arXiv subjects

Matthias Göbel

Publications and source records attributed to Matthias Göbel.

7 recordsLinked to original sources

arXiv2026

Finite-range EFT for the $E1$ strength distribution of ${}^6$He

Halo effective field theory (Halo EFT) is a powerful tool to describe halo nuclei and predict low-energy observables with quantified uncertainties. However, in the case that there is a leading-order interaction determined by two or more effective-range parameters, such as the $^2P_{3/2}$ $nα$ interaction in $^6$He, the standard implementation in the dimer formalism leads to an energy-dependent interaction. This complicates the construction of a Hilbert space of states, especially beyond the two-body problem. As an alternative, we propose the use of a finite-range formulation of Halo EFT, which avoids these complications. For definiteness, we use separable interactions with Yamaguchi-like form factors, but other choices are possible. We solve for the ${}^6$He bound state in this finite-range EFT up to next-to-leading order (NLO) in the Halo EFT power counting and calculate the ground-state $E1$ strength distribution of $^6$He at this order. The shape of the resulting distribution agrees with that obtained in the dimer formalism of the EFT, but finite-range EFT does not require the use of a non-standard wave function normalization condition. We also calculate the root-mean-square charge radius of $^6$He and find $2.06 \pm 0.35$~fm at LO and $2.00 \pm 0.09$~fm at NLO, in agreement with experimental data. To calculate the full $E1$ strength distribution final-state interactions must be incorporated. We approximate the full-three-body scattering operator first by single Møller operators and then by products of up to three Møller operators. The resulting NLO $E1$ strength distribution agrees with the experimental data within theory uncertainties.

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arXiv2026

Renormalizing Two-Neutron Halo Nuclei Without Neutron-Core Interaction

We consider the Effective Field Theory (EFT) scheme proposed by Hongo and Son (HS) to describe two-neutron halo nuclei where the neutron-core interaction is subleading. In this EFT, the ratio of the mean-square matter radius and charge radius is universal in so far that it only depends on the two-neutron separation energy of the nucleus and the neutron-neutron scattering length. By investigating the divergence structure of this theory, we find that one further renormalization condition is required to predict both radii separately. Our renormalization scheme uses one of the mean square radii or the scattering amplitude as input. We use the HS scheme to calculate the matter radii of the two-neutron halo nuclei $^{11}$Li, $^{14}$Be, $^{17}$B, $^{19}$B, and $^{22}$C and compare to the values obtained with standard Halo EFT. In this comparison we use both the physical value of the neutron-core scattering length and rescaled values. We observe good convergence against the HS scheme for the case of a negligible neutron-core interaction. Similar agreement for the radii is also found in the case of the halo nucleus $^6$He, where the $nc$ interaction is in the p-wave. Our renormalization scheme makes the restriction in the ultraviolet cutoff range from the Landau pole explicit. We calculate the position of the Landau pole for various halo nuclei. In all cases the Landau pole restricts the cutoff to rather low values. Finally, we derive an explicit expression for the three-to-three neutron-neutron-core scattering amplitude and discuss its cut structure.

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arXiv2025

Neutron-neutron distribution of the triton from pionless EFT

We compute the neutron-neutron relative-energy distribution of the triton following the hard knockout of the proton in pionless effective field theory. This distribution can be used to study universality as well as to obtain information on the neutron-neutron interaction. Especially, one can infer the scattering length from fitting theory predictions for the shape of the distribution to experimental data. To obtain the distribution for the triton, we first solve the ground-state three-body problem using momentum-space Faddeev equations. Next, we include the neutron-neutron final-state interaction by applying the corresponding Møller operator to the ground state. We present leading-order (LO) and next-to-leading order (NLO) pionless effective field theory results with quantified uncertainties. At NLO, we include the effective ranges semi-perturbatively. We conclude, that pionless EFT works reliably as expected and that the neutron-neutron distribution of the triton shows a significant sensitivity to the scattering length.

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arXiv2025

Nucleon-nucleon correlation functions from different interactions in comparison

Correlation functions as they can be observed in heavy-ion collisions using the femtoscopy technique are a powerful tool to study the interaction among different baryons or mesons. Specifically, the multi-nucleon correlation functions have been under intense experimental and theoretical investigation in the recent years. Due to the interest of using this observable as an input in the construction of potentials between hadrons we revisit the nucleon-nucleon correlation function and calculate it using different nuclear interactions at high precision. Since the nucleon-nucleon potential is determined to reproduce the two-nucleon scattering data, we would like to critically evaluate the amount of this information captured by the correlation function. We study the dependence of the correlations on the nuclear force giving detailed insights into the calculations, in particular the convergence behavior in the partial waves. The coupling between the different partial-wave channels is taken into account and the relevance of this effect is quantified. To make contact with precedent studies the results based on the Argonne V18 interaction are presented. Then we consider also the Norfolk NV2-IIa and NV2-IIb chiral EFT interactions. The analysis of the differences between the correlations of the various interactions shows that for momenta between 0 and 500 MeV there are variations of up to 5.9 % for the $nn$ system, of up to 1.8 % for the $np$ system, and of 1.4 % for the $pp$ system.

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arXiv2023

Universality of $nn$ distributions of $s$-wave $2n$ halos and the unitary limit

We calculate neutron-neutron relative-energy distributions of $s$-wave two-neutron ($2n$) halo nuclei using Halo Effective Field Theory (Halo EFT) at leading order. At this order these systems are described by the $2n$ separation energy, the neutron-core ($nc$) virtual-state energy and the neutron-neutron ($nn$) scattering length. We focus on knockout reactions where the removal of the core is sudden, such that the final-state interactions are dominated by the $nn$ interaction. We consider the neutron relative-energy distribution for the nuclei $^{11}$Li, $^{14}$Be, $^{17}$B, $^{19}$B, and $^{22}$C. We show that the ground-state neutron momentum distributions of all these nuclei stem from a single curve, which can be obtained by taking both the neutron-core and neutron-neutron interaction to the unitary limit. This universal description can be extended to the final distribution measured in experiment by including $nn$ final-state interactions via the approximate technique of enhancement factors. For all the nuclei considered we find good agreement between the full leading-order Halo EFT calculation and the universal prediction obtained in this way. The universality of the ground-state momentum distribution in two-neutron Borromean halos can thus be tested by dividing the experimental results from sudden core knockout by the enhancement factor and comparing to the unitary-limit prediction.

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arXiv2022

Final-state interactions and spin structure in $E1$ breakup of $^11$Li in Halo EFT

We calculate the $E1$ breakup of the $2n$ halo nucleus $^{11}$Li in Halo Effective Field Theory (Halo EFT) at leading order. In Halo EFT, $^{11}$Li is treated as a three-body system of a $^{9}$Li core and two neutrons. We present a detailed investigation of final-state interactions (FSI) in the neutron-neutron $(nn)$ and neutron-core $(nc)$ channels. We employ Moller operators to formulate an expansion scheme that satisfies the non-energy-weighted cluster sum rule and successively includes higher-order terms in the multiple-scattering series for the FSI. Computing the $E1$ strength up to third order in this scheme, we observe apparent convergence and good agreement with experiment. The neutron-neutron FSI is by far the most important contribution and largely determines the maximum value of the $E1$ distribution. However, inclusion of $nc$ FSI does shift the peak position to slightly lower energies. Moreover, we investigate the sensitivity of the $E1$ response to the spin structure of the neutron-${}^9$Li interaction. We contrast results for an interaction that is the same in the spin-1 and spin-2 channels with one that is only operative in the spin-2 channel, and find that good agreement with experimental data is only obtained if the interaction is present in both spin channels. The latter case is shown to be equivalent to a calculation in which the spin of $^9$Li is neglected.

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arXiv2021

Neutron-neutron scattering length from the $^6$He$(p,pα)nn$ reaction

We propose a novel method to measure the neutron-neutron scattering length using the $^{6}$He$(p,pα)nn$ reaction in inverse kinematics at high energies. The method is based on the final state interaction (FSI) between the neutrons after the sudden knockout of the $α$ particle. We show that the details of the neutron-neutron relative energy distribution allow for a precise extraction of the $s$-wave scattering length. We present the state-of-the-art in regard to the theory of this distribution. The distribution is calculated in two steps. First, we calculate the ground-state wave function of $^6$He as a $αn n$ three-body system. For this purpose we use Halo effective field theory (Halo EFT), which also provides uncertainty estimates for the results. We compare our results at this stage to model calculations done with the computer code FaCE. In a second step we determine the effects of the $nn$ FSI using the $nn$ t-matrix. We compare these FSI results to approximate FSI approaches based on standard FSI enhancement factors. While the final distribution is sensitive to the $nn$ scattering length, it depends only weakly on the effective range. Throughout we emphasize the impact of theoretical uncertainties on the neutron-neutron relative energy distribution, and discuss the extent to which those uncertainties limit the extraction of the neutron-neutron scattering length from the reaction $^{6}$He$(p,pα)nn$.

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