arXiv subjects

M. C. Atkinson

Publications and source records attributed to M. C. Atkinson.

At least 19 recordsLinked to original sources

arXiv2026

Extension of the dispersive optical model to improve the description of high-momentum components

An improved treatment of high-momentum components in nuclei is introduced in the framework of the dispersive optical model (DOM). The well-established feature that the peak of the spectral function appears at higher excitation energy in the $A$-1 system with increasing momentum has so far not been successfully accounted for in the DOM. To achieve this feature, it is necessary to abandon the factorization of energy dependence and geometry of the DOM self-energy. The volume absorption below the Fermi energy has thus been represented by a decreasing radius at larger missing energy implying that a numerical treatment of the dispersion relations is necessitated. Earlier DOM results for ${}^{48}$Ca are also improved with this approach, demonstrating that a small neutron skin can still be accompanied by protons having a larger high-momentum tail than neutrons.

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arXiv2026

Single-particle structure of the semi-magic nucleus ${}^{90}$Zr from a nonlocal dispersive optical model

A nonlocal dispersive-optical-model (DOM) analysis has been carried out for neutrons and protons in the semi-magic nucleus $^{90}$Zr. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, the charge distribution, and the binding energy have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. The resulting spectroscopic factors and other DOM ingredients yield a good description of the $(e,e'p)$ cross sections when the open-shell proton system is described with an extension of the DOM that treats pairing. The distinct difference between the open-shell proton system and a closed one is illustrated by the smooth transition from mostly full to mostly empty orbits.

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arXiv2026

Dispersive-optical-model analysis of the asymmetry dependence of neutron skins

New dispersive optical model analyses of ${}^{54}$Fe and ${}^{90}$Zr together with updated results for ${}^{40}$Ca, ${}^{48}$Ca, and the earlier result for ${}^{208}$Pb shed light on the behavior of neutron skins in nuclei. Starting with a negative skin for ${}^{40}$Ca, a trend increasing somewhat stronger than linear emerges when the neutron skin of these nuclei is considered as a function of asymmetry, $(N-Z)/A$, and linked to the Green's function Monte Carlo results for asymmetric He nuclei. This general trend is consistent with the expectation that nuclei near the neutron drip line are expected to have very large neutron skins. The present analysis therefore motivates the question of which nuclei provide the most relevant link to neutron star physics.

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arXiv2024

Learning from knockout reactions using a dispersive optical model

We present the empirical dispersive optical model (DOM) as applied to direct nuclear reactions. The DOM links both scattering and bound-state experimental data through a dispersion relation which allows for fully-consistent, data-informed predictions for nuclei where such data exists. In particular, we review investigations of the electron-induced proton knockout reaction from both $^{40}$Ca and $^{48}$Ca in a distorted-wave impulse approximation (DWIA) utilizing the DOM for a fully-consistent description. Viewing these reactions through the lens of the DOM allows us to connect the documented quenching of spectroscopic factors with increased high-momentum proton content in neutron-rich nuclei. A similar DOM-DWIA description of the proton-induced knockout from $^{40}$Ca, however, does not currently fit in the consistent story of its electron-induced counterpart. With the main difference in the proton-induced case being the use of an effective proton-proton interaction, we suggest that a more sophisticated in-medium interaction would lead to consistent results.

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arXiv2024

Investigating the weak charge of $^{48}$Ca using a dispersive optical model

A new nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{48}$Ca that reproduces the weak-form-factor measurement of CREX. In addition to elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution, the CREX-measured weak form factor has been fit to extract the neutron and proton self-energies both above and below the Fermi energy. The resulting single-particle propagators yield a weak form factor of $F_W = 0.125 \pm 0.05$ and a neutron skin of $R_\mathrm{skin} = 0.152 \pm 0.05$ fm, in good agreement with CREX. The rearrangement of the neutron distribution to accommodate such a thin neutron skin results in the high-momentum content of the neutrons exceeding that of the protons, in contrast to what is expected from high-energy two-nucleon knockout measurements by the CLAS collaboration and ab initio asymmetric matter calculations. The present analysis also emphasizes the importance of neutron experimental data in constraining weak charge observables necessary for a precise description of neutron densities. Notably, the neutron reaction cross section and further parity-violating experiments weak form factor measurements are essential to generate a unique way to determine the $^{48}$Ca neutron distribution in this framework.

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arXiv2024

Ab initio calculation of the $^3$He$(\alpha,\gamma)^7$Be astrophysical S factor with chiral two- and three-nucleon forces

The $^3$He$(\alpha,\gamma)^7$Be radiative capture reaction plays a key role in the creation of elements in stars as well as in the production of solar neutrinos, the observation of which is one of the main tools to study the properties of our sun. Since accurate experimental measurements of this fusion cross section at solar energies are difficult due to the strong Coulomb repulsion between the reactants, the onus falls on theory to provide a robust means for extrapolating from the region where experimental data is available down to the desired astrophysical regime. We present the first microscopic calculations of $^3$He$(\alpha,\gamma)^7$Be with explicit inclusion of three-nucleon forces. Our prediction of the astrophysical $S$ factor qualitatively agrees with experimental data. We further incorporate experimental bound-state and scattering information in our calculation to arrive at a more quantitative description. This process reveals that our current model lacks sufficient repulsion in the $1/2^+$ channel of our model space to simultaneously reproduce elastic-scattering data. This deficit suggests that $^3$He$(\alpha,\gamma)^7$Be probes aspects of the nuclear force that are not currently well-constrained.

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arXiv2024

Neutron skins: A perspective from dispersive optical models

An overview is presented of neutron skin predictions obtained using an empirical nonlocal dispersive optical model (DOM). The DOM links both scattering and bound-state experimental data through a subtracted dispersion relation which allows for fully-consistent, data-informed predictions for nuclei where such data exists. Large skins were predicted for both ${}^{48}$Ca ($R^{48}_\textrm{skin}=0.25 \pm 0.023$ fm in 2017) and $^{208}$Pb ($R^{208}_\textrm{skin}=0.25 \pm 0.05$ fm in 2020). While the DOM prediction in $^{208}$Pb is within 1$\sigma$ of the subsequent PREX-2 measurement, the DOM prediction in $^{48}$Ca is over 2$\sigma$ larger than the thin neutron skin resulting from CREX. From the moment it was revealed, the thin skin in ${}^{48}$Ca has puzzled the nuclear-physics community as no adequate theories simultaneously predict both a large skin in ${}^{208}$Pb and a small skin in ${}^{48}$Ca. The DOM is unique in its ability to treat both structure and reaction data on the same footing, providing a unique perspective on this $R_\textrm{skin}$ puzzle. It appears vital that more neutron data be measured in both the scattering and bound-state domain for ${}^{48}$Ca to clarify the situation.

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arXiv2022

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

Ab initio calculation of the $\beta$-decay from $^{11}$Be to a p${+}^{10}$Be resonance

The exotic $\beta$-delayed proton emission is calculated in $^{11}$Be from first principles using chiral two- and three-nucleon forces. To investigate the unexpectedly-large branching ratio measured in [PRL 123, 082501 (2019)] we calculate the proposed $(1/2^+,1/2)$ proton resonance in $^{11}$B using the no-core shell model with continuum. This calculation helps to address whether this enhancement is caused by unknown dark decay modes or an unobserved proton resonance. We report a branching ratio of $b_p = (1.3\pm0.5)\times10^{-6}$, suggesting that its unexpectedly-large value is caused by an unobserved proton resonance in $^{11}$B.

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arXiv2022

First application of dispersive optical model to ($p$,$2p$) analysis within distorted wave impulse approximation framework

Both ($e$,$e'p$) and ($p$,$2p$) reactions have been performed to study the proton single-particle character of nuclear states with its related spectroscopic factor. Recently, the dispersive optical model (DOM) was applied to the ($e$,$e'p$) analysis revealing that the traditional treatment of the single-particle overlap function, distorted waves, and nonlocality must be further improved to achieve quantitative nuclear spectroscopy. We apply the DOM wave functions to the traditional ($p$,$2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e$,$e'p$) cross section with the result of the ($p$,$2p$) analysis. Additionally, we make a comparison with a phenomenological single-particle wave function and optical potential. Uncertainty arising from a choice of $p$-$p$ interaction is also investigated. We implement the DOM wave functions to the distorted wave impulse approximation (DWIA) framework for ($p$,$2p$) reactions. DOM + DWIA analysis on $^{40}$Ca($p$,$2p$)$^{39}$K data generates a proton $0d_{3/2}$ spectroscopic factor of 0.560, which is meaningfully smaller than the DOM value of 0.71 shown to be consistent with the ($e$,$e'p$) analysis. Uncertainties arising from choices of single-particle wave function, optical potential, and $p$-$p$ interaction do not explain this inconsistency. The inconsistency in the spectroscopic factor suggests there is urgent need for improving the description of $p$-$p$ scattering in a nucleus and the resulting in-medium interaction with corresponding implications for the analysis of this reaction in inverse kinematics.

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arXiv2020

Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

The energy density is calculated in coordinate space for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of $^{8}$Be is also calculated using the Green's function Monte-Carlo method employing the Argonne/Urbana two and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4$πr^2$ phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with \textit{ab initio} self-consistent Green's function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this paper indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13-14 MeV when the interior of $^{208}$Pb is considered.

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arXiv2020

Isotopically resolved neutron total cross sections at intermediate energies

The neutron total cross sections $σ_{tot}$ of $^{16,18}$O, $^{58,64}$Ni, $^{103}$Rh, and $^{112,124}$Sn have been measured at the Los Alamos Neutron Science Center (LANSCE) from low to intermediate energies (3 $\leq E_{lab} \leq$ 450 MeV) by leveraging waveform-digitizer technology. The $σ_{tot}$ relative differences between isotopes are presented, revealing additional information about the isovector components needed for an accurate optical-model description away from stability. Digitizer-enabled $σ_{tot}$-measurement techniques are discussed and a series of uncertainty-quantified dispersive optical model (DOM) analyses using these new data is presented, validating the use of the DOM for modeling light systems ($^{16,18}$O) and systems with open neutron shells ($^{58,64}$Ni and $^{112,124}$Sn). The valence-nucleon spectroscopic factors extracted for each isotope reaffirm the usefulness of high-energy proton reaction cross sections for characterizing depletion from the mean-field expectation.

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arXiv2020

Systematic Matter and Binding-Energy Distributions from a Dispersive Optical Model Analysis

We present the first systematic nonlocal dispersive optical model analysis using both bound-state and scattering data of $^{16,18}$O, $^{40,48}$Ca, $^{58,64}$Ni, $^{112,124}$Sn, and $^{208}$Pb. In all systems, roughly half the total nuclear binding energy is associated with the most-bound 10% of the total nucleon density. The extracted neutron skins reveal the interplay of asymmetry, Coulomb, and shell effects on the skin thickness. Our results indicate that simultaneous optical model fits of inelastic scattering and structural data on isotopic pairs are effective for constraining asymmetry-dependent nuclear structural quantities otherwise difficult to observe experimentally.

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arXiv2020

A dispersive optical model analysis of $^{208}$Pb generating a neutron-skin prediction beyond the mean field

A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{208}$Pb. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, the charge distribution, and the binding energy have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we have determined the charge and matter distributions in $^{208}$Pb. The predicted spectroscopic factors are consistent with results from the $(e,e'p)$ reaction and inelastic-electron-scattering data to very high spin states. Sensible results for the high-momentum content of neutrons and protons are obtained with protons appearing more correlated, in agreement with experiment and \textit{ab initio} calculations of asymmetric matter. A neutron skin of $0.25\pm0.05$ fm is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a non-negligible role in the formation of the neutron skin in finite nuclei.

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arXiv2019

Investigating the link between proton reaction cross sections and the quenching of proton spectroscopic factors in $^{48}$Ca

The nucleon self-energies of $^{40}$Ca and $^{48}$Ca are determined using a nonlocal dispersive optical model (DOM). By enforcing the dispersion relation connecting the real and imaginary part of the self-energy, scattering and structure data are used to constrain these self-energies. The ability to calculate both bound and scattering states simultaneously puts these self-energies in a unique position to consistently describe exclusive knockout reactions such as $(e,e'p)$. The present analysis reveals the importance of high-energy proton reaction cross-section data in constraining spectroscopic factors required for the description of the $(e,e'p)$ cross sections. In particular, it is imperative that high-energy proton reaction cross-section data are measured for $^{48}$Ca in the near future so that the quenching of the spectroscopic factors in the $^{48}$Ca$(e,e'p)^{47}$K reaction can be unambiguously constrained using the DOM. Measurements of proton reaction cross sections in inverse kinematics employing rare isotope beams with large neutron excess will provide corresponding constraints on proton spectroscopic factors for exotic nuclei. Moreover, DOM generated spectral functions indicate that the quenching of spectroscopic factors compared to $^{40}$Ca is not only due to long-range correlation, but also partly due to the increase in high-momentum protons in $^{48}$Ca on account of the strong neutron-proton interaction. Single-particle momentum distributions of protons and neutrons in $^{48}$Ca calculated from these spectral functions confirm that neutron excess causes a higher fraction of high-momentum protons than neutrons.

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arXiv2019

Combining nuclear reactions and structure with the dispersive optical model

A review of recent applications of the nonlocal dispersive optical model (DOM) is presented that allows a simultaneous description of nuclear structure and nuclear reactions. An assessment of the quality of the resulting potentials for $^{40}$Ca and $^{48}$Ca is discussed for the description of the $(e,e'p)$ reaction to valence hole states and the possibility of interpreting the data in terms of absolute spectroscopic factors. The relevance of these results in the context of conflicting interpretations between transfer and knockout reactions is pointed out as well as the importance of proton reaction cross sections for isotopes with neutron excess. Application of the nonlocal DOM to $^{48}$Ca incorporates the effect of the 8 additional neutrons and allows for an excellent description of elastic scattering data of both protons and neutrons. The corresponding neutron distribution constrained by all available data generates a prediction for the neutron skin that is larger than most mean-field and available \textit{ab initio} results. Results are presented for the most recent nonlocal DOM analysis of $^{208}$Pb.

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arXiv2018

Validity of the distorted-wave impulse-approximation description of ${}^{40}$Ca$(e,e'p)^{39}$K data using only ingredients from a nonlocal dispersive optical model

The nonlocal implementation of the dispersive optical model (DOM) provides all the ingredients for distorted-wave impulse-approximation (DWIA) calculations of the $(e,e'p)$ reaction. It provides both the overlap function, including its normalization, and the outgoing proton distorted wave. This framework is applied to describe the knockout of a proton from the $0\textrm{d}\frac{3}{2}$ and $1\textrm{s}\frac{1}{2}$ orbitals in ${}^{40}$Ca with fixed normalizations of 0.71 and 0.60, respectively. Data were obtained in parallel kinematics for three outgoing proton energies: 70, 100, and 135 MeV. Agreement with the data is as good as, or better than, previous descriptions employing local optical potentials and overlap functions from Woods-Saxon potentials - both with standard nonlocality corrections - whose normalization (spectroscopic factor) and radius were fitted to the data. The present analysis suggests that slightly larger spectroscopic factors are obtained when nonlocal optical potentials are employed than those generated with local potentials. The results further suggest that the chosen kinematical window around 100 MeV proton energy provides the best and cleanest method to employ the DWIA for the analysis of this reaction. The conclusion that substantial ground-state correlations cannot be ignored when describing a closed-shell atomic nucleus is therefore confirmed in detail. To reach these conclusions, it is essential to have a complete description of the nucleon single-particle propagator that accounts for all elastic nucleon-scattering observables in a wide energy domain up to 200 MeV. The current nonlocal implementation of the DOM fulfills this requirement.

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arXiv2017

The neutron skin thickness of $^{48}$Ca from a nonlocal-dispersive-optical-model analysis

A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{48}$Ca. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator resulting from these self-energies we have determined the charge and neutron matter distributions in $^{48}$Ca. A neutron skin of 0.249$\pm$0.023~fm is deduced. The energy dependence of the total neutron cross sections is shown to have strong sensitivity to the skin thickness.

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