Short-lived nuclear systems with light to medium masses are showing halo phenomena in regions of the nuclear chart that were still unexplored when halo nuclei were discovered 40 years ago. We study these exotic systems with three-body models, including nucleon-nucleon correlations, with the aim of reproducing measurable properties like radii and electromagnetic transition strengths. On the nucleon-rich side, drip-line fluorine isotopes are showing clear signs of a halo structure. Recently, we proposed that F29 is a moderate two-neutron halo nucleus with a large radius and a strong B(E1) response to the continuum. The three-body model places it at the borders of the island of inversion, which is corroborated by new data. According to our models, the next interesting isotope, F31, also has large spatial extension due to p-wave components and enhanced B(E1) response, pointing to a speculative halo structure. On the proton-rich side, we have studied the Sb102 system, composed of a Sn100 core plus a proton-neutron-correlated subsystem. We find that the weakening of the proton-neutron correlations with respect to the bare deuteron indicates that this is a one-proton emitter. We propose that the presence of a resonant state and its decay might provide a crucial benchmark for this system.

In the SU3-IBM the oblate shape is described by the SU(3) third-order Casimir operator in the large-N limit. However for finite N, this interaction can produce a boson number odd-even effect. In this Letter, we find that, the unique odd-even effect really exists in the nuclei ^196-204Hg. This finding implies that realistic low-lying excitations are sensitive to certain boson number N. The boson number hypothesis is verified for the first time since the advent of the interacting boson model. This also proves the accuracy and validity of the SU3-IBM directly. The SU(3) symmetry and the higher-order interactions are both indispensable for understanding the nuclear quadrupole deformations.

We present a new revision of nuclear fusion reaction cycles, whereby a solid room temperature lithium-6 deuteride (6LiD) is burnt with neutrons beams. New calculations of the time evolution of a network of differential equations for the abundancies of various nuclear species are presented. Data on nuclear cross-sections and non-thermal reaction rates are used to forecast the full time evolution of the most relevant thermonuclear reactions. Two cycles are considered: the Jetter n+6Li and Post cycles p+6Li. According to our calculations, there are great expectations for energy extraction in devices not based on plasma confinement, but rather on controlled nuclear burning into final products (mainly alpha particles).

One-proton emission from the Sb-102 nucleus is discussed, assuming an inert 100Sn core and the valence proton and neutron. There are experimentally measured bound states in the 100Sn-neutron system, whereas no particlebound 100Sn-proton state has been observed. With time-dependent three-body calculations, the 1+ ground state of Sb-102 is suggested as a possible proton emitter. This conclusion is reached by assuming a weakening effect on the proton-neutron (pn) interaction with respect to a bare deuteron. An analogous phenomenon is necessary to reproduce the empirical binding energies of Sc-42 and( 18)F. Continuous shift from the unbound to bound regions by changing the pn-interaction strength is demonstrated. The lower limit of lifetime is evaluated as tau less than or similar to 4.4x10(-18) s in the no-pn-interaction limit. However, the actual lifetime is expected as longer with a finite pn interaction. Observation of a resonant state in Sb-102 and its decay would provide a benchmark of the pn-pairing correlation.

New calculations of the time evolution and isotopic composition for a network of nuclear reactions breathe new life into an old idea in nuclear fusion, burning solid room-temperature 6Li deuteride (6LiD) with neutrons. Modern-day compilations of nuclear cross sections are nowadays available, and we use them to predict the full course of networks of thermonuclear reactions, reexamining the Jetter (n + 6Li) and Post cycles (p + 6Li), named after U. Jetter and R. F. Post, that offer great prospects for energy production in devices not based on plasma confinement. We present ideal calculations, i.e. not including the energy loss due to the stopping power, and more realistic calculations that include the Bethe-Bloch formula. We find that a significant amount of energy can, in principle, be generated.

Recently, it has been argued that a spherical-like spectrum emerges in the SU3-IBM,opening up new approaches to understand the γ-softness in realistic nuclei. In a previous paper,γ-softness with degeneracy of the ground and quasi-γ bands was observed. In this paper, anotherspecial point connected with the middle degenerate point is discussed, which is found to be relatedwith the properties of 196Pt. This emergent γ-softness has also been shown to be important forunderstanding the prolate-oblate asymmetric shape phase transition. The low-lying spectra, B(E2)values and quadrupole moments in 196Pt are discussed showing that the new model can accountfor several observed features. This is the first part of the discussions on the γ-soft-like spectrum of 196 Pt.

A mapping from the triaxial rotor Hamiltonian to that of the O(6) limit in the interacting boson model (IBM) is established, which is achieved by introducing the symmetry-conserving high-order interactional terms The validity of the proposed mapping scheme is further examined for the cases with gamma = 0 and gamma = pi/6, respectively. It is shown that the rotor model results can be well reproduced in its O(6) image especially for the low-spin states. It thus provides an alternative way to understand the triaxiality in the finite-N systems and additional insight into the O(6) IBM theory.

We investigate geometric configurations of $$\alpha $$ ( $$^4$$ He nucleus) clusters in the second $$J^\pi =2^+$$ state of $$^{12}$$ C, which has been discussed as a rotational band member of the second $$0^+$$ state, the Hoyle state. The ground and excited $$0^+$$ and $$2^+$$ states are described by a three- $$\alpha $$ cluster model. The three-body Schrödinger equation with orthogonality conditions is accurately solved by the stochastic variational method with correlated Gaussian basis functions. To analyse the structure of these resonant states in a convenient form, we introduce a confining potential. The two-body density distributions together with the spectroscopic information clarify the structure of these states. We find that main configurations of both the second $$0^+$$ and $$2^+$$ states are acute-angled triangle shapes originating from the $$^8$$ Be( $$0^+$$ ) $$+\alpha $$ configuration. However, the $$^{8}\textrm{Be}+\alpha $$ components in the second $$2^+$$ state become approximately 2/3 because the $$^8$$ Be subsystem is hard to excite, indicating that the state is not an ideal rigid rotational band member of the Hoyle state.

We are reporting here on a series of theoretical investigations with both algebraic models and geometric cluster models of alpha clusters in ^12 C, focusing on the structure of the ground state, the first excited 0^+ state and the second excited 2^+ state with the purpose, in particular, of establishing if the rotational bands are compatible with rigid structures or rather if they are quantum mixture of different configurations. In a first series of paper (Vitturi et al., Transition densities and form factors in the triangular α -cluster model of 12C with application to 12C+ α scattering. Phys Rev C 101:014315, 2020; Casal et al., Alpha-induced inelastic scattering and alpha-transfer reactions in 12C and 16O within the Algebraic Cluster Model. Eur Phys J A 57:33, 2021), we assume a rigid equilateral triangle shape and study in detail several properties that descend from the algebraic framework, such as the energy spectrum, electromagnetic observables and calculate the transition densities in order to extract elastic and inelastic cross-sections for various processes. In a second series of papers (Moriya et al., Three- α Configurations in the 0 ^+ States of 12C. Few-Body Syst 62:46, 2021; Moriya et al., Three- α configurations of the second J^π = 0 ^+ state in 12C. Eur. Phys J A 59:37, 2023), we solve the three-body Schrödinger equation with orthogonality conditions using the stochastic variational method with correlated Gaussian basis functions. The two-body density distributions indicate that the main configurations of both the 0_2^+ and 2_2^+ states are acute iscosceles triangle shapes coming from ^8 Be( 0^+ )+ α configurations and find some hints that the second 2^+ state is not an ideal rigid rotational band member of the Hoyle state band.

We investigate geometric configurations of $α$ ($^4$He nucleus) clusters in the second $J^π=2^+$ state of $^{12}$C, which has been discussed as a rotational band member of the second $0^+$ state, the Hoyle state. The ground and excited $0^+$ and $2^+$ states are described by a three-$α$ cluster model. The three-body Schrödinger equation with orthogonality conditions is accurately solved by the stochastic variational method with correlated Gaussian basis functions. To analyse the structure of these resonant states in a convenient form, we introduce a confining potential. The two-body density distributions together with the spectroscopic information clarify the structure of these states. We find that main configurations of both the second $0^+$ and $2^+$ states are acute-angled triangle shapes originating from the $^8$Be($0^+$)$+α$ configuration. However, the $^8$Be$+α$ components in the second $2^+$ state become approximately 2/3 because the 8Be subsystem is hard to excite, indicating that the state is not an ideal rigid rotational band member of the Hoyle state.

Recently, it has been argued that a spherical-like spectrum emerges in the SU3-IBM, opening up new approaches to understand the {\gamma}-softness in realistic nuclei. In a previous paper, {\gamma}-softness with degeneracy of the ground and quasi-{\gamma} bands was observed. In this paper, another special point connected with the middle degenerate point is discussed, which is found to be related with the properties of 196Pt. This emergent {\gamma}-softness has also been shown to be important for understanding the prolate-oblate asymmetric shape phase transition. The low-lying spectra, B(E2) values and quadrupole moments in 196Pt are discussed showing that the new model can account for several observed features. This is the first part of the discussions on the {\gamma}-soft-like spectrum of 196Pt.

We explore two-particle transfer reactions as a crucial probe of the occurrence of shape coexistence in shape phase transitions. The (t,p) reactions to the ground state and to excited 0+ states are calculated for the isotope chain of even-even Zirconium isotopes starting from stable nuclei up to beyond current experimental limits. Two-particle spectroscopic factors derived from Monte Carlo Shell Model calculations are used, together with the sequential description of the two-particle transfer reaction mechanism. The calculation shows a clear signature for a shape phase transition between 98Zr and 100Zr, which displays coexistence of a deformed ground state with an excited spherical 0+ state. Furthermore, we show that there is a qualitative difference with respect to the case of a normal shape phase transition that can be discriminated with two-neutron transfer reactions.

An unbound intermediate system ( A +1) with the presence of a resonance, can aid in the pairing enhancement in a two-neutron transfer reaction from a bound system A to another bound system ( A +2). This enhancement is a consequence of the constructive interference via the several reaction channels available in the ( A +1) system. We test this feature through our study in 6 He, modeled as two neutrons in the orbitals of an intermediate 5 He nucleus. Weighing up the natural case of an unbound 5 He with a hypothetically bound 5 He, we find that the inclusion of a properly modeled continuum favours the pairing correlations leading to enhanced two-neutron transfer cross-sections.

In this contribution, the motivations for a Focus Point on the future nuclear physics researches in the Italian laboratories are described. The organization of the preliminary workshops and of the final reports in this series is described.

The penetrability of the Coulomb barrier of 6Li by a proton is studied using a quantum cluster model. We focus on the role of quadrupole deformations in the nucleus ground-state, in terms of which a 6Li–p form factor with tensor components is computed. We find that the diagonal part of the tensor term reduces the average barrier penetrability of the system. However, the tensor interaction due only to the mechanism studied at present is very small, regardless of the specific adopted construction, and yields negligible effects.

Recent advances obtained in the last few years by the Theoretical Nuclear Physics group in Padova with various collaborators on alpha-cluster models and on nuclear correlations in stable and unstable light nuclei are reviewed in this contribution. The algebraic cluster model assumes triangular and tetrahedral arrangement of α particles for 12 C and 16 O respectively. The description of the low-lying states achieved in this model, that is a consequence of the requirement of discrete symmetries, is extremely good. We have made several calculations of α -transfer form factors and reaction cross-sections obtaining a good agreement with available data, thus corroborating the main hypotheses of the model [1]. We have speculated about smoking-gun nuclear fluorescence experiment that might shed light on the exact spatial arrangement of alpha particles in 12 C [2]. We will also talk about the successful predictions on the positioning of 29 F on the southern shore of the island of inversion [3] and on recent calculations on its halo character and dipole response [4, 5]. Extension of these calculations to 31 F [6], pointing out the presence of a halo, are also discussed.

Lying at the lower edge of the `island of inversion', neutron-rich Fluorine isotopes ($^{29-31}$F) provide a curious case to study the configuration mixing in this part of the nuclear landscape. Recent studies have suggested that a prospective two-neutron halo in the dripline nucleus $^{31}$F could be linked to the occupancy of the $pf$ intruder configurations. Focusing on configuration mixing, matter radii and neutron-neutron ($nn$) correlations in the ground-state of $^{31}$F, we explore various scenarios to analyze its possible halo nature as well as the low-lying electric dipole ($E$1) response within a three-body approach. We use an analytical, transformed harmonic oscillator basis under the aegis of a hyperspherical formalism to construct the ground state three-body wave function of $^{31}$F. The $^{31}$F ground-state configuration mixing and its matter radius are computed for different choices of the $^{30}$F structure coupled to the valence neutron. The admixture of {$p_{3/2}$, $d_{3/2}$, and $f_{7/2}$} components is found to play an important role, favouring the dominance of inverted configurations with dineutron spreads for two-neutron halo formation. The increase in matter radius with respect to the core radius, $\Delta r \geqslant$ 0.30 fm and the dipole distributions along with the integrated $B(E1)$ strengths of $\geqslant$ 2.6 $e^2$fm$^2$ are large enough to be compatible with other two-neutron halo nuclei. Three-body results for $^{31}$F indicate a large spatial extension in its ground state due to the inversion of the energy levels of the normal shell model scheme. The increase is augmented by and is proportional to the extent of the $p_{3/2}$ component in the wave function. Additionally, the enhanced dipole distributions and large $B(E1)$ strengths all point to the two-neutron halo character of $^{31}$F.

We study an exactly solvable algebraic Hamiltonian for odd systems that allows to span the whole range between prolate and oblate spectra, while maintaining the SU^BF(3) ⊗ U^F_s(2) dynamical symmetry, thanks to the mixing of quadratic and cubic Casimir operators of SU^BF(3) . We choose a j = 1/2, 3/2, and 5/2 fermionic basis that is coupled to coherent states for the boson part. With this, we diagonalize the Boson–Fermion Hamiltonian obtaining potential energy surfaces for each component. We find a very rich variety of behaviours: the various orbitals do not display the same shape, some are prolate, while others are oblate, and they make the transition following different paths.