

The $^{85}$Kr(d,p$\gamma$)$^{86}$Kr reaction has been carried out at 10 MeV/u in inverse kinematics at Argonne's ATLAS facility using the HELIOS spectrometer and the Apollo array. The neutron capture cross section on the radioisotope $^{85}$Kr (T$_{1/2}$ = 10.7 yr), an s-process branching point nucleus, carries a significant uncertainty due to the challenges of direct measurements. However, $^{85}$Kr can be accelerated as a pure beam, and the (d,p$\gamma$) reaction has been demonstrated to be a reliable indirect probe of the (n,$\gamma$)-reaction cross section. Neutron excitations from around 2-14 MeV in $^{86}$Kr were populated, where S$_n$=9.86 MeV, with a Q-value resolution of about 150 keV. The $\gamma$-ray emission probabilities as a function of excitation energy [P$_{p\gamma}$(E$_{ex}$)] were determined. The $2^+ \to 0^+$ and $4^+ \to 2^+$ $\gamma$-rays are clearly observed, showing the characteristic constant value of P$_{p\gamma}$ below S$_n$ and a decrease above S$_n$. These data are used to extract the cross sections for $^{85}$Kr(n,$\gamma$) reaction, complementing recent direct, high-precision measurements on the stable Kr isotopes. The technique has significant potential for future indirect (n,$\gamma$)-reaction studies.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract No. DE-AC02- 06CH11357. This research used resources of ANL’s ATLAS facility, which is a DOE Office of Science User Facility.

The development of collectivity along the N = Z is one of the subjects that has
recently attracted great experimental efforts. In particular, heavy N=Z nuclei
in the mass region A=80 are expected to be some of the most deformed ground
states which have been found [1] in mid-mass nuclei, typically 8p−8h, 12p−12h
for e.g. the cases of 76Sr, 80Zr. This strong enhancement of collectivity with respect to lighter N=Z nuclei has its origin in cross shell excitations across the N=40 shell gap to g9/2, d5/2 and s1/2 which are intruder quadrupole partners generating deformations. These structures can be interpreted in terms of algebraic Nilsson-SU3 self-consistent model to describe the intruder relative evolution in the vicinity of 80Zr [2]. In this presentation, we will expose some of the latest developments in microscopic nuclear structure calculations for exotic nuclei far from stabilitity at the N=Z [3]. The new theoretical calculations for the very region of 80Zr will be presented for the first time within the interacting shell model framework using an enlarged model space outside a 56 Ni core comprising the pseudo-SU3 p3/2f5/2p1/2 and quasi-SU3g9/2d5/2s1/2 orbitals for both protons and neutrons. We will present and compare results from both exact Shell Model diagonalization [4] and our newly developed DNO Shell Model approach employing beyond mean field techniques [5]. These theoretical calculations allow a very good description of the rapid transition (A=60−100) from spherical to deformed structures which can be intepreted in terms of “simple” many particles - many holes configurations. The whole Island of Collectivity in the region and sudden shape change recently observed between 84Mo and 86Mo is interpreted as an effect on the N = 50 gap induced by the addition of the two neutrons, a fingerprint of three-body forces.
[1] R. D. O. Llewellyn et al., Phys. Rev. Lett. 124, 152501 (2020).
[2] A. P. Zuker et al., Phys. Rev. C 92, 024320 (2015)
[3] D. D. Dao, F. Nowacki, A. Poves in preparation
[4] E. Caurier, G. Martı́nez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker, Rev. Mod.
Phys. 77, 427 (2005).
[5] D. D. Dao and F. Nowacki, Phys. Rev. C 105, 054314 (2022).

Super-radiance was first studied by Dicke [1] within the context of coherence effects in spontaneous radiation processes. Since then, the phenomenon has been referenced in many areas of modern science, among them: quantum optics, condensed matter, biophysics, and nuclear physics (See the reviews in Refs. [2,3]).

In atomic nuclei, seen as a complex open quantum many-body system, the effect arises from the coupling to continuum states that can be treated in terms of a non-hermitian hamiltonian (non-hermitian super-radiance). Increasing coupling to the continuum leads to the separation of long-lived and short-lived (super-radiant) resonance states.

In a recent Nature physics communications [3], Volya and collaborators reported strong evidence for the phenomenon in alpha cluster decays of mirror nuclei 18O and 18Ne. The authors state that “these findings may be the clearest manifestation of the super-radiance in nuclear physics to date.”

In this work we study the effect of continuum coupling on two-neutron transfer reactions such as (t,p). Following the framework discussed in Ref. [3], we consider the simple case of a two-level model to obtain two-neutron transfer amplitudes (TNAs). Our results show a clear transition between the normal and super-radiance regimes, which is marked by a sharp reduction of the ground-state to ground-state transition strength, being now shared between the long-lived and super-radiant resonance states.

Some examples of possible experimental studies, where the effect could be observed, will be discussed.

[1] R. J. Dicke, Phys. Rev. 93, 99 (1954).
[2] N. Auerbach, V. Zelevinsky, Rep. Prog. Phys. 74, 106301 (2011)
[3] I. Rotter, J.P. Bird, Rep. Prog. Phys. 78, 114001 (2015)
[4] A. Volya, M. Barbui, V. Z. Goldberg, and G. V. Rogachev, Nature Comm. Physics 5:322 (2022)

• This work was supported by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344

The rapid (r) neutron-capture process produces half the elements heavier than iron and is located on the neutron-rich side of the nuclear chart. Promising site candidates such as core-collapse supernovae (CCSNe) and neutron star mergers still show large discrepancies between observed and calculated abundances. The calculations mostly rely on theoretical neutron-capture cross sections which depend on two reaction processes: direct radiative capture and compound nuclear (CN) mechanism. Neutron capture on 130Sn strongly influences final abundances around the second and third r-process peaks, however, the CN mechanism lacks empirical data.
Turning attention to the neutron-deficient side of the nuclear chart, light nuclei in this region may be produced in the neutrino-induced rapid-proton capture (νp) process, proposed to occur in the innermost ejecta of CCSNe. This is a promising solution to synthesize isotopes not adequately produced in the proton capture (p) process (occurring within the O/Ne layer of CCSNe), particularly 92,94Mo and 94,96Ru. The 56Ni(n,p)56Co reaction is a crucial branching point between the vp- and p- processes and thus governs the abundances of heavier elements, however, its cross section lacks measurement.
To address these knowledge gaps of the 130Sn(n,γ) and 56Ni(n,p) reactions, the surrogate technique was employed using (d,p) transfer reactions on 130Sn and 56Ni, respectively. This experiment campaign was led by the SAKURA collaboration using the BigRIPS-OEDO beamline housed at RIBF in RIKEN, Japan. The heavy radioactive ion beams were produced and separated by the BigRIPS accelerator. Using OEDO the 130Sn (56Ni) beam was decelerated to ~ 22 (15) MeV/u and focused onto a CD2 solid target, thus populating excited states under inverse kinematics. Light charged particles were detected at backward lab angles using the TiNA array. Heavy reaction products were momentum-analyzed at forward angles by the SHARAQ spectrometer and identified using the Bρ-dE-range technique. This approach has a distinct advantage whereby the gamma-emission probabilities of compound nuclear states may be determined with no gamma-ray detection necessary. In this talk, the experimental procedure and preliminary results are presented, with an emphasis on the capabilities of OEDO.

The Active Target Time Projection Chamber (AT-TPC) has been used in experiments aimed at the exploration of structural effects in radioactive nuclei using one step reactions such as transfer or elastic and inelastic scattering. When used as a solenoidal spectrometer by placing it inside a magnetic field, the AT-TPC allows to perform this type of measurement in inverse kinematics with much reduced beam intensities, down to 100 particles per second, while preserving a good resolution and a wide range of angular coverage. This presentation will showcase the performance of this detector, based on recent results obtained on nuclei in the beryllium to carbon region using pure proton, deuterium and alpha targets. Highlights will include results on resonances in $^{11}$Be that are indicative of cluster configurations, as well as new results on single particle configuration in unbound states of neutron-rich carbon isotopes.
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract No. DE-AC02- 06CH11357. This research used resources of ANL’s ATLAS facility, which is a DOE Office of Science User Facility and used resources of the Facility for Rare Isotope Beams (FRIB) Operations, which is a DOE Office of Science User Facility under Award Number DE-SC0023633.

Several properties of atomic nuclei are known to be sensitive to the neutron-to-proton (isospin) asymmetry. In particular, the evolution of the single-particle strength as a function of isospin has been the subject of experimental and theoretical debate.
Quasi-free scattering (QFS) reaction is an established method to probe the structure of atomic nuclei. This reaction in inverse kinematics using radioactive-ion beams at relativistic energies has been successfully employed as an effective tool to study very exotic nuclei with high luminosity. Recent studies [1, 2] reported on the evolution of the proton single-particle strength as a function of isospin asymmetry using (p,2p) QFS reactions along the Oxygen isotopic chain and found a weak or no dependence. The reduction of the single-particle strength has been attributed to nucleon-nucleon correlations and a recent phenomenological study [3] has quantified the long and short-range part of these correlations and their dependency with isospin. The QFS result is at variance with nucleon-removal reactions with heavy targets [4] where they report a single-particle strength is strongly correlated with isospin.
To shed light on this puzzle, we performed a systematic study of (p,2p) and (p,pn) cross sections along the calcium isotopic chain (from 39Ca to 50Ca) at 500 MeV/nucleon using proton and carbon targets. The experiment was performed with the large acceptance spectrometer GLAD with the R3B setup at GSI-FAIR. The difference in reactions with the targets and the identification of reactions with recoil protons are investigated. The results of the analysis and comparison to the theoretical calculations will be discussed in this contribution.

[1] L. Atar et al., Phys. Rev. Lett. 120, 52501 (2018).
[2] Shoichiro Kawase et al., Prog. Theor. Exp. Phys. 2018, 021D01.
[3] S. Paschalis, M. Petri, A. O. Macchiavelli, O. Hen, E. Piasetzky, Phys. Lett. B 800, 135110 (2020).
[4] J. A. Tostevin and A. Gade, Phys. Rev. C 90, 057602 (2014).

Astrophysical objects such as neutron star formation and structure and supernovae explosion, as well as nuclei properties and structure are described using the equation of state of nuclear matter. However, the coefficients of the equation state describing the nuclear matter with a huge charge asymmetry, notably the symmetry energy, is lacking constraints [1,2].
When a medium-to-heavy neutron-rich nuclei near the neutron drip-line is submitted to an external electric field, its response is concentrated in the Giant Dipole Resonance (GDR) and particularly in its low lying part, referred as the Pygmy Dipole Resonance (PDR). The electric dipole polarizability aD, which represents the inversely energy-weighted sum of dipole strength, allow to quantify this response.
Neutron skin presents a strong correlation to symmetry energy and can be constrained through the use of aD [3,4], and theoretical calculation has shown that the PDR strength has a rapid increase with the neutron number number in the range 15 < N ≤ 16, 28 < N ≤ 34, and 50 < N ≤ 56 [5]. In this context, both 50Ca and 52Ca, who respectively have 30 and 32 neutrons, has been a subject to experimental investigation: they were produced in flight at RIBF – RIKEN and they have been submitted to coulomb excitation using a 208Pb target in order to probe the neutron number dependence of PDR. We will present preliminary results for 50Ca.

[1] F. J. Fattoyev and J. Piekarewicz – Phys. Rev. C 86, 015802 (2012)
[2] J. Margueron et al – Phys. Rev. C 97, 025805 (2018)
[3] A. Tamii et al. – Phys. Rev. Lett., 107 062502 (2011)
[4] A. Tamii et al. – Eur. Phys. J. A, 50 (2014) 28
[5] T. Inakura et al – Phys. Rev. C 84, 021302R (2011)

Nuclear shell evolution towards the driplines, characterized by the quenching or collapse of conventional magic numbers, may lead to the emergence of new sub-shell closures. Notably, the calcium isotopes, featuring a robust proton Z = 20 shell closure and encompassing the doubly magic isotopes 40Ca and 48Ca, alongside experimental evidence of new neutron sub-shell closures at N = 32 and 34, provide an ideal testing ground for exploring the evolution of shell structure and magic numbers.

Although surface nucleons properties in calcium have been extensively studied, probing the structure of deeply bound nucleons remains a challenge. In this presentation, we will report the first invariant-mass measurement of unbound states in 53Ca and 55Ca, populated from one-neutron knockout reaction at the RIKEN Radioactive Isotopes Beam Factory. The reaction of interest was induced by the secondary beam of 54,56Ca bombarding on a 151-mm-long liquid hydrogen (LH2) target within the MINOS device, featuring a surrounding time projection chamber for reconstructing the reaction vertex. Population to unbound states of 53,55Ca was followed by forward directed neutron emission, detected by two large-acceptance NEBULA and NeuLand plastic scintillator array. The de-excitation γ rays emitted from fragments were detected by the DALI2+ array, consisting of 226 NaI(Tl) crystals surrounding the MINOS device. Reaction residues were identified and measured by the SAMURAI spectrometer.

The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum l assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41) keV in 53Ca and 6000(250) keV in 55Ca indicate a significant l = 3 component, providing the first experimental evidence for the f7/2 single-particle strength of deeply bound hole-states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the νf7/2 single-particle in 56Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and ab initio calculations.

Neutron-rich calcium isotopes show interesting features exhibiting non-canonical neutron shell closures at N=32 and N=34, while their charge radii [1] show a sharp increase after N=28 which is not reproduced by microscopic theories. Matter radii [2] from interaction cross-section measurements indicate that the increase in size of neutron-rich calcium isotopes is mainly due to neutrons and that a core swelling mechanism is at play [3].
Recently, the proton-induced neutron knockout reaction on $^{52}$Ca proved to be able to quantify the size of the p$_{3/2}$ and f$_{7/2}$ neutron single-particle orbital using the analysis of the momentum distributions [4]. The result revealed a large p$_{3/2}$ neutron orbital, 0.61 fm larger compared to the f$_{7/2}$ neutron single-particle orbital, which may explain [5] the large charge radius values obtained for the neutron-rich calcium isotopes [1].
This analysis was extended to $^{53}$Ca and $^{54}$Ca for the neutron orbitals, giving consistent results with the first findings, as well as for $^{52}$Ca, $^{54}$Ca, and $^{55}$Sc for the proton single-particle orbitals. The latest results will be shown in this presentation.
The nucleon knockout direct reaction proves to be a valuable tool, sensitive to the size of the single-particle orbitals - a quantity that has not been deeply explored so far for exotic beams.

References:
[1] R. F. Garcia Ruiz et al., Nature Physics 12, 594–598 (2016).
[2] M. Tanaka et al., Phys. Rev. Lett. 124, 102501 (2020).
[3] W. Horiuchi and T. Inakura Phys. Rev. C 101, 061301(R) (2020).
[4] M. Enciu et al., Phys. Rev. Lett. 129, 262501 (2022).
[5] J. Bonnard, S. M. Lenzi, and A. P. Zuker, Phys. Rev. Lett. 116, 212501 (2016).

The neutron-deficient calcium isotopes have attracted considerable attention recently. Present studies are divided over the amount of proton pf-shell occupancy, ranging from an intact $Z=20$ shell closure [1] to a considerable weakening already in the vicinity of doubly-magic $^{40}$Ca [2,3].

Two-neutron removal, a direct reaction sensitive to the single-particle configurations and couplings of the removed neutrons in the projectile wave function, from $^{38}$Ca populating states of $^{36}$Ca was performed at the National Superconducting Cyclotron Laboratory. Inclusive and final-state exclusive cross sections along with longitudinal momentum distributions are compared to predictions combining eikonal reaction theory and shell-model two-nucleon amplitudes [4,5].

The results yield conclusive evidence for the need of sizeable proton cross-shell excitations into the pf shell already for the $0^+_1$ and $2^+_1$ states of $^{36}$Ca [6]. These findings furthermore enable a close reproduction of additional observables. Ultimately, a schematic modification of sd - pf shell gap is introduced serving as a proxy for the magnitude of proton cross-shell excitations.

[1] Miller et al., Nat. Phys. 15, 432 (2019).
[2] Caurier et al., Phys. Lett. B 522, 240 (2001).
[3] Dronchi et al., Phys. Rev. C 107, 034306 (2023).
[3] Tostevin et al., Phys. Rev. C 74, 064604 (2006).
[4] Simpson et al., Phys. Rev. Lett. 102, 132502 (2009).
[5] Beck et al., Phys. Rev. C 108, L061301 (2023).

Neutron-rich Ca isotopes towards neutron number N = 34 are pivotal for exploring the evolution of the fp-shell orbitals [1]. Beyond the N = 28 shell gap at 48Ca, new magic numbers at N = 32 and 34 were established through spectroscopy of low-lying states [2] and mass measurements [3]. Most recently, the spatial extension of the 1f7/2 and 2p3/2 neutron orbitals was determined via a one-neutron knockout reaction from 52Ca [4], while the single-particle 2p1/2 , 1f5/2 and 1g9/2 orbitals defining the shell gaps at N = 32, 34 remain to be established experimentally. The 50Ca(d, p)51Ca transfer reaction presents itself as well suited-method to access spectroscopic factors in the fp-shell, where the angular distribution of the reaction products allow for deduction of the angular momentum transfer.

In Decemeber of 2022 the SHARAQ12 experiment was performed at the RIKEN Nishina Center, aiming to study the single-particle structure of 51Ca via the (d, p) reaction using a 50Ca secondary beam. The secondary beam was produced at the BigRIPS separator and then degraded to approximately 15 MeV/nucleon at the OEDO [5] beamline. Beam-tracking has been performed with the recently developed Strip-Readout PPAC detectors [6], recoiling protons coming from the interaction of the beam with the secondary target of CD2 (260 μg/cm2) have been identified with the detector setup TINA2 [7], while the heavy recoils have been identified at the QQD SHARAQ spectrometer. In this contribution, I will present the experiment, current status of the analysis, and the implications on the structure of neutron-rich Ca isotopes.

Relativistic Coulomb excitation in inverse kinematics can be utilized to study the electric dipole response of projectile neutron-rich nuclei. In such conditions, collective excitations arise where neutron and proton densities of the excited nucleus are displaced with respect to each other. Additionally, access to greater isospin asymmetries on the neutron-rich side of the nuclide chart provide a suitable environment to probe the symmetry energy, a crucial yet still fairly unknown ingredient of the nuclear equation of state.

In Ref. [1] a novel approach to constrain the slope of the symmetry energy $L$, i.e. the linear coefficient in the expansion of the symmetry energy around saturation density, is explored for the first time by measuring the Coulomb-excitation cross section $\sigma_C$ of neutron-rich nuclei at relativistic energies. This particular cross section correlates with the dipole polarizability $\alpha_D$, and through the established correlation between $\alpha_D$ and $L$, enables constraining the symmetry energy by measuring $\sigma_C$. The advantage of using $\sigma_C$ instead of $\alpha_D$ lies in simpler measurement and analysis procedure.

This approach was further examined in the experiment carried out using the large acceptance spectrometer R$^3$B-GLAD at the GSI accelerator facility as a part of the FAIR Phase-0 campaign [2]. Tin isotopes in the mass range 124-134 were produced as a secondary beam in the fragmentation and fission reactions at energies close to 1 GeV/u and impinged onto the lead target which provided a Lorentz-contracted field to induce Coulomb excitations. De-excitation followed through the emission of gammas and neutrons, which were detected using the CALIFA gamma calorimeter [3] and the NeuLAND neutron detector [4]. The remaining fragment nuclei were detected by tracking detectors located before and after the GLAD magnet, altogether providing a kinematically complete measurement.

[1] A. Horvat, Doctoral thesis, Technische Universität Darmstadt (2019).

[2] R$^3$B Collaboration, https://www.r3b-nustar.de/.

[3] H. Alvarez-Pol, et al., Nucl. Instrum. Meth. A, 767, 453-466 (2014).

[4] K. Boretzky, et al., Nucl. Instrum. Meth. A, 1014, 165701 (2021).

The Sn isotopes, containing the longest chain of isotopes between two doubly-magic nuclei, offer a fundamental testing ground for nuclear theories. Between the $N = 50$ and $N = 82$ shell closures, the $2^{+}_{1}$ energies of all Sn isotopes are well established and show an almost constant value, as expected in the generalized seniority scheme. Within the same framework, the $B(E2)$ values should resemble an inverted parabola peaking at mid-shell. However, measurements in the most proton-rich Sn isotopes have shown a clear deviation from the expected behavior, with an enhancement of the transition probabilities towards $^{100}$Sn. Although different calculations tend to agree on the neutron-rich side of the chain, significant differences are observed in the proton-rich side. This is particularly true for $^{102}$Sn, where the difference between the predictions amounts to almost a factor of 3, making this isotope a good candidate for the investigation of the effects driving the nuclear structure in the vicinity of $^{100}$Sn.

An experiment to measure for the first time the $B(E2)$ values in the $N=52$ isotones towards $^{100}$Sn, including $^{102}$Sn, was performed at the Radioactive Isotope Beam Factory in Japan. A 345 MeV/nucleon beam of $^{124}$Xe was fragmented on a 5-mm-thick Be target at the entrance of the BigRIPS separator. The $N=52$ isotones of interest were identified on an event-by-event basis using the $B\rho-\Delta E-B\rho$ technique. A 0.5-mm Au target placed at the F8 focal plane was used to induce Coulomb excitation. Outgoing fragments were identified using the ZeroDegree spectrometer. The Au target was surrounded by the high-efficiency DALI2$^{+}$ $\gamma$-detector array, composed of 226 NaI(Tl) detectors. Preliminary results on the Coulomb excitation cross sections and transition probabilities for $^{98}$Pd, $^{100}$Cd and $^{102}$Sn will be presented, and their comparison with shell model and ab-initio calculations will be discussed.

An anomaly in the energy differences of mirror nuclei and isobaric analogue states (IAS), not yet well understood from a microscopic point of view, was found more than 50 years ago and is called the Okamoto-Nolen-Schiffer (ONS) anomaly. A systematic study from light to heavy nuclei within the framework of the independent-particle model found that the theoretical values of the energy difference underestimate always the experimental values by 3–9%.
A possible main source to cure the gap is the charge symmetry breaking (CSB) nuclear interaction. However, both the magnitude and the sign of the parameters in CSB interactions have not been well determined from phenomenological studie.

The aim of this study is to provide a quantum chromodynamics (QCD)-based understanding of CSB by making a quantitative link between the Skyrme-type CSB interactions and the CSB effect due to the u-d quark mass difference in QCD. A novel approach is proposed to link the CSB nuclear interaction and the low-energy constants in QCD and the density dependence of chiral condensation of q ̄q pair in the nuclear medium for the first time.

The resulting QCD- based CSB interaction is applied to resolve the ONS anomaly: the numerical results for the mirror nuclei (A = 16±1 and A = 40±1 with the isosymmetric core N = Z = A/2) with the two Skyrme EDFs show good agreement with experimental data both in sign and magnitude within the theoretical error bars. Other several possible effects on ONS anomaly were also considered in the study. Major theoretical uncertainty of the final results originates from the low-energy constants of QCD. Increasing the accuracy of these constants from the experimental data or from the lattice QCD simulations will be instrumental. The QCD-based CSB interaction discussed here would have strong impact on isospin symmetry breaking phenomena such as IAS, the super-allowed β decay in the context of Cabibbo-Kobayashi-Maskawa unitary matrix, and the mass predictions of isobar and isotriplet nuclei near the proton drip line.

Further extension of QCD-based isospin breaking forces (IBS) including the charge invariance breaking (CIB) will be discussed in the study of IAS and also hypernuclei.

The s-wave neutron-nucleus scattering length $a_s$ characterizes the low-energy neutron scattering off nuclei. In the effective-range approximation, the neutron-nucleus scattering cross-section at very low energies tends to $4𝜋a_s^2$, giving to the scattering length a sense of nuclear apparent size experienced by a neutron approaching at low energy. Its specific value is the result of a complex balance between the attractive individual neutron-nucleon potential and the repulsion generated by the Pauli principle with respect to the other neutrons in the nucleus. As such, it oscillates between positive and negative values (respectively for bound and virtual states) with increasing nuclear mass, with absolute values ranging from the about 20 fm of the n-N systems to the few fm for light nuclei.
However, in $^{17}$B the peculiar balance between attraction and repulsion leads to a spectacular increase in absolute value, with an upper limit of $a_s$<-50 fm provided by the only existing measurement [1]. Letting aside the anomalous value in itself, the fact that adding an extra neutron to the system leads to the weakly-bound two-neutron halo nucleus $^{19}$B may have strong physics implications. The three-body system $^{17}$B+n+n would be thus built from two scattering lengths, a large one of about 20 fm and a potentially huge one of tens, hundreds or even thousands of fm, opening the debate about possible Efimov states in $^{19}$B and the description of nuclei at the unitary limit [2].
We have determined this essential observable by using a series of nuclear reactions leading to the $^{17}B$+n final state. The experiments were performed at the RIKEN Nishina Center as part of the SAMURAI Day1 campaign (for experimental details see for example [3]). A series of secondary beams ($^{19}$B, $^{18,19,20}$C, $^{20,21,22}$N) at about 250 MeV/N were tracked onto a carbon target. The reaction products of interest, $^{17}$B and neutrons, were detected respectively by the SAMURAI spectrometer and the NEBULA array, and the energy of the $^{17}$B+n system was reconstructed by invariant mass. With respect to the previous measurement [1], the large acceptance of the SAMURAI+NEBULA setup has allowed for a complete observation of the virtual state, and the better resolution coupled to the high intensity of the secondary beams has led to a precise characterization of its line shape.
The ($^{19}$C,$^{17}$B+n) reaction is found to populate exclusively the virtual state, as expected by the s-wave neutron halo character of $^{19}$C, and has been used for the determination of a n-$^{17}$B scattering length of the order of a thousand fm, taking into account the structure of the initial state. Moreover, the high acceptance and resolution has allowed for the first measurement of the n-$^{17}$B effective range, governing the second term of the effective-range expansion, and for an exploration of the next term, related to the shape of the potential. The ($^{19}$B,$^{17}$B+n) reaction populates the virtual state but also two additional resonances. While the latter represents the first spectroscopy of $^{18}$B, the line shape of the former is found to be very sensitive to the neutron separation energy S$_n$ of $^{19}$B. We will discuss how these results constrain the value of S$_n$($^{19}$B), and as a consequence S$_{2n}$ and the mass of $^{19}$B.

The deuteron elastic and inelastic scattering reactions of $^{10}$Be have been measured with the AT-TPC coupling with SOLARIS in inverse kinematics. The deformation length of the excited states in $^{10}$Be below 9 MeV has been inferred from the differential cross sections with the CCBA calculation. A new $1^-$ state at 7.27(10) MeV, located just near the $\alpha$-emission threshold, has been observed for the first time. It exhausts a large fraction of the isoscalar dipole energy-weighted sum rule, and has isoscalar characteristics, suggesting a strong $\alpha$ cluster structure in $^{10}$Be. The Gamow Coupled Channel approach supports this interpretation and suggests the near-threshold effect might be playing a role in this excitation energy domain. The $2\alpha+2n$ four-body calculation also support this picture and could reasonably reproduce the large E1 strength observed.

This material is based upon work supported by NSF’s National Superconducting Cyclotron Laboratory which is a major facility fully funded by the National Science Foundation under award PHY-1565546; the U.S.\ Department of Energy, Office of Science, Office of Nuclear Physics, under Contract Number DE-AC02-06CH11357 (Argonne). SOLARIS is funded by the DOE Office of Science under the FRIB Cooperative Agreement DE-SC0000661.

Nuclei that present a three-body character have attracted special interest over the past few decades. Of particular relevance is the case of Borromean two-neutron halo nuclei, e.g., 6He, 11Li or 14Be, which exhibit exotic features in nuclear collisions [1]. The correlations between the valence neutrons, often described in terms of pairing, are known to play a fundamental role in shaping the properties of these systems [2,3]. The evolution of these correlations beyond the driplines gives rise to two-neutron emitters, e.g., 13Li, 16Be or 26O [4]. Since they have a marked core+N+N character, three-body models are a natural choice to analyze their structure and processes involving them [5, 6]. The description of the continuum in three-body nuclei, however, is not an easy task. In Ref. [7] we proposed a method to characterize few-body resonances from the time evolution of the lowest eigenstates of a resonant operator in a discrete basis, with the aim of studying the population of these systems in knockout reactions. The relative-energy distributions in their decay can be computed by solving an inhomogeneus equation with a source term involving the resonance eigenstate [8]. The method has been applied to 16Be [9] and 13Li [10], showing signatures of direct two-neutron decay, and in good agreement with recent experimental observations. These unpublished results will be presented, together with prospects for future developments and applications.

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In order to constrain the largely unknown multi-neutron interactions, it is necessary to measure the relevant observables sensitive to them. One such property is the possible existence of narrow resonances related to multi-neutron cluster structures and correlations$^{[1][2]}$. This can be investigated by studying multi-neutron resonances close to the corresponding neutron removal thresholds in neutron-rich light nuclei. Progress over the recent years has presented several evidences of such narrow resonances$^{[3][4][5]}$, which provides an indication for the generalization of the Ikeda conjecture.

With the aim of systematically studying such resonances and characterizing the corresponding nn-relative system, an experiment was performed at the R$^{3}$B setup in GSI, within the FAIR Phase-0 program. Quasi-free scattering $(p,2p)$ reactions are studied in inverse kinematics where a radioactive ion "cocktail" beam is impinged on a 5cm LH$_{2}$ target. The resulting reaction products are measured in the state-of-the-art setup using a large combination of detector systems providing information of the full reaction kinematics. Since the objective is to reconstruct the relative energies of the neutrons excited to the continuum, it is necessary to detect the corresponding neutrons. This is facilitated by the neutron detector NeuLAND$^{[6]}$, which thanks to its high resolution and granularity provides access to the detailed study of multi-neutron resonances. A brief description of the first 2-neutron reconstruction will be provided.

In this communication the results of the nn-relative energies for selected isotopes in the "cocktail" beam will be discussed along with relevant spectroscopic information. The discussion will include the analysis of the $^{15}B(p,2p)^{14}Be$ system with the near threshold $2_{1}^{+}$ state of $^{14}Be$$^{[3][7]}$ as a standardizing tool. This will be followed by a discussion on the study of $^{17}B$ populated via $^{18}C(p,2p)^{17}B$ reaction, serving as an isotope of interest for the current study owing to a previous indication of a possible near threshold state$^{[8]}$.

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Unbound states in the neutron-rich $^{17}$C nucleus were probed via the $^{16}$C(d,p) transfer reaction in inverse kinematics using the Active Target Time Projection Chamber (AT-TPC) placed in the HELIOS solenoid at the ATLAS facility in Argonne National Laboratory. A wide range of excitation energies from the ground state to approximately 10 MeV were measured using a $^{16}$C radioactive beam at 12 MeV/u and a pure deuterium gas active target. Using the large angular coverage and high luminosity of the AT-TPC , the angular distributions of these $^{17}$C resonances were observed, with an aim to make preliminary spin-parity assignments and determine spectroscopic factors. These findings are compared to recent results obtained from invariant mass spectroscopy and shell model calculations. Their study, in particular the p-shell hole negative parity resonances, are especially interesting in probing cross-shell monopole-based interactions.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract No. DE-AC02- 06CH11357. This research used resources of ANL’s ATLAS facility, which is a DOE Office of Science User Facility and used resources of the Facility for Rare Isotope Beams (FRIB) Operations, which is a DOE Office of Science User Facility under Award Number DE-SC0023633.

The large branching ratio observed in the $\beta$-delayed proton emission of $^{11}$Be was explained with the existence of a narrow near-threshold proton emitting resonance in $^{11}$B. The direct measurement of this process raised a heated debate around the properties of this resonance and the unusually large $\beta$-decay
branching ratio populating it. Since then, there were several experiments that reported the observation of such an elusive resonance. While there is a widespread agreement on the existence of this resonance, from both theoretical and experimental stand points, there are still many open questions around its nature. One of the main challenges lies in the description of the complex structure of $^{11}$B and the role of the continuum coupling with four different particle emission thresholds in about 2 MeV of excitation energy. Moreover, the properties of the states in the vicinity of these thresholds, critical to understand the structure of $^{11}$B, are either not known or poorly constrained. With the intention of clarifying such an entangled situation, we performed an experiment to investigate the $^{11}$B structure at high excitation energy through the $^{10}$B(d,p) reaction in inverse kinematics using the HELIOS spectrometer. The detection of the protons in coincidence with heavy recoils in inverse kinematics enabled the determination of low-probability branching ratios of several states around particle emission threshold and their widths. The much debated near-proton-threshold resonance at 11.4 MeV was observed thanks to the high-quality recoil identification.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract No. DE-AC02- 06CH11357. This research used resources of ANL’s ATLAS facility, which is a DOE Office of Science User Facility and used resources of the Facility for Rare Isotope Beams (FRIB) Operations, which is a DOE Office of Science User Facility under Award Number DE-SC0023633. This work has received financial support from Xunta de Galicia (CIGUS Network of Research Centers) and from the Spanish Ministerio de Economía y Competitividad through the Programmes “Ramón y Cajal” with the Grant No. RYC2019-028438-I.

Nuclear resonant states far from the stability line provide a stringent test of nuclear forces at extreme isospin asymmetry. In this talk, I will report on the low-lying resonant states of extremely neutron-rich $^{9}$He and $^{10}$He populated via the (p, 2p) reaction from the 2n-halo nucleus $^{11}$Li at ~250 MeV/nucleon. The obtained $^{9}$He spectrum shows a clear peak at 1.2 MeV with a width of ~ 1 MeV, which is probably a p-wave resonance. The resonance parameters play a key role to understand the $^{8}$He-neutron interactions. The $^{10}$He spectrum was obtained from the three-body invariant mass of $^{8}$He+2n, with much higher statistics than previous measurements [1,2]. The spectrum was compared to the theoretical calculation that combines the coupled-channel three-body model of ${11}$Li [3] and the quasi-free knockout (p, 2p) reaction model [4,5]. Two low-lying 0$^{+}$ resonant states of $^{10}$He were identified at ~ 1 MeV and at ~2 MeV, which have a [s$_{1/2}$ s$_{1/2}$]0$^{+}$ configuration and a [p$_{1/2}$ p$_{1/2}$]0$^{+}$ configuration, respectively.

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[5] Y. Kubota et al., Phys. Rev. Lett. 125, 252501 (2020).

The ratio method [1-3] is a novel method to extract important structural information of halo nuclei, such as binding energies and ANCs (Asymptotic Normalizing Coefficients). It is based on the Recoil Excitation Breakup (REB) model [4], which predicts that the uncertainty of halo structures related to the reaction dynamics is strongly reduced by taking the ratio of angular distributions for breakup and scattering. Accordingly, this new reaction observable exhibits a largely improved accuracy compared to traditional methods, such as Coulomb breakup. We will present the first experimental test of the method for the 11Be + 12C collision at Elab=20 MeV/u. The experiment was performed at the Texas A&M University cyclotron. Angular differential cross sections for elastic and inclusive neutron breakup cross sections were measured with a Si + phoswich detector array, BlueSTEAl [5], at CM angles =10-30 deg. The measured cross sections were well-reproduced by theory calculations using CDCC and Dynamical Eikonal Approximation (DEA) [6]. The ratio of the inclusive breakup to elastic cross section demonstrates the validity of the new method. Further calculations have shown that it is independent of optical potentials used to describe the projectile-target interaction and is sensitive to the halo structure. We have extended our analysis to available 11Be + 208Pb data, confirming that the ratio method works well both for nuclear-dominated and Coulomb-dominated reactions. This augurs well for our plan to extract structure information of further exotic halo nuclei (e.g., A=20-40). In this contribution, we will present the research results above and discuss our future plans to apply the ratio method with exotic beams at FRIB.

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*The work at Brookhaven National Laboratory was sponsored by the Office of Nuclear Physics, Office of Science of the U.S. Department of Energy under Contract No.DE-AC02-98CH10886 with Brookhaven Science Associates, LLC.

The Gamow-Teller Giant Resonance in $^{11}$Li was measured via the $^{11}$Li(p,n)$^{11}$Be charge-exchange reaction at 182 MeV/u in inverse kinematics at the RIKEN Radioactive Isotope Beam Factory. There is no available data for isovector spin-flip giant resonances in nuclei with large isospin asymmetry factors, where (N−Z)/A > 0.25 [1]. Our work aims to investigate this unexplored region, with $^{11}$Li ((N−Z)/A = 0.45).
The (p,n) charge-exchange reactions in inverse kinematics, coupled with the missing-mass technique, serve as powerful tools for investigating the Gamow-Teller Giant Resonance in radioactive isotopes across a broad excitation energy range (up to 50 MeV), without being constrained by the Q-value limitations of β decay [1]. In our previous work on $^{132}$Sn [2], we demonstrated that accurate information about giant resonances can be obtained for unstable nuclei by using this probe. The combined setup [3] of the PANDORA low-energy neutron spectrometer [4] and SAMURAI large-acceptance magnetic spectrometer [5], together with a thick liquid hydrogen target, allowed us to perform the experiment with high luminosity. Recoil neutrons with kinetic energy of 0.1–10 MeV were identified with PANDORA, while SAMURAI was used for tagging the decay channels of the reaction residues.
The β decay of $^{11}$Li is complex. The $^{11}$Li β-decay involves the largest number of decay channels ever detected [6], and experimental results have been reported for cases where the daughter breaks into fragments, and emission of one, two, and three neutrons, α particles and $^{6}$He, tritons, and deuterons have been observed in several β-decay studies [8,9]. However, the B(GT) values were not clearly deduced as these studies were affected by the Q value.
In this talk, the results of our completed analysis will be presented. Deduced double differential cross-section up to about 40 MeV, including the Gamow-Teller (GT) Giant Resonance region in $^{11}$Li, will be reported. A comparison of the deduced B(GT) values with those from β-decay studies reveals significant differences, emphasizing the limitations imposed by Q values in the latter. We will also discuss the nature of seven newly identified decay channels of $^{11}$Be. Our observation that the GT peak occurs below the Isobaric Analog State in $^{11}$Li will be discussed in connection with the variation of residual spin-isospin interaction in exotic nuclei.

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The latest generation of radioactive ion beam facilities provides unparalleled access to neutron-rich unstable isotopes. One of the areas of active investigation is the study of the shell evolution near the neutron magic numbers N=20 [1-4] and N=28 [5-6] for such unstable nuclei. The nuclei near these magic numbers display exotic structural features such as dampening of shell gaps, formation of halos, and deformed structures.

Recently, the 29F system, a light neutron-rich N=20 isotone, was identified as the heaviest two-neutron Borromean-halo nucleus found till date [1-4]. Motivated by this observation, it is interesting to explore the “N=28” shell closure for nuclei with a small proton number as well, to see whether we can find similar Borromean structure formation.

In this talk, I will compare and contrast the shell evolution across the neutron magic numbers N=20 and 28 within a three-body (core+N+N) framework based on the hyperspherical-harmonics formalism by using an analytical-transformed harmonic-oscillator basis. New three-body results will be presented for the ground state structural properties of putative two-neutron Borromean halos in Na and Mg isotopes with N=28 [7].
[1] S. Bagchi, et al., PRL 124, 222504 (2020).
[2] J. Singh, et al., PRC 101, 024310 (2020).
[3] J. Casal, J. Singh, et al., PRC 102, 064627 (2020).
[4] L. Fortunato, et al., Commun. Phys. 3, 132 (2020).
[5] D. S. Ahn, et al., PRL 129, 212502 (2022).
[6] K.Y. Zhang, et al., PRC 107, L041303 (2023).
[7] Jagjit Singh et al., arXiv:2401.05160 [nucl-th] (2024).

One and two proton removal from neutron-rich medium-mass nuclei are commonly used to populate different final states in a nucleus of interest. (p,2p) and (p,3p) knockout reactions have been investigated in inverse kinematics within the first two SEASTAR campaigns that took place at RIBF in RIKEN, Japan [1]. These studies have been extended to the third SEASTAR campaign where medium-mass radioactive nuclei in the region of 54Ca were sent at about 270 MeV/nucleon onto a 15 cm long liquid hydrogen target surrounded by the MINOS time-projection chamber. MINOS enabled to track the angular distribution of the knocked out protons. (p,2p) and (p,3p) cross sections have been obtained and compared to theoretical reaction models. In particular, the difference in sensitivity of (p,2p) and (p,3p) to the population of individual final states in the same nucleus will be discussed.

References:
[1] A. Frotscher et al., Phys. Rev. Lett. 125, 012591 (2020)

Constructing effective interactions (`optical potentials’) between a proton or neutron and a nucleus for computing elastic scattering has a long tradition. A renewed interest in considering this challenging task stems from the possibility of combining today’s ab inito structure work with elastic scattering from light up to medium-heavy nuclei using the framework of the spectator expansion of multiple scattering theory to compute its leading order term consistently. The calculation of the effective interaction in leading order in the spectator expansion relies on two basic input quantities, which are the fully off-shell nucleon-nucleon (NN) amplitudes in their Wolfenstein representation and the translationally invariant non-local scalar and spin-projected density matrices of the target nucleus.
For light nuclei (up to $^{16}$O), the structure information can be obtained from the no-core shell model (NCSM). For heavier nuclei (up to $^{40}$Ca), a systematic down-selection scheme was developed in the framework of the symmetry-adapted (SA) NCSM to reduce the full space of basis states to a subset that describes equilibrium and dynamical shapes. Within this selected model space, the spurious center-of-mass motion can be factored out exactly.
Calculations of elastic scattering observables, namely differential cross sections and spin observables, for proton scattering for nuclei with 0+ ground states from Carbon to Calcium in the energy range from 65 to 200 MeV will be presented and compared to experimental data.

The SCRIT (Self-Confining RI Ion Target) electron scattering facility [1] was constructed at RIKEN in Japan to enable electron scattering from short-lived unstable nuclei. Electron scattering is a powerful tool for exploring the structure of atomic nuclei because of the well-understood mechanism of electromagnetic interaction. However, its application to short-lived unstable nuclei has been challenging because of the difficulty in preparing thick targets, even though there has been a long-standing desire to investigate exotic features of unstable nuclei using electron scattering [2].
Recently, we achieved a milestone by realizing the world's first electron scattering from online-produced unstable nuclei, $^{137}$Cs, at the SCRIT facility after years of development [3,4]. Cesium nuclides were produced through the photo-fission of uranium by irradiating 28 g of uranium with a 15-W electron beam and then ionized using a surface ionization-type ion source in an ISOL system. Finally, a luminosity of 10$^{26}$ cm$^{-2}$s$^{-1}$ was achieved. This experiment serves as a perfect emulation of electron scattering from short-lived unstable nuclei produced online after upgrading the power of the ISOL driver.
In this contribution, we will present recent progress and prospects of the SCRIT electron scattering facility and discuss several topics also that may be only feasible in the future using the SCRIT method.

References:
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[2] T. Suda and H. Simon, Prog. Part. Nucl. Phys. 96, 1 (2017)
[3] T. Ohnishi et al., Nucl. Instr. Meth. B541 (2023) 380-384
[4] K. Tsukada et al., Phys. Rev. Lett. 131 (2023) 092502

Deviations from the typical liquid-drop-like saturated density of the nucleus are a focal point in the exploration of nuclear structure. Phenomena of nucleon localization, such as clustering or bubble structures, provide a distinctive perspective on the macroscopic consequences of nuclear interaction. Experimental evidence of a depletion of the proton distribution in the core region of the nucleus was first claimed in 34Si and is driven by the presence of a sub-shell closure in combination with an empty s1/2 orbital [1].
We exploited a proton-transfer direct reaction to probe the wavefunction of 46Ar, extrapolating the probability of population of the d3/2 hole-state relative to the s1/2 in 47K. The experiment, performed at the Spiral 1 facility in GANIL with a post-accelerated radioactive 46Ar beam impinging on a high-density cryogenic 3He target relied on a state-of-the-art experimental setup for a precise reconstruction of the kinematics of the reaction. The heavy reaction fragment was identified by the high-acceptance magnetic spectrometer, VAMOS [2], while the high-granularity silicon DSSSD detector, MUGAST [3], allowed the measurement of the angular distribution of the light ejectile while also performing particle identification. The AGATA [4] gamma-ray tracking germanium array measured the gamma rays produced by the decay of the 47K excited states.
The experimental results point to an empty s1/2 orbital and are well reproduced by ab initio calculations. The comparison of theory and data constitutes a strong indication of the bubble phenomenon in this nucleus.

References
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The equation of state of nuclear matter(EOS), which describes the macroscopic properties of nuclei, is essential not only to describe the structure and collisions of nuclei but also to understand the astrophysical problems, such as the mechanism of supernova explosions and the structure of neutron stars. Since nuclear matter is composed of two Fermi particles, protons and neutrons, the equation of state has a term that depends on the density difference between the two, which is called the symmetry energy. From previous studies, it is known that the first-order density dependence of the symmetry energy is closely related to the thickness of the neutron skin [1].

In this study, interaction cross sections ${\sigma}_{\rm{I}}$ and charge changing cross sections ${\sigma}_{\rm{CC}}$ for $^{58-77}$Ni on a carbon target at 260 MeV/nucleon have been measured to derive matter radii and charge radii respectively. Recently, the charge radii of Ni isotopes up to mass number 70 were measured by isotope shift method [2]. In order to derive the neutron skin thickness in the more neutron-rich region, we attempted to derive the charge radii from charge changing cross section measurements. The experiment was performed at the Radioactive Isotope Beam Factory(RIBF) at RIKEN by using the BigRIPS fragment separator. The present ${\sigma}_{\rm{I}}$ data are the first systematic ones along the isotopic chain in Ni mass region.

In the neutron-rich region of Ni isotopes, the present ${\sigma}_{\rm{I}}$, for example, for $^{72}$Ni is largely enhanced in comparison with the Glauber calculation using the nucleon densities based on the systematics of stable nuclei, but is well reproduced with matter radii of Hartree-Fock calculations [3]. And the present ${\sigma}_{\rm{CC}}$ for $^{72}$Ni is reproduced by the simple Glauber calculation assuming that the neutron-number dependence of charge radius is the same as that for Cu isotopes, charge radii of which are already known. In the region near the stability line, charge-changing cross section is considered to be fairly enhanced by the charged-particle evaporation effect, whereas this effect reduces for very neutron-rich nuclei [4]. With the present results, it is expected that this effect is negligible for Ni isotopes with A ${\geq}$ ${\sim}$72. So, in such a mass region, it is considered that the charge radius can be determined from ${\sigma}_{\rm{CC}}$ by a Glauber calculation without this evaporation effect.

In this presentation, we’ll report the matter radii and charge radii derived from the experimental cross sections using Glauber calculations. Also, in the region where the charge radii are known, from A = 58 to 70, we’ll discuss the neutron skin thickness of Ni isotopes, which is obtained by the present data combined with known charge radii. On the other hand, in the neutron-rich region with A ${\geq}$ 71, we’ll discuss the neutron skin thickness by combining present ${\sigma}_{\rm{I}}$ and ${\sigma}_{\rm{CC}}$ data.

References
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The experimental evidence points to the existence, at short distances, of strongly correlated neutron-proton pairs much like they are in the deuteron or in free scattering processes. As it moves through the nuclear medium, a “bare” nucleon in the presence of the nucleon-nucleon interaction becomes “dressed” in a quasi-deuteron cloud [1], about 20% of the time. A phenomenological analysis of the quenching of spectroscopic factors [2] and recent data from Jefferson Lab [3] point to an isospin dependence of the independent-particle model content in a dressed nucleon. It is expected that this dependence should also be reflected in the dressed amplitude and thus, in the virtual quasi-deuteron content in the ground state.

Following from the qualitative arguments above, quasi-free scattering (QFS) of deuterons for which the fast reaction time $t_R$ becomes comparable to the time scale of the virtual excitations, $t_R \sim \hbar / \Delta E$, could offer a sensitive probe to examine these concepts.

In this contribution, we will discuss these ideas within a single-j approximation and put forward an experimental case that can serve as a template to test the above conjecture, i.e., measuring the (p,pd) QFS cross-section for knocking out a deuteron in $^{10,14,16}$C relative to $^{12}$C as an additional tool to probe short-range correlations and their isospin dependency.

[1] K. Brueckner, in Proceedings of the Rutherford Jubilee Int. Conf. Manchester 1961 (Heywood & Company LTD, London, 1961)

[2] S. Paschalis, M. Petri, A. O. Macchiavelli, O. Hen, and E. Piasetzky, Physics Letters B 800 (2020) 135110

[3] M. Duer, et al., Nature 560 (2018) 617

*This work was supported by the Royal Society, UK STFC, and the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy

Developing a unified description of finite nuclei based on the underlying interactions between individual nucleons is a long-sought goal in nuclear physics. Two-nucleon removal reactions offer a promising tool to investigate nucleon-nucleon correlations, the fundamental ingredients in nuclear forces. A well-documented case is the electron-induced (e, e’pN) pair removal measurements on a C target at 4.6 GeV that selected high momentum transfer and large missing momentum events, suggesting that np pairs are about 20 times more prevalent than that like-nucleon pairs in short-range correlations [1]. The systematic (e, e’pN) measurements with medium-to-heavy stable nuclei revealed a marked increase of the fraction of high-momentum protons with the neutron excess in nucleus [2].

To study how the np correlations evolve towards unstable nuclei with large isospin asymmetry, two-nucleon removal reactions in inverse kinematics are desired [3]. In this talk, we will present the results of np removal from12C with a Be target at 190 MeV/u together with the (p,2pn) reactions from neutron-rich nuclei at 250 MeV/u. Both measurements were performed at the RIBF with the BigRIPS and SAMURAI spectrometers. Significant two-step contributions from the evaporation were observed and subtracted in both cases. The partial cross sections to the individual final states of 10B were achieved and compared with the calculations using the ab-initio structure inputs. The reaction kinematics of (p,2pn) is under analysis and will be compared with the sequential picture discovered in the (p,3p) reactions [4].

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The isospin character of the p-n pair and n-n pair at medium relative momentum has been observed in comparison with A=6 nuclei, 6Li, and 6He. We have measured the 6Li(p,dp) and 6He(p,dn) cross sections for the neutron pick-up domain with 70A MeV incident heavy ion on the solid hydrogen target[1] via inverse kinematics at RIPS facility in RIKEN. All the reaction products at forward angles, including recoiled nucleons N [p or n], were measured by plastic scintillator telescopes and identified unambiguously. The momentum transfer covers up to 1.0 fm-1 through a wide angular coverage, thus picking up the high-momentum neutrons correlated with protons in nuclei. In the (p,dp) reaction, we observed a strong population of deuteron-like states d+4He in 6Li but a weak population of neutron pairs ’n-n’+4He in 6He.
The data were compared with plane-wave and distorted-wave impulse approximation (DWIA) calculations with realistic elastic d(p,p)d and charge exchange reaction ’n-n’(p,n)d cross sections with the common procedure, which was successfully applied to the 16O(p,dp)[2]. The calculations with assumed spectroscopic amplitudes from theoretical estimation based on a three-body model[3] fairly reproduce the observed ratio of cross sections between 6Li and 6He. It indicates that the present DWIA framework works well at medium relative momenta. The observed strong isospin dependence in the NN pair indicates the presence of NN correlation in A=6 nuclei. In this talk, we will present new results of the experiment with 6Li(p,dp)4He and 6He(p,dn)4He and discuss the applied detailed reaction analysis.

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[2] S. Terashima et al. Phys. Rev. Lett. 121(2018) 242501
[3] W. Horiuchi and Y. Suzuki. Phys. Rev. C76(2007)024311

Unlike standard like-particle pairing (neutron-neutron, proton-proton) that only exists in the T=1 channel, proton-neutron pairing can exist in both T=1 and T=0 channels. The consequences of this coexistence are not yet fully understood, but could explain phenomena such as the overbinding of self-conjugate nuclei.

Proton-neutron pairing can be studied by spectroscopy as in ref. [1], or by transfer reactions, as in ref. [2] , since the two-nucleon transfer reaction cross-section is expected to be enhanced by pairing. The relative proton-neutron pairing strengths between T=1 and T=0 channels can be accessed by measuring transfer cross-sections to the low-lying (J=0$^+$, T=1) and (J=1$^+$, T=0) states in odd-odd N=Z nuclei. We chose to use (p,$^3$He) reaction as its selection rules allow to populate both states at once.

As pairing is a collective effect, it is expected to be stronger in the middle of high j orbitals. The f$_{7/2}$ shell is the highest j shell currently accessible with sufficient beam intensity for two-nucleon transfer reactions in N=Z nuclei. We are thus investigating $^{48}$Cr, which lies in the middle of this shell, and comparing it with previous experiments in the same region [2]. Moreover, $^{48}$Cr is a good candidate to study the interplay between pairing and deformation since it is known to be a good rotor up to spin 10$^+$ [3].

The experiment to measure the two-nucleon transfer reaction $^{48}$Cr(p,$^3$He)$^{46}$V was performed at GANIL. A radioactive $^{48}$Cr beam was produced by fragmentation of a primary $^{50}$Cr beam and selected by the LISE spectrometer, before impinging on a CH$_2$ target. A forward array of DSSD-CsI telescopes (MUGAST) was used to detect and identify light charged particles, and was coupled to 12 EXOGAM Germanium clovers around the target, a zero-degree detection (ZDD) and MWPC detectors to reconstruct event by event the beam position on the target.

I will present preliminary cross-sections and angular distributions for the low-lying states of $^{46}$V. They will be compared with second-order Distorted Wave Born Approximation (DWBA) calculations for two-nucleon transfer performed with both realistic and single particle two-nucleon amplitudes (TNA). The results will be put in perspective with the systematics in the f-shell : $^{56}$Ni(p,$^3$He), $^{52}$Fe(p,$^3$He) and $^{40}$Ca(p,$^3$He).

[1] Cederwall, B., Moradi, F., Bäck, T. et al. Evidence for a spin-aligned neutron-proton paired phase from the level structure of Pd. Nature 469, 68-71 (2011). https://doi.org/10.103/nature09644

[2] Le Crom, B., Assié, M. et al. Neutron-proton pairing in the N=Z radioactive fp-shell nuclei Ni and Fe probed by pair transfer, Physics Letters B 829 (2022), 137057. https://doi.org/10.1016/j.physletb.2022.137057

[3] Robinson, S. J. Q. and Hoang, T. and Zamick, L. and Escuderos, A. and Sharon, Y. Y. Shell model calculations of B(E2) values, static quadrupole moments, and g factors for a number of N = Z nuclei. Phys. Rev. C 89 (2014), 014316. https://link.aps.org/doi/10.1103/PhysRevC.89.014316

The formation of short-range correlated nucleon-nucleon pairs (SRCs), primarily composed of neutron-proton pairs [1], appears to be a universal feature in atomic nuclei [2]. Interestingly, measurements in electron scattering indicate that protons become significantly more correlated in asymmetric nuclei as a function of neutron excess. This has potential implications for the description of cold dense nuclear matter as for neutron stars. However, available data are limited to stable nuclei which have maximum neutron excess of ~1.6 and, at the same time as they become more neutron-rich, they also become more heavy. To overcome these limitations, we performed a pilot experiment at the R³B setup at GSI-FAIR [3] as part of the FAIR Phase-0 experimental program to measure SRC in the most neutron-rich nucleus yet, $^{16}$C. We employ hard proton knockout reactions in inverse kinematics of $^{16}$C beam at 1.25 GeV/nucleon, as well as $^{12}$C beam as reference, to study SRC behavior. In this talk, I will discuss preliminary results of SRC behavior in neutron-rich nuclei and prospects for the follow-up research program at FAIR.

[1] R. Subedi, R. Shneor, Science, 1156675, 2008.
[2] M. Duer et al. (CLAS Collaboration), Nature, 560:617, 2018.
[3]https://www.gsi.de/work/forschung/nustarenna/nustarenna_divisions/kernreaktionen/activities/r3b.