arXiv subjects

J. Casal

Publications and source records attributed to J. Casal.

At least 19 recordsLinked to original sources

arXiv2026

Decay of three-body resonances in a discrete basis

We present a theoretical framework for calculating the asymptotic properties and decay dynamics of three-body resonances described in a discrete basis. The method involves solving an inhomogeneous Schrödinger equation to determine the non-normalizable resonant state by identifying a normalizable source state, which captures the short-range internal structure. The long-range behavior is then calculated using the free three-body propagator, providing accurate asymptotic coefficients necessary for describing decay correlations. We apply this formalism to the two-neutron decay of the 0$^{+}$ ground-state and the 2$^{+}$ excited-state resonances of $^{16}\text{Be}$ ($^{14}\text{Be}+n+n$), working within the hyperspherical expansion method with an analytical transformed harmonic oscillator basis. Our results show that the decay is strongly dominated by the lowest hypermomentum components at large separations, reflecting effective three-body barrier penetration dynamics that shape the final state. The calculated relative-energy distributions exhibit clear neutron-neutron correlations for both states, arising from mixing between different asymptotic channels, and are consistent with a direct two-neutron emission mechanism, in agreement with recent experimental observations. This work provides a reliable tool for linking the internal structure of three-body resonances to their decay properties.

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arXiv2026

Is $^{40}$Mg a Borromean halo nucleus? A case built on the electric-dipole response

We investigate the low-energy electric-dipole response of $^{40}$Mg using a $^{38}$Mg$+n+n$ three-body model. This model is implemented using a three-body hyperspherical formalism with an analytical transformed harmonic oscillator basis. In this study, two different neutron-neutron interactions are considered: a scalar Gaussian density-dependent central potential and a more realistic finite-range potential which includes central, spin-orbit, and tensor components. We examine how electric-dipole response is affected by the choice of the interaction.

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arXiv2025

The effect of inversion of $p$ and $f$ orbits on halo formation in heavy sodium isotopes

The role of the inversion of the $p$ and $f$ shell-model orbits in the emergence of halo structures in the ground states of neutron-rich $^{34,37,39}$Na is investigated. Families of two- and three-body models are constructed with effective core-neutron interactions, with parameter choices based on a combination of the available experimental data and systematic trends, as well as the GPT $n$-$n$ interaction and a phenomenological three-body force. Our results indicate a possible one-neutron halo in $^{34}$Na, while $^{37,39}$Na exhibit features of Borromean halos. The halo formation is driven by the weakening of the shell gap and inversion of the $2p_{3/2}$ and $1f_{7/2}$ orbits expected to occur somewhere near these masses. We further show that the electric dipole response provides a clear and sensitive probe of halo structure in these isotopes.

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arXiv2025

Neutron-transfer induced breakup of the Borromean nucleus $^9$Be

We address the problem of evaluating neutron-transfer induced breakup cross sections caused by the Borromean nucleus $^{9}$Be, using the reaction $^{197}$Au($^{9}$Be,$^{8}$Be)$^{198}$Au as a test case. This reaction was recently measured over a wide range of incident energies around the Coulomb barrier. To deal with the high density of $^{198}$Au states that can be potentially populated in this reaction, we employ the Ichimura, Austern, Vicent model, in which the spectrum of physical states for this system is replaced by the solutions of a complex n+$^{197}$Au potential, accounting effectively for the fragmentation of single-particle states into physical states. Furthermore, to account for the unbound nature of the emitted $^{8}$Be system, we employ a three-body model of $^{9}$Be. The calculated stripping cross sections are found to be in good agreement with existing data over a wide range of incident energies. The importance of taking into account the energy spread of the single-particle strength of the outgoing $^{8}$Be and the target-like residual nucleus is discussed.

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arXiv2025

Evolution of two-neutrons configuration from 11Li to 13Li

In this work we investigate the two-neutron decay of 13Li and of the excited states of 11Li populated via one-proton removal from 14Be and 12Be, respectively. A phenomenological model is used to describe the decay of 11Li and 13Li. While the first one displays important sequential components, the second one appears dominated by the direct two-neutron decay. A microscopic three-body model is used to extract information on the spatial configuration of the emitted neutrons before the decay and shows that the average distance between the neutrons increases going from 11Li to 13Li.

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arXiv2024

The art of modeling nuclear reactions with weakly bound nuclei: status and perspectives

We give an overview of the theoretical description of nuclear reactions involving weakly-bound nuclei. Some of the more widespread reaction formalisms employed in the analysis of these reactions are briefly introduced, including various recent developments. We put special emphasis on the continuum-discretized coupled-channel (CDCC) method and its extensions to incorporate core and target excitations as well as its application to three-body projectiles. The role of the continuum for one-nucleon transfer reactions is also discussed. The problem of the evaluation of inclusive breakup cross sections is addressed within the Ichimura-Austern-Vincent (IAV) model. Other methods, such as those based on a semiclasical description of the scattering process, are also briefly introduced and some of their applications are discussed and a brief discussion on topics of current interest, such as nucleon-nucleon correlations, uncertainty evaluation and non-locality is presented.

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arXiv2024

Prediction of two-neutron halos in the $N=28$ isotones $^{40}$Mg and $^{39}$Na

The ground states of the nuclei $^{40}$Mg and $^{39}$Na are investigated using the hyperspherical formalism. Since they are located at the edge of the "big island of inversion", we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective $n$-$n$ and $^{38}$Mg$+n$ interactions is built for $^{40}$Mg based on the available data. We also give predictions for the low-lying spectrum of $^{38}$Na$=^{37}$Na$+n$ and two-neutron separation energy of the $^{39}$Na nucleus. Depending on parameter choice, we report an increase in the matter radii in the range $0.1$-$0.5$ fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in $^{40}$Mg for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for $^{39}$Na. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the $2p_{3/2}$ and $1f_{7/2}$ orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

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arXiv2024

Mass, spectroscopy and two-neutron decay of $^{16}$Be

The structure and decay of the most neutron-rich beryllium isotope, $^{16}$Be, has been investigated following proton knockout from a high-energy $^{17}$B beam. Two relatively narrow resonances were observed for the first time, with energies of $0.84(3)$ and $2.15(5)$ MeV above the two-neutron decay threshold and widths of $0.32(8)$ and $0.95(15)$ MeV respectively. These were assigned to be the ground ($J^π=0^+$) and first excited ($2^+$) state, with $E_x=1.31(6)$ MeV. The mass excess of $^{16}$Be was thus deduced to be $56.93(13)$ MeV, some $0.5$ MeV more bound than the only previous measurement. Both states were observed to decay by direct two-neutron emission. Calculations incorporating the evolution of the wavefunction during the decay as a genuine three-body process reproduced the principal characteristics of the neutron-neutron energy spectra for both levels, indicating that the ground state exhibits a strong spatially compact dineutron component, while the 2$^+$ level presents a far more diffuse neutron-neutron distribution.

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arXiv2023

Searching for universality of dineutron correlation at the surface of Borromean nuclei

The dineutron correlation is systematically studied in three different Borromean nuclei near the neutron dripline, 11Li, 14Be and 17B, via the (p, pn) knockout reaction measured at the RIBF facility in RIKEN. For the three nuclei, the correlation angle between the valence neutrons is found to be largest in the same range of intrinsic momenta, which can be associated to the nuclear surface. This result reinforces the prediction that the formation of the dineutron is universal in environments with low neutron density, such as the surface of neutron-rich Borromean nuclei.

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arXiv2023

Three-$α$ configurations of the second $J^π=2^+$ state in $^{12}$C

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.

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arXiv2022

Exploring the halo character and dipole response in the dripline nucleus $^{31}$F

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, $Δr \geqslant$ 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.

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arXiv2021

A global study of $^9$Be + p at 2.72 A MeV

Background: In our recent experiment, $^9$Be+p at 5.67A MeV, the breakup decay rates to the 3 configurations, $α$+$α$+n, $^8$Be$^*$+n and $^5$He+$^4$He of $^9$Be, were observed and quantified, in a full kinematics approach. Unfolding step by step the accessibility to the above configurations, it will require similar studies at lower and higher energies as well as the interpretation of the data in a theoretical framework. Purpose: Investigate the breakup decay rate of $^9$Be+p at 2.72A MeV, where the $α$+$α$+n configuration is mainly accessible. Compare and interpret data at 2.72A MeV and 5.67A MeV into a 4-body CDCC formalism; Point out and discuss couplings to continuum. Methods: Our experimental method includes an exclusive breakup measurement in a full kinematic approach of $^9$Be incident on a proton target at 2.72A MeV, together with elastic scattering and other reaction channels measurements under the same experimental conditions. The interpretation of the data at 2.72A MeV and 5.67A MeV is considered in a 4-body CDCC approach, using the Transformed Harmonic Oscillator method for the 3-body projectile. Results: An elastic scattering angular distribution at 2.72A MeV is measured, which compares very well with CDCC calculations, indicating a strong coupling to continuum. At the same energy, the measured breakup and total reaction cross sections present good agreement with the calculated values. Further on, the elastic scattering and breakup cross section data at 5.67A MeV are found in very good agreement with the CDCC calculations. The present results support further our 3-body model for the structure of $^9$Be, validating relevant radiative reaction rates obtained previously.

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arXiv2021

Opening angle and dineutron correlations in knockout reactions with Borromean two-neutron halo nuclei

Background. Knockout reactions with proton targets provide an invaluable tool to access the properties of two-neutron halo nuclei. Recently, experimental results for the average opening angle as a function of the intrinsic neutron momentum in 11Li have shown a localization of dineutron correlations on the nucleus surface. Purpose. Study the model dependence and the effect of distortion and absorption on the opening angle distributions to assess the reliability of this observable to extract properties of Borromean two-neutron halo nuclei. Method. A quasifree sudden model is used to describe the knockout process, where absorption effects are modeled by the eikonal S-matrix between the proton target and the core of the Borromean nucleus. Final states in momentum space are built within a three-body model for the projectile, which enables the description of momenta and opening angle distributions. Results. A strong dependence on absorption effects is found for the opening angle at large intrinsic momenta, while the region of lower momenta is mostly insensitive to them. Reasonable agreement with the available data is obtained for 11Li at low momenta with weights for s and p waves different from those previously reported, showing a model dependence in their extraction. For 19B, test calculations show marked sensitivity to small p-wave components. Conclusions. The opening angle for (p,pn) knockout reactions on Borromean nuclei at small intrinsic momenta is a reliable observable mostly sensitive to the structure of the Borromean nucleus. For larger momenta, the reaction mechanism leads to a larger distortion of the distribution. In the case of nuclei with small components of opposite parity to the dominant ones, this observable can be used to explore them. The relation between dineutron in coordinate space and opening angle in momentum space is found to be model-dependent.

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arXiv2021

Systematic calculations of reactions with exotic and stable nuclei to establish a unified theoretical approach

We report on systematical optical model (OM) and continuum discretized coupled channel (CDCC) calculations applied to describe the elastic scattering angular distributions of exotic and stable nuclei projectiles on heavy targets. Our optical potential (OP) is composed of the nuclear microscopic double folding São Paulo potential (SPP), derived from the nonlocal nature of the interaction, and the Coulomb dipole polarization (CDP) potential, derived from the semiclassical theory of Coulomb excitation. The OP is compared to the trivial equivalent local potential (TELP), extracted from CDCC calculations. The OM and CDCC predictions corroborate each other and account for important differences in the nuclei reaction mechanisms, which are directly related to their structural properties. Thus, OM and CDCC establish a common basis for analyzing or even predicting exotic and stable nuclei reactions.

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arXiv2021

Three-$α$ configurations in the $0^{+}$ states of $^{12}\mathrm{C}$

Geometric configurations of three-$α$ particles in the ground- and first-excited $J^π=0^+$ states of $^{12}$C are discussed within two types of $α$-cluster models which treat the Pauli principle differently. Though there are some quantitative differences especially in the internal region of the wave functions, equilateral triangle configurations are dominant in the ground state, while in the first excited $0^+$ state isosceles triangle configurations dominate, originating from $^8{\rm Be}+α$ configurations.

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arXiv2021

The MUGAST-AGATA-VAMOS campaign : set-up and performance

The MUGAST-AGATA-VAMOS set-up at GANIL combines the MUGAST highly-segmented silicon array with the state-of-the-art AGATA array and the large acceptance VAMOS spectrometer. The mechanical and electronics integration copes with the constraints of maximum efficiency for each device, in particular γ-ray transparency for the silicon array. This complete set-up offers a unique opportunity to perform exclusive measurements of direct reactions with the radioactive beams from the SPIRAL1 facility. The performance of the set-up is described through its commissioning and two examples of transfer reactions measured during the campaign. High accuracy spectroscopy of the nuclei of interest, including cross-sections and angular distributions, is achieved through the triple-coincidence measurement. In addition, the correction from Doppler effect of the γ-ray energies is improved by the detection of the light particles and the use of two-body kinematics and a full rejection of the background contributions is obtained through the identification of heavy residues. Moreover, the system can handle high intensity beams (up to 108 pps). The particle identification based on the measurement of the time-of-flight between MUGAST and VAMOS and the reconstruction of the trajectories is investigated.

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arXiv2020

Electric dipole response of low-lying excitations in the two-neutron halo nucleus $\boldsymbol{^{29}}$F

The neutron-rich $^{28,29}$F isotopes have been recently studied via knockout and interaction cross-section measurements. The $2n$ halo in $^{29}$F has been linked to the occupancy of $pf$ intruder configurations. We investigate bound and continuum states in $^{29}$F, focusing on the $E1$ response of low-lying excitations and the effect of dipole couplings on nuclear reactions. $^{29}\text{F}$ ($^{27}\text{F}+n+n$) wave functions are built within the hyperspherical harmonics formalism, and reaction cross sections are calculated using the Glauber theory. Continuum states and $B(E1)$ transition probabilities are described in a pseudostate approach using the analytical THO basis. The corresponding structure form factors are used in CDCC calculations to describe low-energy scattering. Parity inversion in $^{28}$F leads to a $^{29}$F ground state characterized by 57.5% of $(p_{3/2})^2$ intruder components, a strong dineutron configuration, and an increase of the matter radius with respect to the core radius of $ΔR=0.20$ fm. Glauber-model calculations for a carbon target at 240 MeV/nucleon provide a total reaction cross section of 1370 mb, in agreement with recent data. The model produces also a barely bound excited state corresponding to a quadrupole excitation. $B(E1)$ calculations into the continuum yield a total strength of 1.59 e$^2$fm$^2$ up to 6 MeV, and the $E1$ distribution exhibits a resonance at $\approx$ 0.85 MeV. Results using a standard shell-model order for $^{28}$F lead to a considerable reduction of the $B(E1)$ distribution. The four-body CDCC calculations for $^{29}\text{F}+^{120}\text{Sn}$ around the Coulomb barrier are dominated by dipole couplings, which totally cancel the Fresnel peak in the elastic cross section. These results are consistent with a two-neutron halo and may guide future experimental campaigns.

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arXiv2020

Three-body structure of $^{19}$B: Finite-range effects in two-neutron halo nuclei

The structure and $B(E1)$ transition strength of $^{19}$B are investigated in a $^{17}\text{B}+n+n$ model, triggered by a recent experiment showing that $^{19}$B exhibits a well pronounced two-neutron halo structure. Preliminary analysis of the experimental data was performed by employing contact $n$-$n$ interactions, which are known to underestimate the $s$-wave content in other halo nuclei such as $^{11}$Li. In the present work, the three-body hyperspherical formalism with finite-range two-body interactions is used to describe $^{19}$B. In particular, two different finite-range $n$-$n$ interactions will be used, as well as a simple central Gaussian potential whose range is progressively reduced. The purpose is to determine the main properties of the nucleus and investigate how they change when using contact-like $n$-$n$ potentials. Special attention is also paid to the dependence on the prescription used to account for three-body effects, i.e., a three-body force or a density-dependent $n$-$n$ potential. We have found that the three-body model plus finite-range potentials provide a description of $^{19}$B consistent with the experimental data. The results are essentially independent of the short-distance details of the two-body potentials, giving rise to an $(s_{1/2})^2$ content of about 55%, clearly larger than the initial estimates. Very little dependence has been found as well on the prescription used for the three-body effects. The total computed $B(E1)$ strength is compatible with the experimental result, although we slightly overestimate the data around the low-energy peak of the $dB(E1)/d\varepsilon$ distribution. Finally, we show that a reduction of the $n$-$n$ interaction range produces a significant reduction of the $s$-wave contribution, which then should be expected in calculations using contact interactions.

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