arXiv subjects

M. Piarulli

Publications and source records attributed to M. Piarulli.

At least 19 recordsLinked to original sources

arXiv2025

Electromagnetic radii of light nuclei from variational Monte Carlo calculations

We present variational Monte Carlo calculations of charge and magnetic radii in $A \le 10$ nuclei. The calculations are based on the Norfolk two- and three-nucleon interactions, and associated one- and two-nucleon electromagnetic charge and current operators derived up to next-to-next-to-next-to leading order in the chiral expansion. The charge and magnetic radii are extracted from the respective form factors. We find that the charge radii are within 5\% of the experimental values for the nuclei considered. For the magnetic radii, a comparison is available only with $^3$H and $^3$He electron scattering data that are affected by large error bars. We hope that our predictions foster an interest in precisely measuring magnetic radii of heavier systems.

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arXiv2024

Longitudinal form factors of $A\,\leq\,10$ nuclei in a chiral effective field theory approach

In this work, we present the elastic electron scattering longitudinal form factors of $A\le 10$ nuclei computed in a variational Monte Carlo approach. We employ the Norfolk family of local chiral interactions and a consistent electromagnetic charge operator. Our calculations are compared both to data and past theoretical evaluations. This work represents, to our knowledge, the first exact many-body calculation of longitudinal form factors in the $7\,\leq\,A\,\leq\,10$ mass range. Finally, we identify $^9$Be and $^{10}$B as candidate targets for renewed experimental interest, as they exhibit the potential to provide more stringent constraints on the theoretical models.

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arXiv2024

Bayesian analysis of nucleon-nucleon scattering data in pionless effective field theory

We perform Bayesian model calibration of two-nucleon ($NN$) low-energy constants (LECs) appearing in an $NN$ interaction based on pionless effective field theory (EFT). The calibration is carried out for potentials constructed using naive dimensional analysis in $NN$ relative momenta ($p$) up to next-to-leading order [NLO, $O(p^2)$] and next-to-next-to-next-to-leading order [N3LO, $O(p^4)$]. We consider two classes of pionless EFT potential: one that acts in all partial waves and another that is dominated by $s$-wave physics. The two classes produce broadly similar results for calibrations to $NN$ data up to $E_{\rm lab}=5$ MeV. Our analysis accounts for the correlated uncertainties that arise from the truncation of the pionless EFT. We simultaneously estimate both the EFT LECs and the parameters that quantify the truncation error. This permits the first quantitative estimates of the pionless EFT breakdown scale, $\Lambda_b$: the 95% intervals are $\Lambda_b \in [50.11,63.03]$ MeV at NLO and $\Lambda_b \in [72.27, 88.54]$ MeV at N3LO. Invoking naive dimensional analysis for the $NN$ potential, therefore, does not lead to consistent results across orders in pionless EFT. This exemplifies the possible use of Bayesian tools to identify inconsistencies in a proposed EFT power counting.

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arXiv2024

Magnetic structure of $A \le 10$ nuclei using the Norfolk nuclear models with quantum Monte Carlo methods

We present Quantum Monte Carlo calculations of magnetic moments, form factors, and densities of $A\le 10$ nuclei within a chiral effective field theory approach. We use the Norfolk two- and three-body chiral potentials and their consistent electromagnetic one- and two-nucleon current operators. We find that two-body contributions to the magnetic moment can be large (up to $\sim33\%$ in $A=9$ systems). We study the model dependence of these observables and place particular emphasis on investigating their sensitivity to using different cutoffs to regulate the many-nucleon operators. Calculations of elastic magnetic form factors for $A\leq 10$ nuclei show excellent agreement with the data out to momentum transfers $q\approx 3$ fm$^{-1}$.

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arXiv2024

Quantum Monte Carlo calculations of magnetic form factors in light nuclei

We present Quantum Monte Carlo calculations of magnetic form factors in $A=6-10$ nuclei, based on Norfolk two- and three-nucleon interactions, and associated one- and two-body electromagnetic currents. Agreement with the available experimental data for $^6$Li, $^7$Li, $^9$Be and $^{10}$B up to values of momentum transfer $q\sim 3$ fm$^{-1}$ is achieved when two-nucleon currents are accounted for. We present a set of predictions for the magnetic form factors of $^7$Be, $^8$Li, $^9$Li, and $^9$C. In these systems, two-body currents account for $\sim40-60\%$ of the total magnetic strength. Measurements in any of these radioactive systems would provide valuable insights on the nuclear magnetic structure emerging from the underlying many-nucleon dynamics. A particularly interesting case is that of $^7$Be, as it would enable investigations of the magnetic structure of mirror nuclei.

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arXiv2023

Nuclear $\beta$ decay as a probe for physics beyond the Standard Model

This white paper was submitted to the 2022 Fundamental Symmetries, Neutrons, and Neutrinos (FSNN) Town Hall Meeting in preparation for the next NSAC Long Range Plan. We advocate to support current and future theoretical and experimental searches for physics beyond the Standard Model using nuclear $\beta$ decay.

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arXiv2022

Densities and momentum distributions in A <=12 nuclei from chiral effective field theory interactions

Current and future electron and neutrino scattering experiments will be greatly aided by a better understanding of the role played by short-range correlations in nuclei. Two-body physics, including nucleon-nucleon correlations and two-body electroweak currents, is required to explain the body of experimental data for both static and dynamical nuclear properties. In this work, we focus on examining nucleon-nucleon correlations from a chiral effective field theory perspective and provide a comprehensive set of new variational Monte Carlo calculations of one- and two-body densities and momentum distributions based on the Norfolk many-body nuclear Hamiltonians for A<=12 systems. Online access to detailed tables and figures is available.

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arXiv2022

Muon capture on deuteron using local chiral potentials

The muon capture reaction $\mu^- + d \rightarrow n + n + \nu_{\mu}$ in the doublet hyperfine state is studied using nuclear potentials and consistent currents derived in chiral effective field theory, which are local and expressed in coordinate-space (the so-called Norfolk models). Only the largest contribution due to the $^1S_0$ $nn$ scattering state is considered. Particular attention is given to the estimate of the theoretical uncertainty, for which four sources have been identified: (i) the model dependence, (ii) the chiral order convergence for the weak nuclear current, (iii) the uncertainty in the single-nucleon axial form factor, and (iv) the numerical technique adopted to solve the bound and scattering $A=2$ systems. This last source of uncertainty has turned out essentially negligible. The $^1S_0$ doublet muon capture rate $\Gamma^D(^1S_0)$ has been found to be $\Gamma^D(^1S_0)=255.8(0.6)(4.4)(2.9)$ s$^{-1}$, where the three errors come from the first three sources of uncertainty. The value for $\Gamma^D(^1S_0)$ obtained within this local chiral framework is compared with previous calculations and found in very good agreement.

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arXiv2022

Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials

We present the equation of state of infinite neutron matter as obtained from highly-realistic Hamiltonians that include nucleon-nucleon and three-nucleon coordinate-space potentials. We benchmark three independent many-body methods: Brueckner-Bethe-Goldstone (BBG), Fermi hypernetted chain/single-operator chain (FHNC/SOC), and auxiliary-field diffusion Monte Carlo (AFDMC). We find them to provide similar equations of state when the Argonne $v_{18}$ and the Argonne $v_{6}^\prime$ nucleon-nucleon potentials are used in combination with the Urbana IX three-body force. Only at densities larger than about 1.5 the nuclear saturation density ($\rho_0 = 0.16\,\rm{fm}^{-3}$) the FHNC/SOC energies are appreciably lower than the other two approaches. The AFDMC calculations carried out with all of the Norfolk potentials fitted to reproduce the experimental trinucleon ground-state energies and $nd$ doublet scattering length yield unphysically bound neutron matter, associated with the formation of neutron droplets. Including tritium $\beta$-decay in the fitting procedure, as in the second family of Norfolk potentials, mitigates but does not completely resolve this problem. An excellent agreement between the BBG and AFDMC results is found for the subset of Norfolk interactions that do not make neutron-matter collapse, while the FHNC/SOC equations of state are moderately softer.

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arXiv2021

Partial muon capture rates in $A=3$ and $A=6$ nuclei with chiral effective field theory

Searches for neutrinoless-double beta decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless-double beta decays take place at momentum transfers on the order of 100 MeV/$c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this work, we present results of {\it ab initio} calculations of partial muon capture rates for $^3$He and $^6$Li nuclei using variational and Green's Function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon ($2N$) interactions, and the energy range of $2N$ scattering data used to fit these interactions.

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arXiv2021

Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei

Classes of two-nucleon ($2N$) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet $np$ scattering length and deuteron binding energy at LO, and $np$ and $pp$ scattering data in the laboratory-energy range 0--15 MeV at NLO and 0--25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for $T\,$=$\,0$ and the other for $T\,$=$\,1$ channels. The cutoffs are taken to vary in the ranges $R_0\,$=$(1.5$--2.3) fm and $R_1\,$=$(1.5$--3.0) fm. The 780 (1,100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a $\chi^2$/datum about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers $A\,$=$\,3$--6 and 16 obtained with selected LO and NLO $2N$ models both by themselves as well as in combination with a LO three-nucleon ($3N$) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental $^3$H binding energy. The inclusion of the $3N$ interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the $^3$He and $^4$He binding energies that cluster around 7.8 MeV and 30 MeV, respectively. However, in $^{16}$O this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with $A\,$=$\,40$, 48, and 90.

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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

Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei

We report Quantum Monte Carlo calculations of weak transitions in $A\leq 10$ nuclei, based on the Norfolk two- and three-nucleon chiral interactions, and associated one- and two-body axial currents. We find that the contribution from two-body currents is at the $2$ - $3\%$ level, with the exception of matrix elements entering the rates of $^8$Li, $^8$B, and $^8$He beta decays. These matrix elements are suppressed in impulse approximation based on the (leading order) Gamow Teller transition operator alone; two-body currents provide a $20$ - $30\%$ correction, which is, however, insufficient to bring theory in agreement with experimental data. For the other transitions, the agreement with the data is satisfactory, and the results exhibit a negligible to mild model dependence when different combinations of Norfolk interactions are utilized to construct the nuclear wave functions. We report a complete study of two-body weak transition densities which reveals the expected universal behavior of two-body currents at short distances throughout the range of $A\,$=$\,3$ to $A\,$=$\,10$ systems considered here.

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arXiv2019

Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions

We report benchmark calculations of the energy per particle of pure neutron matter as a function of the baryon density using three independent many-body methods: Brueckner-Bethe-Goldstone, Fermi hypernetted chain/single-operator chain, and auxiliary-field diffusion Monte Carlo. Significant technical improvements are implemented in the latter two methods. The calculations are made for two distinct families of realistic coordinate-space nucleon-nucleon potentials fit to scattering data, including the standard Argonne $v_{18}$ interaction and two of its simplified versions, and four of the new Norfolk $Δ$-full chiral effective field theory potentials. The results up to twice nuclear matter saturation density show some divergence among the methods, but improved agreement compared to earlier work. We find that the potentials fit to higher-energy nucleon-nucleon scattering data exhibit a much smaller spread of energies.

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arXiv2019

A renormalized approach to neutrinoless double-beta decay

The process at the heart of neutrinoless double-beta decay, $nn \rightarrow p p\, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

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arXiv2018

Zemach moments and radii of 2,3H and 3,4He

We present benchmark calculations of Zemach moments and radii of 2,3H and 3,4He using various few-body methods. Zemach moments are required to interpret muonic atom data measured by the CREMA collaboration at the Paul Scherrer Institute. Conversely, radii extracted from spectroscopic measurements can be compared with ab initio computations, posing stringent constraints on the nuclear model. For a given few-body method, different numerical procedures can be applied to compute these quantities. A detailed analysis of the numerical uncertainties entering the total theoretical error is presented. Uncertainties from the few-body method and the calculational procedure are found to be smaller than the dependencies on the dynamical modeling and the single nucleon inputs, which are found to be <= 2%. When relativistic corrections and two-body currents are accounted for, the calculated moments and radii are in very good agreement with the available experimental data.

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arXiv2018

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $Δ$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with $Δ$ intermediate states are only retained at the OPE level, and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2--3 fm$^{-1}$. However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. A complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.

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arXiv2018

Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term

The Gamow-Teller (GT) matrix element contributing to tritium $β$ decay is calculated with trinucleon wave functions obtained from hyperspherical-harmonics solutions of the Schrödinger equation with the chiral two- and three-nucleon interactions including $Δ$ intermediate states that have recently been constructed in configuration space. Predictions up to N3LO in the chiral expansion of the axial current (with $Δ$'s) overestimate the empirical value by 1--4 \%. By exploiting the relation between the low-energy constant (LEC) in the contact three-nucleon interaction and two-body axial current, we provide new determinations of the LECs $c_D$ and $c_E$ that characterize this interaction by fitting the trinucleon binding energy and tritium GT matrix element. Some of the implications that the resulting models of three-nucleon interactions have on the spectra of light nuclei and the equation of state of neutron matter are briefly discussed. We also provide a partial analysis, which ignores $Δ$'s, of the contributions due to loop corrections in the axial current at N4LO. Finally, explicit expressions for the axial current up to N4LO have been derived in configuration space, which other researchers in the field may find useful.

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