Engineering topics
Nunes, F. M.
Publications and source records attributed to Nunes, F. M..
First Experimental Test of the Ratio Method
The ratio is a new reaction observable suggested to extract accurately structure information on halo nuclei. It corresponds to the ratio of differential cross sections for scattering and breakup, which is predicted to remove the uncertainty related to the reaction dynamics. We present here the first experimental test of the method for the 11 Be + 12 C collision at E Lab = 20A MeV performed at Texas A&M University. Differential cross sections for scattering and inclusive one-neutron breakup have been measured with the new detector array BlueSTEAl. The ratio of cross sections is very smooth and independent of the projectile-target interaction, which demonstrates the validity of the ratio method. We extend our analysis to existing 11 Be + 208 Pb data, confirming that the method works well on any target.
ROSE: A reduced-order scattering emulator for optical models
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 nonaffine 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 nonaffine 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. Finally, planned extensions of ROSE are discussed.
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. Here, 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 σ . 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.
Complete quantification of parametric uncertainties in ( d , p ) transfer reactions
Deuteron-induced transfer reactions are a popular probe in nuclear structure and nuclear astro physics studies. The interpretation of these transfer measurements relies on reaction theory that takes as input effective interactions between the nucleons and the target nucleus. 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 14 C, 16 O, and 48 Ca at energies in the range $E$ $d$ = 7 - 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 constraining the optical potentials. Furthermore, the case of 14 C is an outlier because the cross section is less sensitive to the nuclear interior. When minimal constraints are used on the parameters of the nucleon-target interaction, the 1σ uncertainties on the differential cross sections are large (~ 500-100%). 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%).
Experimental study of the nature of the 1 – and 2 – excited states in 10 Be using the 11 Be (p,d) reaction in inverse kinematics
In this paper, we investigated the structure of two excited states in the nucleus 10 Be, which were suspected to have spatially extended wave functions (or "haloes"). This was done by performing a transfer reaction that removed a neutron from the core of the 11 Be nucleus, a well-known one-neutron halo nucleus. By doing so, we specifically produced configurations, whereas the halo neutron in 11 Be remained when populating excited states in 10 Be. If the two excited states in 10 Be had a strong overlap with those configurations, one would have expected them to be strongly populated in the reaction. We find that this was not quite the case and we postulated that the reason why was because those states had a mixed configuration that not only displayed halo-like, but also cluster-like, properties. The overlap was therefore not as strong as expected (and suggested by previous experiments).
Considering nonlocality 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 nonlocal optical potentials, in this work we assess whether nonlocality in the optical potentials is expected to impact reactions at high energies and then explore different avenues for extending the eikonal method to include nonlocal interactions. Method: We compare angular distributions obtained for nonlocal 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 nonlocality in the high-energy regime. Because knockout reactions are dominated by stripping (transfer to inelastic channels), nonlocality is expected to have a large effect on knockout observables too. Three approaches are explored for extending the eikonal method to nonlocal 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. Here, this paper suggests that nonlocality removes the formal simplicity associated with the eikonal model.
Get on the BAND Wagon: a Bayesian framework for quantifying model uncertainties in nuclear dynamics
In this paper, we describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework.
Extracting capture from transfer reactions
Indirect reaction techniques are very important in astrophysics as they provide information that is complementary to direct measurements or that otherwise cannot be obtained directly. It is then critical to have a reliable reaction theory that can connect the reaction measurement with the astrophysical information desired. This is a brief report on the progress made in the theory for transfer reactions when used to determine neutron capture rates for r-process and proton capture for rp-process nuclei. We will discuss the different types of experiments and their connection to astrophysics. An overview of the current status of the theory will be provided, with emphasis on several recent theory developments, including transfer to continuum, the improvement of the optical potential and uncertainty quantification. Applications to a couple of neutron rich and proton rich cases will be discussed.
Merging ab initio theory and few-body approach for (d, p) reactions
A framework for A(d, p)B reactions is introduced by merging the microscopic approach to computing the properties of the nucleon-target systems and the three-body n + p + A reaction formalism, thus providing a consistent link between the reaction cross sections and the underlying microscopic structure. In this first step toward a full microscopic description, we focus on the inclusion of the neutron-target microscopic properties. The properties of the neutron-target subsystem are encapsulated in the Green's function which is computed with the coupled Cluster theory using a chiral nucleon-nucleon and three-nucleon interactions. Subsequently, this many-body information is introduced in the few-body Green's Function Transfer approach to (d, p) reactions. Our benchmarks on stable targets 40,48 Ca show an excellent agreement with the data. We then proceed to make specific predictions for (d, p) on neutron rich 52,54 Ca isotopes. These predictions are directly relevant to testing the new magic numbers N = 32, 34 and are expected to be feasible in the first campaign of the projected FRIB facility.
Exploring experimental conditions to reduce uncertainties in the optical potential
Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more groups attempting to understand the uncertainties in their calculations. However, recent studies have shown that the uncertainties on the optical potentials are too large for the theory to be useful. The goal of this work is to explore possible experimental conditions that may reduce the uncertainties on elastic scattering and single-nucleon transfer cross sections that come from the fitting of the optical model parameters to experimental data. Using Bayesian methods, we explore the effect of the uncertainties of optical model parameters on the angular grid of the differential cross section, including cross-section data at nearby energies, and changes in the experimental error bars. We also study the effect on the resulting uncertainty when other observables are included in the fitting procedure, particularly the total (reaction) cross sections. We study proton and neutron elastic scattering on 48 Ca and 208 Pb. We explore the parameter space with the Markov-chain Monte Carlo method, produce posterior distributions for the optical model parameters, and construct the corresponding 95% confidence intervals on the elastic-scattering cross sections. We also propagate the uncertainties on the optical potentials to the 48 Ca(d,p) 49 Ca(g.s.) and 208 Pb(d,p) 209 Pb(g.s.) cross sections. We find little sensitivity to the angular grid and an improvement of up to a factor of 2 on the uncertainties by including data at a nearby energy. Although reducing the error bars on the data does reduce the uncertainty, the gain is often considerably smaller than one would naively expect. We also find that the inclusion of total reaction cross section can improve the uncertainty although the magnitude of the effect depends strongly on the cases considered.
Deuteron-α scattering: Separable versus nonseparable Faddeev approach
Deuteron-induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Faddeev-AGS 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. However, it needs to be demonstrated that observables calculated based on separable interactions agree exactly with those based on nonseparable forces. Momentum space AGS equations are solved with separable and nonseparable forces as coupled integral equations. Deuteron-α scattering is calculated via momentum space AGS equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)- 4 He force, for which the Pauli-forbidden S-wave bound state is projected out. Elastic as well as breakup observables are calculated and compared to results in which the interactions in the two-body sub-systems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. We find that the calculations based on the separable representation of the interactions and the original interactions give results that are in excellent agreement. Specifically, integrated cross sections and angular distributions for elastic scattering agree within ≈ 1 %, which is well below typical experimental errors. In addition, the fivefold differential cross sections corresponding to breakup of the deuteron agree extremely well.
Erratum: Informing direct neutron capture on tin isotopes near the N = 82 shell closure [Phys. Rev. C 99 , 041302(R) (2019)]
Erratum to "Informing direct neutron capture on tin isotopes near the N = 82 shell closure [Phys. Rev. C 99, 041302(R) (2019)]
Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions
Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with the elastic and the transfer process for both methods, which are evaluated against data via a comparison of the empirical coverage probabilities. Expectedly, the frequentist approach is not as flexible as the Bayesian approach in exploring parameter space and often ends up in a different minimum. We also show that the two methods produce significantly different correlations. In the end, the frequentist approach produces significantly narrower uncertainties on the considered observables than the Bayesian. Lastly, our study demonstrates that the uncertainties on the reaction observables considered here within the Bayesian approach represent reality more accurately than the much narrower uncertainties obtained using the standard frequentist approach.
Constraining the Neutron Star Compactness: Extraction of the Al 23 ( p , γ ) Reaction Rate for the r p Process
The 23 Al(p,γ) 24 Si reaction is among the most important reactions driving the energy generation in type-I x-ray bursts. However, the present reaction-rate uncertainty limits constraints on neutron star properties that can be achieved with burst model-observation comparisons. In this work, we present a novel technique for constraining this important reaction by combining the GRETINA array with the neutron detector LENDA coupled to the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The 23 Al(d,n) reaction was used to populate the astrophysically important states in 24 Si. This enables a measurement in complete kinematics for extracting all relevant inputs necessary to calculate the reaction rate. For the first time, a predicted close-lying doublet of a $2^{+}_{2}$ and ($4^{+}_{1}, 0^{+}_{2}$) state in 24 Si was disentangled, finally resolving conflicting results from two previous measurements. Furthermore, it was possible to extract spectroscopic factors using GRETINA and LENDA simultaneously. This new technique may be used to constrain other important reaction rates for various astrophysical scenarios.
Constraining spectroscopic factors near the r -process path using combined measurements: Kr 86 ( d , p ) 87 Kr
Background: Current nuclear structure models indicate that the shell structure near the valley of stability, with well-established shell closures at N=50, for example, changes in very neutron-rich nuclei far from stability. Single-particle properties of nuclei away from stability can be probed in single-neutron (d,p) transfer reactions with beams of rare isotopes. The interpretation of these data requires reaction theories with various effective interactions. Often, approximations made to the final bound-state potential introduce a large uncertainty in the extracted single-particle properties, in particular the spectroscopic factor. Purpose: Mitigate this uncertainty using a combined measurement method to constrain the shape of the bound-state potential and to reliably extract the spectroscopic factor. Methods: The 2 H( 86 Kr,p) 87 Kr reaction was measured at 33 MeV/u at the National Superconducting Cyclotron Laboratory (NSCL) as a test of the combined method. The reaction protons were detected with the Oak Ridge Rutgers University Barrel Array (ORRUBA) of position sensitive silicon strip detectors, the first implementation of ORRUBA coupled to the S800 spectrograph with fast beams at NSCL. Results: These measurements at 33 MeV/u are combined with previous studies of the 86 Kr(d,p) reaction at 5.5 MeV/u to demonstrate a successful case of the combined method to constrain the shape of the single-particle potential and deduce asymptotic normalization coefficients and spectroscopic factors. In particular, the single-particle asymptotic normalization coefficient for the ground state of 87 Kr was constrained to b d5/2 =6.46$^{+1.12}_{–0.57}$ fm –1/2 , and therefore the deduced spectroscopic factor is S=0.44$^{+0.09}_{–0.13}$ with uncertainties dominated by experimental statistics. Conclusions: By combining measurements at two very different beam energies, single-particle asymptotic normalization coefficients, at least for low angular momentum transfers, can be constrained. Thus, spectroscopic factors can be deduced with uncertainties dominated by experimental uncertainties, rather than limited knowledge of bound-state potential parameters.
Informing direct neutron capture on tin isotopes near the N = 82 shell closure
Half of the elements heavier than iron are believed to be produced through the rapid neutron-capture process ($r$-process). The astrophysical environment(s) where the $r$-process occurs remains an open question, even after recent observations of neutron-star mergers and the associated kilonova. Features in the abundance pattern of $r$-process ashes may provide critical insight for distinguishing contributions from different possible sites, including neutron-star mergers and core-collapse supernovae. In particular, the largely unknown neutron-capture reaction rates on neutron-rich unstable nuclei near 132 Sn could have a significant impact on the final $r$-process abundances. To better determine these neutron-capture rates, the ($d,p$) reaction has been measured in inverse kinematics using radioactive ion beams of 126 Sn and 128 Sn and a stable beam of 124 Sn interacting with a (CD 2 )$_n$ target. An array of position-sensitive silicon strip detectors, including the Super Oak Ridge Rutgers University Barrel Array, was used to detect light reaction products. In addition to the present measurements, previous measurements of 130,132 Sn($d,p$) were reanalyzed using state-of-the-art reaction theory to extract a consistent set of spectroscopic factors for ($d,p$) reactions on even tin nuclei between the heaviest stable isotope 124 Sn and doubly magic 132 Sn. The spectroscopic information was used to calculate direct-semidirect ($n,γ$) cross sections, which will serve as important input for r-process abundance calculations.