arXiv subjects

Chloë Hebborn

Publications and source records attributed to Chloë Hebborn.

At least 19 recordsLinked to original sources

arXiv2026

Uncertainty quantified three-body model applied to the two-neutron halo $^{22}$C

Two-neutron halo nuclei offer a fascinating probe into the behaviour of quantum few-body systems at the limits of binding. Although few nuclei have already been clearly identified, many of their properties remain poorly constrained. $^{22}$C, one of the heaviest, still lacks a precise identification of its static and dynamic properties, such as its mass and dipole strength in the continuum. One main difficulty is that properties of two-neutron halo nuclei are inferred from experimental data using a theoretical model. Therefore, accurately determining the characteristics of two-neutron halo nuclei requires an accurate theoretical model and careful quantification of the uncertainties. In this work, we examine $^{22}$C with a three-body model, seeing $^{22}$C as a $^{20}$C core and two halo neutrons, and quantify for the first time the uncertainties associated with the $^{20}$C-$n$ interaction using a Bayesian approach. We propagate these uncertainties to properties of bound and scattering states of $^{22}$C, as well as its dipole strength. The comparison of our prediction for the matter radius to experimentally-derived values suggests that $^{22}$C is bound by less than 0.35~MeV and is dominated by a $(s_{1/2})^2$ configuration. Our analysis of the dipole strength shows that final-state interaction needs to be included for an accurate description, the uncertainties on the strength function are about 50\% and are mostly influenced by uncertainties on the ground-state properties, and partial-wave occupation of $^{22}$C depends on the scattering length and the $d_{3/2}$ resonance energy of the $^{20}$C-$n$ unbound system. Such sensitivity of the dipole strength to the properties of both $^{21}$C and $^{22}$C properties motivates a precise measurement of the $^{22}$C dipole strength function, that will allow to precisely and accurately resolve the spectroscopy of these nuclei.

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arXiv2026

Development of an accurate formalism to predict properties of two-neutron halo nuclei: case study of $^{22}$C

When moving away from stability or in loosely-bound systems, few-body clusterized structures like two-neutron halo nuclei appear. These emerge from the interplay between the many- and few-body degrees of freedom, and/or strong coupling between bound and continuum states. This motivates the development of models that can accurately describe few-body dynamics while enforcing shell effects. This work has two goals: understanding how to accurately enforce the Pauli principle in few-body models, as well as presenting new technical developments that allow for more robust and cheaper three-body calculations. We focus on properties of the two-neutron halo 22C, but expect the conclusions to apply to other few-body systems. We use a three-body, hyperspherical harmonics formalism combined with the R-matrix method. We compare predictions for properties of 22C starting from phenomenological interactions and using two methods to remove Pauli-forbidden states, the projection and supersymmetric methods. We also present the algorithms and derivations used. Additionally, we explore model space truncations that allow for reduced computational time. We show convergence of the calculation of both bound and scattering states for $K_{max}\sim 40$. The two methods to enforce the Pauli-exclusion principle lead to different predictions of 22C properties; the projection method is more accurate. We find one efficient channel truncation that reduces the computational cost of our calculations by 20%. Our study clarifies that the projection method is more accurate than the supersymmetric one to enforce the Pauli-exclusion principle. Technical and algorithmic developments enable accurate and efficient computation of two-neutron halo properties. This development paves the way to robust uncertainty quantification in three-body predictions, and is a useful starting point to tackle more complex systems and observables.

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arXiv2025

Connecting ground-state properties of ${}^6$Li to each other and to scattering data

We examine the relationship between the Asymptotic Normalization Coefficient (ANC) of $^6$Li and other low-energy observables in the $α$-deuteron system. Our analysis uses a set of calculations carried out within the {\it ab initio} No Core Shell Model with Continuum (NCSMC) using a variety of inter-nucleon interactions and basis sizes, and yielding ${}^6$Li deuteron separation energies between 1.3 and 1.8 MeV [Phys. Rev. Lett. 129, 042503 (2022)]. These NCSMC calculations show that the square of the ANC is strongly correlated with the separation energy over this range. In this work, we investigate the origin of this correlation using the phenomenological $R$-matrix, a single-channel potential and a perturbative approach. We show that this correlation occurs because the depth of the $α$-deuteron central potential changes by only a small relative amount as the separation energy varies. We then investigate if the ANC can be accurately extracted from $α$-deuteron phase shifts in an ideal case in which low-energy data are available and there are no experimental errors. We find that both $R$-matrix and Coulomb-modified effective-range theory (CM-ERE) yield extracted ANCs close to, although not exactly equal to, the true value, provided the extrapolation is constrained by the known position of the bound-state pole and at least three terms are included in the fit function. The $R$-matrix approach converges faster than the CM-ERE as the number of parameters increases and is also more robust against the inclusion of low-energy and high-energy phase shift data. Finally, our study also shows that a naive quantification of uncertainties by comparing different truncations used in both theories is not accurate, and suggests the accuracy of ANCs extracted from phase shift data needs further investigation.

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arXiv2025

Systematic study of the validity of the eikonal model including uncertainties

Nuclear reactions at intermediate beam energies are often interpreted using the eikonal model. In the analysis of complex reaction probes, where few-body reaction methods are needed, the eikonal method may be used as an efficient way for describing the fragment-target reaction process. In this work, we perform a systematic study to test the validity of the eikonal approximation for nucleon-nucleus reactions. We also quantify uncertainties due to the nucleon optical potential on reaction observables. We inspect the validity of the eikonal model and its semiclassical correction by comparing it to exact solutions (obtained from solving the optical model equation with a finite differences method) for a wide range of reactions. We also study the effect of relativistic corrections, both kinematic and dynamic, by effectively incorporating the relativistic effects at intermediate energies. The uncertainties from a Bayesian global optical potential (KDUQ) are propagated to the observables of interest. Our study includes neutron and proton reactions on $^{27}$Al, $^{40}$Ca, $^{90}$Zr and $^{208}$Pb, for a wide range of energies $E_{lab}=0-400$ MeV. Our results show that for the proton absorption cross section, the eikonal model can be used down to around $60$ MeV and the semiclassical correction extends its use to $30$ MeV. However, the validity of the eikonal model for the neutron total cross section only goes down to $\approx120$ MeV, a range extended to $\approx 50$ MeV when using the semiclassical correction. We find the semi-classical correction to the eikonal model to be less effective in describing the angular distributions. The $1σ$ uncertainty intervals on the observables we studied is less than $5$% for most of the energies considered, but increases rapidly for higher energies, namely energies outside the range of KDUQ ($E_{lab}>200$ MeV).

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arXiv2025

Systematic study of the propagation of uncertainties to transfer observables

A systematic study of parametric uncertainties in transfer reactions is performed using the recently developed uncertainty quantified global optical potential (KDUQ). We consider reactions on the doubly-magic spherical nucleus $^{48}$Ca and explore the dependence of the predicted $(d,p)$ angular distribution uncertainties at different beam energies and for different properties of the final single-particle state populated by the reaction. Our results show that correlations between the uncertainties associated with the bound state potential and with the optical potentials may be important for correctly determining the uncertainty in the transfer cross sections (in our case, these do not add in quadrature). In general, we find small uncertainties in the predicted transfer observables: half-width of the 68% credible interval is roughly $5-10$%, which is comparable to the experimental error on the transfer data. Finally, our results show that the relative magnitude of the parametric uncertainty in transfer observables increases with the beam energy and does not depend strongly on the properties of the final state.

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arXiv2024

Impact of the $^6$Li asymptotic normalization constant onto $α$-induced reactions of astrophysical interest

Indirect methods have become the predominant approach in experimental nuclear astrophysics for studying several low-energy nuclear reactions occurring in stars, as direct measurements of many of these relevant reactions are rendered infeasible due to their low reaction probability. Such indirect methods, however, require theoretical input that in turn can have significant poorly-quantified uncertainties, which can then be propagated to the reaction rates and have a large effect on our quantitative understanding of stellar evolution and nucleosynthesis processes. We present two such examples involving $α$-induced reactions, $^{13}$C($α,n)^{16}$O and $^{12}$C$(α,γ)^{16}$O, for which the low-energy cross sections have been constrained with $(^6$Li$,d)$ transfer data. In this Letter, we discuss how a first-principle calculation of $^6$Li leads to a 21% reduction of the $^{12}$C$(α,γ)^{16}$O cross sections with respect to a previous estimation. This calculation further resolves the discrepancy between recent measurements of the $^{13}$C$(α,n)^{16}$O reaction and points to the need for improved theoretical formulations of nuclear reactions.

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arXiv2023

Sensitivity of one-neutron knockout observables of loosely- to more deeply-bound nuclei

For the last few decades, one-nucleon knockout reactions on light composite targets -- $^9$Be or $^{12}$C -- have been extensively used to study the single-particle (s.p.) structure of nuclei far from stability. To determine which information can be accurately inferred from knockout cross sections, we conduct a sensitivity analysis of these observables considering various s.p. descriptions within the usual eikonal description of the reaction. This work shows that total one-neutron knockout cross sections are not sensitive to the short-range part of the s.p. wave function. Rather, they scale with the mean square radius of the overlap function. Using a perturbative expression of the cross section, we can easily explain our numerical predictions analytically. This analysis suggests that (i) spectroscopic factors extracted from knockout data suffer from sizeable model uncertainties associated with the choice of s.p. wave functions and (ii) knockout reactions constitute an excellent probe of the radius of the nucleus and therefore offer an alternative technique to infer the neutron-skin thickness of exotic nuclei.

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arXiv2023

New perspectives on spectroscopic factor quenching from reactions

The evolution of single-particle strengths as the neutron-to-proton asymmetry changes informs us of the importance of short- and long-range correlations in nuclei and has therefore been extensively studied for the last two decades. 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, constituting a two-decade old puzzle. This work presents 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. Our results demonstrate that, taking into account these uncertainties, the spectroscopic strengths of loosely-bound nucleons extracted from both probes agree with each other and, although there are still discrepancies for deeply-bound nucleons, the slope of the asymmetry dependence of the single-particle strengths inferred from transfer and knockout reactions are consistent within $1σ$. Both probes are consistent with a small asymmetry dependence of these strengths. The uncertainties obtained in this work represent a lower bound and are already significantly larger than the original estimates.

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arXiv2023

Quantifying uncertainties due to optical potentials in one-neutron knockout reactions

One-neutron knockout reactions have been widely used to extract information about the single-particle structure of nuclei from the valley of stability to the driplines. The interpretation of knockout data relies on reaction models, where the uncertainties are typically not accounted for. In this work we quantify uncertainties of optical potentials used in these reaction models and propagate them, for the first time, to knockout observables using a Bayesian analysis. We study two reactions in the present paper, the first of which involves a loosely-bound halo projectile, $^{11}$Be, and the second a tightly-bound projectile, $^{12}$C. We first quantify the parametric uncertainties associated with phenomenological optical potentials. Complementing to this approach, we also quantify the model uncertainties associated with the chiral forces that can be used to construct microscopic optical potentials. For the phenomenological study, we investigate the impact of the imaginary terms of the optical potential on the breakup and stripping components of the knockout cross sections as well as the impact of the angular range. For the $^{11}$Be case, the theoretical uncertainty from the phenomenological method is on the order of the experiment uncertainty on the knockout observables; however, for the $^{12}$C case, the theoretical uncertainty is significantly larger. The widths of the confidence intervals for the knockout observables obtained for the microscopic study and the phenomenological approach are of similar order of magnitude. Based on this work we conclude that structure information inferred from the ratio of the knockout cross sections, will carry a theoretical uncertainty of at least $20\%$ for halo nuclei and at least $40\%$ for tightly-bound nuclei.

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arXiv2022

Green's Function Knockout Formalism

Knockout nuclear reactions, in which a nucleon is removed from a nucleus as a result of the collision with another nucleus, have been widely used as an experimental tool, both to populate isotopes further removed from stability, and to obtain information about the single-particle nature of the nuclear spectrum. In order to fully exploit the experimental information, theory is needed for the description of both the structure of the nuclei involved, and the dynamics associated with the nucleon removal mechanisms. The standard approach, using theoretical shell-model spectroscopic factors for the structure description coupled with an eikonal model of reaction, has been successful when used in the context of the removal of valence nucleons in nuclei close to stability. However, it has been argued that the reaction theory might need to be revisited in the case of exotic nuclei, more specifically for highly asymmetric nuclei in which the deficient species (neutrons or protons) is being removed. We present here a new formalism for the nucleon-removal and -addition reaction through knockout and transfer reactions, that treats consistently structure and reaction properties using dispersive optical potentials. In particular, our formalism includes the dynamical effects associated with the removal of a neutron from the projectile, which might explain the long standing puzzle of the quenching of spectroscopic factors in nuclei with extreme neutrons-to-protons ratios.

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arXiv2022

Ab initio prediction of the $^4{\rm He}(d,γ)\,^6\rm Li$ big bang radiative capture

The rate at which helium ($^4$He) and deuterium ($d$) fuse together to produce lithium-6 ($^6$Li) and a $γ$ ray, $^4$He$(d,γ)^6$Li, is a critical puzzle piece in resolving the roughly three orders of magnitude discrepancy between big bang predictions and astronomical observations for the primordial abundance of $^6$Li. The accurate determination of this radiative capture rate requires the quantitative and predictive description of the fusion probability across the big bang energy window ($30$ keV $\lesssim E\lesssim 400$ keV), where measurements are hindered by low counting rates. We present first-principles (or, ab initio) predictions of the $^4$He$(d,γ)^6$Li astrophysical S-factor using validated nucleon-nucleon and three-nucleon interactions derived within the framework of chiral effective field theory. By employing the ab initio no-core shell model with continuum to describe $^4{\rm He}$-$d$ scattering dynamics and bound $^6\rm Li$ product on an equal footing, we accurately and consistently determine the contributions of the main electromagnetic transitions driving the radiative capture process. Our results reveal an enhancement of the capture probability below 100 keV owing to previously neglected magnetic dipole (M1) transitions and reduce by an average factor of 7 the uncertainty of the thermonuclear capture rate between $0.002$ and $2$ GK.

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arXiv2022

Ab initio informed evaluation of the radiative capture of protons on $^7$Be

The radiative capture of protons by $^7$Be, which is the source of $^8$B that $β$-decays emitting the majority of solar neutrinos measured on earth, has not yet been measured at astrophysically relevant energies. The recommended value for its zero-energy S-factor, $S_{17}$(0) = 20.8$\pm$(0.7)exp$\pm$(1.4)theory eV$\cdot$b, relies on theoretical extrapolations from higher-energy measurements, a process that leads to significant uncertainty. We performed a set of first-principle (or, ab initio) calculations of the $^7$Be($p$, $γ$)$^8$B reaction to provide an independent prediction of the low-energy S-factor with quantified uncertainties. We demonstrate underlying features in the predicted S-factor allowing the combination of theoretical calculations and measurements to produce an evaluated S-factor of $S_{17}$(0) = 19.8$\pm$0.3 eV$\cdot$b. We expect the calculations and uncertainty quantification process described here to set a new standard for the evaluation of light-ion astrophysical reactions.

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arXiv2021

Considering non-locality in the optical potentials within eikonal models

Background: For its simplicity, the eikonal method is the tool of choice to analyze nuclear reactions at high energies ($E>100$ MeV/nucleon), including knockout reactions. However, so far, the effective interactions used in this method are assumed to be fully local. Purpose: Given the recent studies on non-local optical potentials, in this work we assess whether non-locality in the optical potentials is expected to impact reactions at high energies and then explore different avenues for extending the eikonal method to include non-local interactions. Method: We compare angular distributions obtained for non-local interactions (using the exact R-matrix approach for elastic scattering and the adiabatic distorted wave approximation for transfer) with those obtained using their local-equivalent interactions. Results: Our results show that transfer observables are significantly impacted by non-locality in the high-energy regime. Because knockout reactions are dominated by stripping (transfer to inelastic channels), non-locality is expected to have a large effect on knockout observables too. Three approaches are explored for extending the eikonal method to non-local interactions, including an iterative method and a perturbation theory. Conclusions: None of the derived extensions of the eikonal model provide a good description of elastic scattering. This work suggests that non-locality removes the formal simplicity associated with the eikonal model.

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arXiv2021

Halo effective field theory analysis of one-neutron knockout reactions of $^{11}\rm Be$ and $^{15}\rm C$

Background: One-nucleon knockout reactions provide insightful information on the single-particle structure of nuclei. When applied to one-neutron halo nuclei, they are purely peripheral, suggesting that they could be properly modeled by describing the projectile within a Halo Effective Field Theory (Halo-EFT). Purpose: We reanalyze the one-neutron knockout measurements of $^{11}$Be and $^{15}$C-both one-neutron halo nuclei-on beryllium at about 60MeV/nucleon. We consider Halo-EFT descriptions of these nuclei which already provide excellent agreement with breakup and transfer data. Method: We include a Halo-EFT description of the projectile within an eikonal-based model of the reaction and compare its outcome to existing data. Results: Excellent agreement with experiment is found for both nuclei. The asymptotic normalization coefficients inferred from this comparison confirm predictions from \emph{ab initio} nuclear-structure calculations and values deduced from transfer data. Conclusions: Halo-EFT can be reliably used to analyze one-neutron knockout reactions measured for halo nuclei and test predictions from state-of-the-art nuclear structure models on these experimental data.

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arXiv2021

Detailed Study of the Eikonal Reaction Theory for the breakup of one-neutron halo nuclei

Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The Eikonal Reaction Theory (ERT) has been developed by Yahiro, Ogata and Minomo in Prog. Theor. Phys. 126, 167 (2011) to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models. Purpose: We extend these comparisons to more differential breakup cross sections expressed as functions of the relative energy or parallel momentum between the core and halo neutron. Method: ERT predictions of these cross sections are compared to state-of-the-art calculations. Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators {affects ERT differential} cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable. Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

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arXiv2020

Simplified dynamical eikonal approximation

Background: Breakup reactions are often used to probe the nuclear structure of halo nuclei. The eikonal model diverges for Coulomb breakup since it relies on the adiabatic approximation. To correct this weakness, a Coulomb-corrected eikonal method (CCE) using the Coulomb first-order-perturbation approximation was developed. Purpose: Since the CCE mixes two reaction models and treats the Coulomb and nuclear interactions on different footings, we study here an alternative approach. We develop a simplification to the dynamical eikonal approximation (S-DEA) which has a similar numerical cost as the usual eikonal model, and study its efficiency for both nuclear- and Coulomb-dominated breakup reactions. Methods: We compare the energy and parallel-momentum cross sections obtained with the dynamical eikonal approximation, the usual eikonal approximation, the CCE and the S-DEA. Results: The S-DEA leads to precise energy distributions for both breakup reactions. The corresponding parallel-momentum distributions obtained with the S-DEA are improved compared to the ones computed with the eikonal model. It is more efficient for nuclear-dominated breakup than the CCE since it reproduces better the shape and magnitude of the distribution. However, for the Coulomb breakup, the distribution lacks asymmetry. Conclusions: The simplification of the DEA developed in this work improves significantly the eikonal descriptions of breakup energy distribution for both Coulomb- and nuclear-dominated reactions. The asymmetry of the parallel-momentum distribution is enhanced for nuclear-dominated breakup. This study confirms that the asymmetry is due to dynamical effects. A direct prospect of this work would be to extend this model to two-neutron halo-nucleus projectiles.

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arXiv2019

Sensitivity of one-neutron knockout of halo nuclei to their nuclear structure

Halo nuclei are located far from stability and exhibit a very peculiar structure. Due to their very short lifetime, they are often studied through reactions. Breakup reactions are of particular interest since their cross sections are large for these loosely-bound nuclei. Inclusive measurements of breakup--also called knockout reactions--have even higher statistics. In this proceeding, we study which nuclear-structure information can be inferred from the parallel-momentum distribution of the core of one-neutron halo nuclei after the knockout of its halo neutron. In particular, we analyse the influence of the ground-state wavefunction, the presence of excited states within the halo-nucleus spectrum and resonances in the core-neutron continuum. Our analysis shows that such observables are sensitive to the tail of the ground-state wavefunction. The presence of excited state decreases the breakup strength, and this flux is transferred to the inelastic-scattering channel. This indicates a conservation of the flux within each partial wave. We also show that the parallel-momentum distributions are insensitive to the existence of resonances within the continuum, they can thus be ignored in practice. This independence on the continuum argues that the parallel-momentum distributions are ideal observables to extract very precisely the ANCs of halo nuclei.

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arXiv2019

Sensitivity of one-neutron knockout to the nuclear structure of halo nuclei

Background: Information about the structure of halo nuclei are often inferred from one-neutron knockout reactions. Typically the parallel-momentum distribution of the remaining core is measured after a high-energy collision of the exotic projectile with a light target. Purpose: We study how the structure of halo nuclei affects knockout observables considering an eikonal model of reaction. Method: To evaluate the sensitivity of both the diffractive and stripping parallel-momentum distributions to the structure of halo nuclei, we consider several descriptions of the projectile within a halo effective field theory. We consider the case of 11Be, the archetypical one-neutron halo nucleus, impinging on 12C at 68 MeV/nucleon, which are usual experimental conditions for such measurements. The low-energy constants of the description of 11Be are fitted to experimental data as well as to predictions of an ab initio nuclear-structure model. Results: One-neutron knockout reaction is confirmed to be purely peripheral, the parallel-momentum distribution of the remaining core is only sensitive to the asymptotics of the ground-state wavefunction and not to its norm. The presence of an excited state in the projectile spectrum reduces the amplitude of the breakup cross section; the corresponding probability flux is transferred to the inelastic-scattering channel. Although the presence of a resonance in the core-neutron continuum significantly affects the energy distribution, it has no impact on the parallel-momentum distribution. Conclusions: One-neutron knockout cross section can be used to infer information about the tail of the ground-state wavefunction, viz. its asymptotic normalization coefficient (ANC). The independence of the parallel-momentum distribution on the continuum description makes the extraction of the ANC from this observable very reliable.

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