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A new generation of phenomenological optical potentials requires robust calibration and uncertainty quantification, motivating the use of Bayesian statistical methods. These Bayesian methods usually require calculating observables for thousands or even millions of parameter sets, making fast and accurate emulators highly desirable or even essential. Emulating scattering across different energies or with interactions such as optical potentials is challenging because of the non-affine parameter dependence, meaning the parameters do not all factorize from individual operators. Here we introduce and demonstrate the Reduced Order Scattering Emulator (ROSE) framework, a reduced basis emulator that can handle non-affine problems. ROSE is fully extensible and works within the publicly available BAND Framework software suite for calibration, model mixing, and experimental design. As a demonstration problem, we use ROSE to calibrate a realistic nucleon-target scattering model through the calculation of elastic cross sections. This problem shows the practical value of the ROSE framework for Bayesian uncertainty quantification with controlled trade-offs between emulator speed and accuracy as compared to high-fidelity solvers. Planned extensions of ROSE are discussed., Comment: 19 pages, 9 figures

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 $1\sigma$. 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., Comment: 14 pages: 7 pages of the main text (including one and a half of reference) and 7 pages of supplemental material. Accepted for publication in Phys. Rev. Lett

Previous work quantified the uncertainty associated with the optical potentials between the nucleons and the target. In this study, we extend that work by also including the parameters of the mean field associated with the overlap function of the final bound state, thus obtaining the full parametric uncertainty on transfer observables. We use Bayesian Markov Chain Monte Carlo simulations to obtain parameter posterior distributions. We use elastic-scattering cross sections to constrain the optical potential parameters and use the asymptotic normalization coefficient of the final state to constrain the bound state interaction. We then propagate these posteriors to the transfer angular distributions and obtain confidence intervals for this observable. We study (d,p) reactions on 14C, 16O, and 48Ca at energies in the range E=10-24 MeV. Our results show a strong reduction in uncertainty by using the asymptotic normalization coefficient as a constraint, particularly for those reactions most sensitive to ambiguities in the mean-field. For those reactions, the importance of constraining the bound state interaction is equal to that of constrain the optical potentials. The case of 14C is an outlier because it populates a halo state, and the observable is less sensitive to the nuclear interior. We conclude that when minimal constraints are used on the parameters of the nucleon-target interaction, the 68% confidence interval uncertainties on the differential cross sections are very large (~ 140-185%). However, if elastic-scattering data and the asymptotic normalization coefficient are used in the analysis, with an error of 10% (5%), this uncertainty reduces to ~30% (~15%).

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., Comment: Accepted for publication in Phys. Rev. C, 13 pages (including 2 of appendices and 1 of reference), 5 figures, 2 tables

Breakup reactions are one of the favored probes to study loosely bound nuclei, particularly those in the limit of stability forming a halo. In order to interpret such breakup experiments, the continuum discretized coupled channel method is typically used. In this study, the first Bayesian analysis of a breakup reaction model is performed. We use a combination of statistical methods together with a three-body reaction model (the continuum discretized coupled channel method) to quantify the uncertainties on the breakup observables due to the parameters in the effective potential describing the loosely bound projectile of interest. The combination of tools we develop opens the path for a Bayesian analysis of not only breakup processes, but also a wide array of complex processes that require computationally intensive reaction 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., Comment: 8 pages, 5 figures

For one-neutron halo nuclei, the cross section for elastic scattering and breakup at intermediate energy exhibit similar angular dependences. The Recoil Excitation and Breakup (REB) model of reactions elegantly explains this feature. It also leads to the idea of a new reaction observable to study the structure of loosely-bound nuclear systems: the Ratio. This observable consists of the ratio of angular distributions for different reaction channels, viz. elastic scattering and breakup, which cancels most of the dependence on the reaction mechanism; in particular it is insensitive to the choice of optical potentials that simulate the projectile-target interaction. This new observable is very sensitive to the structure of the projectile. In this article, we review the Ratio Method and its extension to low beam energies and proton-halo nuclei., Comment: Submitted to the European Physical Journal A as a contribution to the Special Issue on "Cluster structure and dynamics of nuclei" dedicated to the memory of Mahir S. Hussein (1944-2019). 12 pages, 7 figures

Background: Separable interactions have a long history in nuclear physics. In the last few years, separable expansions have been used to represent the optical potential between a nucleon (proton or neutron) and a target. Purpose: We explore the non-local properties of these separable optical potentials as well as their convergence behavior. Method: For a couple of cases, we use the generalized Ersnt-Shakin-Thaler scheme to generate separable interactions starting from local optical potentials. We study the variation of the interaction with energy range and rank. Results: We find that, overall the off-diagonal behavior of the converged separable interaction deviates from the Gaussian form assumed by Perey and Buck. However, in the region surrounding the maximum depth the Gaussian form works quite well. Focusing on this region, we study potentials describing neutron elastic scattering on $^{16}$O and $^{48}$Ca for beam energies in the range of $ E=$10-50 MeV and explore several measures of non-locality of the separable interactions. Conclusions: When the energy range considered for generating the separable interaction is $0\le E_{range}\le 50$ MeV, the resulting non-locality is large and target dependent. Contrarily, the nonlocality obtained including larger energy ranges in the separable procedure is independent of the target and other details of the original local potential. We find that, even when including in the expansion many support points with energy ranges $0\le E_{range}\le 2400$ MeV, the resulting potential retains non-local behavior. Connections with microscopic optical potentials as well as other transformations used in the nucleon-nucleon domain are made., Comment: 9 pages, 7 figures

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions., Comment: 14 pages including 3 figures

Single-neutron transfer reactions populating states in the continuum are interesting both for structure and astrophysics. In their description often global optical potentials are used for the nucleon-target interactions, and these interactions are typically local. In our work, we study the effects of nonlocality in $(d,p)$ reactions populating continuum states. This work is similar to that of [1] but now for transfer to the continuum. A theory for computing cross sections for inclusive processes $A (d,p) X$ was explored in [2]. Therein, local optical potentials were used to describe the nucleon-target effective interaction. The goal of the present work is to extend the theory developed in [2] to investigate the effects of including nonlocality in the effective interaction on the relevant reaction observables. We implement the R--matrix method to solve the non--local equations both for the nucleon wavefunctions and the propagator. We then apply the method to systematically study the inclusive process of $(d,p)$ on $^{16}$O, $^{40}$Ca, $^{48}$Ca and $^{208}$Pb at 10, 20 and 50 MeV. We compare the results obtained when non--local interactions are used with those obtained when local equivalent interactions are included. We find that nonlocality affects different pieces of the model in complex ways. Depending on the beam energy and the target, the non-elastic breakup can either increase or decrease. While the non-elastic transfer cross section for each final spin state can change considerably, the main prediction of the model [2], namely the shape of the spin distributions, remains largely unaltered by nonlocality. [1] L. J. Titus and F. M. Nunes. Testing the Perey effect. Phys. Rev. C, 89:034609, Mar 2014. [2] G. Potel, F. M. Nunes, and I. J. Thompson. Establishing a theory for deuteron-induced surrogate reactions. Phys. Rev. C, 92:034611, Sep 2015.

This white paper informs the nuclear astrophysics community and funding agencies about the scientific directions and priorities of the field and provides input from this community for the 2015 Nuclear Science Long Range Plan. It summarizes the outcome of the nuclear astrophysics town meeting that was held on August 21-23, 2014 in College Station at the campus of Texas A&M University in preparation of the NSAC Nuclear Science Long Range Plan. It also reflects the outcome of an earlier town meeting of the nuclear astrophysics community organized by the Joint Institute for Nuclear Astrophysics (JINA) on October 9- 10, 2012 Detroit, Michigan, with the purpose of developing a vision for nuclear astrophysics in light of the recent NRC decadal surveys in nuclear physics (NP2010) and astronomy (ASTRO2010). The white paper is furthermore informed by the town meeting of the Association of Research at University Nuclear Accelerators (ARUNA) that took place at the University of Notre Dame on June 12-13, 2014. In summary we find that nuclear astrophysics is a modern and vibrant field addressing fundamental science questions at the intersection of nuclear physics and astrophysics. These questions relate to the origin of the elements, the nuclear engines that drive life and death of stars, and the properties of dense matter. A broad range of nuclear accelerator facilities, astronomical observatories, theory efforts, and computational capabilities are needed. With the developments outlined in this white paper, answers to long standing key questions are well within reach in the coming decade., Comment: 131 pages, community white paper based on 2012 JINA Town Meeting in Detroit, MI, and 2014 APS Town Meeting in College Station, TX, corrected author names

We present in this paper a formalism for deuteron-induced inclusive reactions. We disentangle direct elastic breakup contributions from other processes (which we generically call non-elastic breakup) implying a capture of the neutron both above and below the neutron emission threshold. The reaction is described as a two step process, namely the breakup of the deuteron followed by the propagation of the neutron-target system driven by an optical potential. The final state interaction between the neutron and the target can eventually form an excited compound nucleus. Within this context, the direct neutron transfer to a sharp bound state is a limiting case of the present formalism., Comment: To appear in the proceedings of the 14th International Conference on Nuclear Reaction Mechanisms, Varenna, Italy

The goal of this work is to establish on firm grounds a theory for deuteron induced neutron capture reactions. This includes formulating elastic and inelastic breakup in a consistent manner. We describe this process both in post and prior form distorted wave Born approximation, and we apply our method to the 53Nb(d,p)X at Ed =15 MeV and 25 MeV, obtaining a good description of the data. We look at the various partial wave contributions, as well as elastic versus inelastic contributions. We also connect our formulation with transfer to neutron bound states., Comment: 11 pages, submitted to Physical Review C

Background: The triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of $^{12}$C in stars. The theory of this process is well established at high temperatures but rather ambiguous in the low temperature regime where measurements are impossible. Purpose: Develop a new three-body method, which tackles properly the scattering boundary condition for three charged particles and takes into account both the resonant and the non-resonant reaction mechanisms on the same footing, to compute the triple-alpha reaction rate at low temperatures. Methods: We combine the R-matrix expansion, the R-matrix propagation method, and the screening technique in the hyperspherical harmonics basis. Results: Both the $2^+_1$ bound state and the $0^+_2$ resonant state in $^{12}$C are well reproduced. We also study the cluster structure of these states. We calculate the triple-alpha reaction rate for $\mathrm{T}=0.01-0.1$ GK. Conclusions: We obtain the same rate as NACRE for temperatures above 0.07 GK, but the new rate is largely enhanced at lower temperatures ($\approx 10^{12}$ at 0.02 GK). The differences are caused by the direct capture contribution to the reaction when three alpha particles can not reach the resonant energies.

The FRIB (Facility for Rare Isotope Beams) Theory Users Group participated in the Joint ATLAS-HRIBF-NSCL-FRIB SuperUsers Meeting, hosted by Michigan State University August 18-20, 2011. Prior to the meeting a survey of the FRIB Theory Users Group was conducted to assess the health of the low-energy nuclear theory community and to identify perceived areas of need, in anticipation of the new demands on theory that will accompany FRIB. Meeting discussions focused on survey results and on possible responses. These discussions are summarized here., Comment: 14 pages

We review here theoretical models for describing various types of reactions involving light nuclei on the driplines. Structure features to be extracted from the analysis of such reaction data, as well as those that need to be incorporated in the reaction models for an adequate description of the processes, are also under focus. The major unsolved theoretical issues are discussed, along with some suggestions for future directions of the field., Comment: 53 page review article to appear in JPhysG (Topical Review)

This white paper informs the nuclear astrophysics community and funding agencies about the scientific directions and priorities of the field and provides input from this community for the 2015 Nuclear Science Long Range Plan. It summarizes the outcome of the nuclear astrophysics town meeting that was held on August 21-23, 2014 in College Station at the campus of Texas AM University in preparation of the NSAC Nuclear Science Long Range Plan. It also reflects the outcome of an earlier town meeting of the nuclear astrophysics community organized by the Joint Institute for Nuclear Astrophysics (JINA) on October 9-10, 2012 Detroit, Michigan, with the purpose of developing a vision for nuclear astrophysics in light of the recent NRC decadal surveys in nuclear physics (NP2010) and astronomy (ASTRO2010). The white paper is furthermore informed by the town meeting of the Association of Research at University Nuclear Accelerators (ARUNA) that took place at the University of Notre Dame on June 12-13, 2014. In summary we find that nuclear astrophysics is a modern and vibrant field addressing fundamental science questions at the intersection of nuclear physics and astrophysics. These questions relate to the origin of the elements, the nuclear engines that drive life and death of stars, and the properties of dense matter. A broad range of nuclear accelerator facilities, astronomical observatories, theory efforts, and computational capabilities are needed. With the developments outlined in this white paper, answers to long standing key questions are well within reach in the coming decade.