arXiv subjects

J. E. Escher

Publications and source records attributed to J. E. Escher.

At least 19 recordsLinked to original sources

arXiv2025

Microscopic optical potentials from a Greens function approach

Optical potentials are a standard tool in the study of nuclear reactions, as they describe the interaction between a target nucleus and a projectile. The use of phenomenological optical potentials built using experimental data on stable isotopes is widespread. Although successful in their dedicated domain, it is unclear whether these phenomenological potentials can provide reliable predictions for unstable isotopes. To address this problem, optical potentials based on microscopic nuclear structure input calculations prove to be crucial and are an important current line of research. In this work we present an explicit implementation of the Feshbach formalism for the systematic derivation of optical potentials using input from nuclear structure models. Numerical tools for the derivation of Green's functions associated with nonlocal potentials are presented. The new optical potential, based on the valence shell model, is applied to the calculations of n+24Mg elastic scattering and yields a close agreement with the experimental data.

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arXiv2025

Ab initio informed 20Ne(p, p$α$)16O reaction elucidates the emergence of alpha clustering from chiral potentials

We report on the first \textit{ab initio} informed $α$ knock-out reaction in the intermediate-mass region, with the aim to probe the underlying chiral potential and its impact on the emergence of alpha clustering in this mass region. The theoretical predictions of the $α+^{16}$O clustering in the $^{20}$Ne ground state, based on the \textit{ab initio} symmetry-adapted no-core shell model, yield a triple differential cross section for $^{20}$Ne(p, p$α$)$^{16}$O that is in a remarkable agreement with the data. This allows us to examine predictions of surface and in-medium $α$-cluster features from a chiral potential and to compare these to the successful antisymmetrized molecular dynamics approach.

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arXiv2025

Coupling between collective modes in the deformed $^{98}$Zr nucleus: Insights from consistent HFB+QRPA calculations with the Gogny interaction

The Zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. Investigations of the coupling present within isoscalar modes and within isovector modes are scarce but important for advancing our understanding of the microscopic picture of nuclei. To explore some of these underlying coupling features, and to test the predictive power of a state-of-the-art nuclear structure approach, we provide a detailed analysis of the properties of $^{90,96,98}$Zr. This region includes a benchmarking case and offers insights into nuclear deformation phenomena. To investigate the coupling between collective modes in deformed nuclei, we focused our analysis on the ground and excited-state properties of these isotopes, employing a consistent approach with the axially-symmetric deformed Hartree-Fock-Bogoliubov (HFB) and the Quasiparticle Random Phase Approximation (QRPA) framework, both using the Gogny D1M force. This approach effectively describes both low-lying and giant-resonance states. We devoted special attention to the deformed $^{98}$Zr nucleus, where we confirm the existence of coupling between monopole and quadrupole excitations through the $K^π = 0^{+}$ QRPA components and demonstrate an analogous dipole-octupole coupling through the $K^π = 0^{-}$ and $K^π = 1^{-}$ components. Intrinsic transition densities and associated radial projections illustrate the coupling. Our work complements and extends earlier studies carried out using density-functional-based methods and notably, we included the complete Coulomb interaction also in the pairing fields, i.e. we treat terms exactly that are approximated in typical calculations that use the Gogny D1 and D2 interaction families.

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arXiv2023

Optical potentials for the rare-isotope beam era

We review recent progress and motivate the need for further developments in nuclear optical potentials that are widely used in the theoretical analysis of nucleon elastic scattering and reaction cross sections. In regions of the nuclear chart away from stability, which represent a frontier in nuclear science over the coming decade and which will be probed at new rare-isotope beam facilities worldwide, there is a targeted need to quantify and reduce theoretical reaction model uncertainties, especially with respect to nuclear optical potentials. We first describe the primary physics motivations for an improved description of nuclear reactions involving short-lived isotopes, focusing on its benefits for fundamental science discoveries and applications to medicine, energy, and security. We then outline the various methods in use today to build optical potentials starting from phenomenological, microscopic, and ab initio methods, highlighting in particular the strengths and weaknesses of each approach. We then discuss publicly-available tools and resources facilitating the propagation of recent progresses in the field to practitioners. Finally, we provide a set of open challenges and recommendations for the field to advance the fundamental science goals of nuclear reaction studies in the rare-isotope beam era.

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arXiv2022

Uncertainty-quantified phenomenological optical potentials for single-nucleon scattering

Optical-model potentials (OMPs) continue to play a key role in nuclear reaction calculations. However, the uncertainty of phenomenological OMPs in widespread use -- inherent to any parametric model trained on data -- has not been fully characterized, and its impact on downstream users of OMPs remains unclear. Here we assign well-calibrated uncertainties for two representative global OMPs, those of Koning-Delaroche and Chapel Hill '89, using Markov-Chain Monte Carlo for parameter inference. By comparing the canonical versions of these OMPs against the experimental data originally used to constrain them, we show how a lack of outlier rejection and a systematic underestimation of experimental uncertainties contributes to bias of, and overconfidence in, best-fit parameter values. Our updated, uncertainty-quantified versions of these OMPs address these issues and yield complete covariance information for potential parameters. Scattering predictions generated from our ensembles show improved performance both against the original training corpora of experimental data and against a new "test" corpus comprising many of the experimental single-nucleon scattering data collected over the last twenty years. Finally, we apply our uncertainty-quantified OMPs to two case studies of application-relevant cross sections. We conclude that, for many common applications of OMPs, including OMP uncertainty should become standard practice. To facilitate their immediate use, digital versions of our updated OMPs and related tools for forward uncertainty propagation are included as Supplementary Material.

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arXiv2022

Horizons: Nuclear Astrophysics in the 2020s and Beyond

Nuclear Astrophysics is a field at the intersection of nuclear physics and astrophysics, which seeks to understand the nuclear engines of astronomical objects and the origin of the chemical elements. This white paper summarizes progress and status of the field, the new open questions that have emerged, and the tremendous scientific opportunities that have opened up with major advances in capabilities across an ever growing number of disciplines and subfields that need to be integrated. We take a holistic view of the field discussing the unique challenges and opportunities in nuclear astrophysics in regards to science, diversity, education, and the interdisciplinarity and breadth of the field. Clearly nuclear astrophysics is a dynamic field with a bright future that is entering a new era of discovery opportunities.

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arXiv2020

Alpha clustering and alpha-capture reaction rate from ab initio symmetry-adapted description of $^{20}$Ne

We introduce a new framework for studying clustering and for calculating alpha partial widths using ab initio wave functions. We demonstrate the formalism for $^{20}$Ne, by calculating the overlap between the $^{16}$O$+α$ cluster configuration and states in $^{20}$Ne computed in the ab initio symmetry-adapted no-core shell model. We present spectroscopic amplitudes and spectroscopic factors, and compare those to no-core symplectic shell-model results in larger model spaces, to gain insight into the underlying physics that drives alpha-clustering. Specifically, we report on the alpha partial width of the lowest $1^-$ resonance in $^{20}$Ne, which is found to be in good agreement with experiment. We also present first no-core shell-model estimates for asymptotic normalization coefficients for the ground state, as well as for the first excited $4^{+}$ state in $^{20}$Ne that lies in a close proximity to the $^{16}$O$+α$ threshold. This outcome highlights the importance of correlations for developing cluster structures and for describing alpha widths. The widths can then be used to calculate alpha-capture reaction rates for narrow resonances of interest to astrophysics. We explore the reaction rate for the alpha-capture reaction $^{16}$O$(α,γ)^{20}$Ne at astrophysically relevant temperatures and determine its impact on simulated X-ray burst abundances.

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arXiv2018

Towards Neutron Capture on Exotic Nuclei: Demonstrating $(d,pγ)$ as a Surrogate Reaction for $(n,γ)$

The neutron-capture reaction plays a critical role in the synthesis of the elements in stars and is important for societal applications including nuclear power generation and stockpile-stewardship science. However, it is difficult - if not impossible - to directly measure neutron capture cross sections for the exotic, short-lived nuclei that participate in these processes. In this Letter we demonstrate a new technique which can be used to indirectly determine neutron-capture cross sections for exotic systems. This technique makes use of the $(d,p)$ transfer reaction, which has long been used as a tool to study the structure of nuclei. Recent advances in reaction theory, together with data collected using this reaction, enable the determination of neutron-capture cross sections for short-lived nuclei. A benchmark study of the $^{95}$Mo$(d,p)$ reaction is presented, which illustrates the approach and provides guidance for future applications of the method with short-lived isotopes produced at rare isotope accelerators.

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arXiv2018

Radiative-capture cross sections for the $^{139}$La($n,γ$) reactionusing thermal neutrons and structural properties of $^{140}$La

A set of prompt partial $γ$-ray production cross sections from thermal neutron-capture were measured for the $^{139}$La($n,γ$) reaction using a guided beam of subthermal (thermal and cold) neutrons incident upon a $^{\rm nat}$La$_{2}$O$_{3}$ target at the Prompt Gamma Activation Analysis facility of the Budapest Research Reactor. Absolute $^{140}$La cross sections were determined relative to the well-known comparator $^{35}$Cl($n,γ$) cross sections from the irradiation of a stoichiometric $^{\rm nat}$LaCl$_{3}$ sample. The total cross section for radiative thermal neutron-capture on $^{139}$La from the sum of experimentally measured cross sections observed to directly feed the $^{140}$La ground state was determined to be $σ_{0}^{\rm expt} = 8.58(50)$ b. To assess completeness of the decay scheme and as a consistency check, the measured cross sections for transitions feeding the ground state from levels below a critical energy of $E_{c} = 285$ keV were combined with a modeled contribution accounting for ground-state feeding from the quasicontinuum to arrive at a total cross section of $σ_{0} = 9.36(74)$ b. In addition, a neutron-separation energy of $S_{n} = 5161.005(21)$ keV was determined from a least-squares fit of the measured primary $γ$-ray energies to the low-lying levels of the $^{140}$La decay scheme. Furthermore, several nuclear structure improvements are proposed for the decay scheme. The measured cross-section and separation-energy results are comparable to earlier measurements of these quantities.

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arXiv2017

Neutron Transfer Reactions for Deformed Nuclei Using Sturmian Basis States

We study the spin-parity distribution P(J$^π$,E) of $^{156}$Gd excited states above the neutron separation energy $S_{n}=8.536$ MeV \cite{156Gd_list_of_levels} that are expected to be populated via the 1-step neutron pickup reaction $^{157}$Gd($^{3}$He,$^{4}$He)$^{156}$Gd. In analogy with the rotor plus particle model \cite{Bohr&Mottelson-II}, we view excited states in $^{156}$Gd as rotational excitations built on intrinsic states consisting of a neutron hole in the $^{157}$Gd core, that is, a neutron removal from a deformed Woods-Saxon type single-particle state \cite{Woods-Saxon:1954} in $^{157}$Gd. The particle-core interaction usually dominated by a Coriolis coupling are accounted via first order perturbation theory \cite{VGGueorguiev:07062002}. The reaction cross section to each excited state in $^{156}$Gd is calculated as coherent contribution using a standard reaction code \cite{CHUCK} based on spherical basis states. The spectroscopic factor associated with each state is the expansion coefficient of the deformed neutron state in a spherical Sturmian basis along with the spherical form factors \cite{VGGueorguiev:07062002}. The total cross section, as a function of the excitation energy, is generated using Lorentzian smearing distribution function. Our calculations show that, within the assumptions and computational modeling, the reaction $^{3}$He+$^{157}$Gd $\rightarrow$ $^{4}$He+$^{156}$Gd$^{\star}$ has a smooth formation probability P(J$^π$,E) within the energy range relevant to the desired reaction $^{155}$Gd+n $\rightarrow$ $^{156}$Gd$^{\star}$. The formation probability P(J$^π$,E) resembles a Gaussian distribution with centroids and widths that differ for positive and negative parity states.

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arXiv2017

Toward a complete theory for predicting inclusive deuteron breakup away from stability

We present an account of the current status of the theoretical treatment of inclusive $(d,p)$ reactions in the breakup-fusion formalism, pointing to some applications and making the connection with current experimental capabilities. Three independent implementations of the reaction formalism have been recently developed, making use of different numerical strategies. The codes also originally relied on two different but equivalent representations, namely the prior (Udagawa-Tamura, UT) and the post (Ichimura-Austern-Vincent, IAV) representations. The different implementations have been benchmarked, and then applied to the Ca isotopic chain. The neutron-Ca propagator is described in the Dispersive Optical Model (DOM) framework, and the interplay between elastic breakup (EB) and non-elastic breakup (NEB) is studied for three Ca isotopes at two different bombarding energies. The accuracy of the description of different reaction observables is assessed by comparing with experimental data of $(d,p)$ on $^{40,48}$Ca. We discuss the predictions of the model for the extreme case of an isotope ($^{60}$Ca) currently unavailable experimentally, though possibly available in future facilities (nominally within production reach at FRIB). We explore the use of $(d,p)$ reactions as surrogates for $(n,γ)$ processes, by using the formalism to describe the compound nucleus formation in a $(d,pγ)$ reaction as a function of excitation energy, spin, and parity. The subsequent decay is then computed within a Hauser-Feshbach formalism. Comparisons between the $(d,pγ)$ and $(n,γ)$ induced gamma decay spectra are discussed to inform efforts to infer neutron captures from $(d,pγ)$ reactions. Finally, we identify areas of opportunity for future developments, and discuss a possible path toward a predictive reaction theory.

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arXiv2015

Separable Potentials for (d,p) Reaction Calculations

An important ingredient for applications of nuclear physics to e.g. astrophysics or nuclear energy are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not possible, indirect methods like $(d,p)$ reactions must be used instead. Those $(d,p)$ reactions may be viewed as effective three-body reactions and described with Faddeev techniques. An additional challenge posed by $(d,p)$ reactions involving heavier nuclei is the treatment of the Coulomb force. To avoid numerical complications in dealing with the screening of the Coulomb force, recently a new approach using the Coulomb distorted basis in momentum space was suggested. In order to implement this suggestion, one needs to derive a separable representation of neutron- and proton-nucleus optical potentials and compute their matrix elements in this basis.

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arXiv2015

Towards a Faddeev-AGS description of $(d,p)$ reactions with heavy nuclei: Regularizing integrals with Coulomb functions

The repulsive Coulomb force poses severe challenges when describing $(d, p)$ reactions for highly charged nuclei as a three-body problem. Casting Faddeev-AGS equations in a Coulomb basis avoids introducing screening of the Coulomb force. However, momentum space partial-wave $t$-matrix elements need to be evaluated in this basis. When those $t$-matrices are separable, the evaluation requires the folding of a form factor, depending on one momentum variable, with a momentum space partial-wave Coulomb function, which has a singular behavior at the external momentum $q$. We developed an improved regularization scheme to calculate Coulomb distorted form factors as the integral over the Coulomb function and complex nuclear form factors.

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arXiv2014

Separable Optical Potentials for (d,p) Reactions

An important ingredient for applications of nuclear physics to e.g. astrophysics or nuclear energy are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not possible, indirect methods like (d,p) reactions must be used instead. Those (d,p) reactions may be viewed as effective three-body reactions and described with Faddeev techniques. An additional challenge posed by (d,p) reactions involving heavier nuclei is the treatment of the Coulomb force. To avoid numerical complications in dealing with the screening of the Coulomb force, recently a new approach using the Coulomb distorted basis in momentum space was suggested. In order to implement this suggestion, one needs not only to derive a separable representation of neutron- and proton-nucleus optical potentials, but also compute the Coulomb distorted form factors in this basis.

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arXiv2014

Separable Representation of Proton-Nucleus Optical Potentials

Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulomb-distorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton- and neutron-nucleus scattering. We present a generalization of the Ernst-Shakin-Thaler scheme in which a momentum space separable representation of proton-nucleus scattering matrix elements can be calculated in the Coulomb basis. The viability of this method is demonstrated by comparing S-matrix elements obtained for p$+^{48}$Ca and p$+^{208}$Pb for a phenomenological optical potential with corresponding coordinate space calculations.

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arXiv2014

Revisiting surface-integral formulations for one-nucleon transfers to bound and resonance states

One-nucleon transfer reactions, in particular (d,p) reactions, have played a central role in nuclear structure studies for many decades. Present theoretical descriptions of the underlying reaction mechanisms are insufficient for addressing the challenges and opportunities that are opening up with new radioactive beam facilities. We investigate a theoretical approach that was proposed recently to address shortcomings in the description of transfers to resonance states. The method builds on ideas from the very successful R-matrix theory; in particular it uses a similar separation of the parameter space into interior and exterior regions, and introduces a parameterization that can be related to physical observables, which, in principle, makes it possible to extract meaningful spectroscopic information from experiments. We carry out calculations, for a selection of isotopes and energies, to test the usefulness of the new approach.

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arXiv2014

A structural evaluation of the tungsten isotopes via thermal neutron capture

Total radiative thermal neutron-capture $γ$-ray cross sections for the $^{182,183,184,186}$W isotopes were measured using guided neutron beams from the Budapest Research Reactor to induce prompt and delayed $γ$ rays from elemental and isotopically-enriched tungsten targets. These cross sections were determined from the sum of measured $γ$-ray cross sections feeding the ground state from low-lying levels below a cutoff energy, E$_{\rm crit}$, where the level scheme is completely known, and continuum $γ$ rays from levels above E$_{\rm crit}$, calculated using the Monte Carlo statistical-decay code DICEBOX. The new cross sections determined in this work for the tungsten nuclides are: $σ_{0}(^{182}{\rm W}) = 20.5(14)$ b and $σ_{11/2^{+}}(^{183}{\rm W}^{m}, 5.2 {\rm s}) = 0.177(18)$ b; $σ_{0}(^{183}{\rm W}) = 9.37(38)$ b and $σ_{5^{-}}(^{184}{\rm W}^{m}, 8.33 μ{\rm s}) = 0.0247(55)$ b; $σ_{0}(^{184}{\rm W}) = 1.43(10)$ b and $σ_{11/2^{+}}(^{185}{\rm W}^{m}, 1.67 {\rm min}) = 0.0062(16)$ b; and, $σ_{0}(^{186}{\rm W}) = 33.33(62)$ b and $σ_{9/2^{+}}(^{187}{\rm W}^{m}, 1.38 μ{\rm s}) = 0.400(16)$ b. These results are consistent with earlier measurements in the literature. The $^{186}$W cross section was also independently confirmed from an activation measurement, following the decay of $^{187}$W, yielding values for $σ_{0}(^{186}{\rm W})$ that are consistent with our prompt $γ$-ray measurement. The cross-section measurements were found to be insensitive to choice of level density or photon strength model, and only weakly dependent on E$_{\rm crit}$. Total radiative-capture widths calculated with DICEBOX showed much greater model dependence, however, the recommended values could be reproduced with selected model choices. The decay schemes for all tungsten isotopes were improved in these analyses.

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arXiv2013

Separable Representation of Phenomenological Optical Potentials of Woods-Saxon Type

Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g. (d,p) reactions, should be used.} Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. While there exist several separable representations for the nucleon-nucleon interaction, the optical potential between a neutron (proton) and a nucleus is not readily available in separable form. The purpose of this paper is to introduce a separable representation for complex phenomenological optical potentials of Woods-Saxon type. Results: Starting from a global optical potential, a separable representation thereof is introduced based on the Ernst-Shakin-Thaler (EST) scheme. This scheme is generalized to non-hermitian potentials. Applications to n$+^{48}$Ca, n$+^{132}$Sn and n$+^{208}$Pb are investigated for energies from 0 to 50 MeV and the quality of the representation is examined. Conclusions: We find a good description of the on-shell t-matrix for all systems with rank up to 5. The required rank depends inversely on the angular momentum. The resulting separable interaction exhibits a different off-shell behavior compared to the original potential, reducing the high momentum contributions.

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