Showing 1–50 of 99 results for author: Marcucci, L E

Emulation of Proton-Deuteron Scattering via the Reduced Basis Method and Active Learning: Detailed Description

Authors: Alex Gnech, Xilin Zhang, Christian Drischler, R. J. Furnstahl, Alessandro Grassi, Alejandro Kievsky, Laura E. Marcucci, Michele Viviani

Abstract: Nucleon-deuteron ($Nd$) scattering can be used to constrain three-nucleon forces in chiral effective field theory ($χ$EFT). However, high-fidelity calculations, such as the Hyperspherical Harmonic (HH) method, are computationally expensive, making it difficult or even prohibitive to explore the vast parameter space of $χ$EFT\xspace. To address this challenge, specifically for proton-deuteron (… ▽ More Nucleon-deuteron ($Nd$) scattering can be used to constrain three-nucleon forces in chiral effective field theory ($χ$EFT). However, high-fidelity calculations, such as the Hyperspherical Harmonic (HH) method, are computationally expensive, making it difficult or even prohibitive to explore the vast parameter space of $χ$EFT\xspace. To address this challenge, specifically for proton-deuteron ($pd$) scattering below the deuteron breakup threshold, we developed model-driven emulators based on the Reduced Basis Method (RBM) and active learning techniques, as presented in \href{https://arxiv.org/abs/2511.01844}{arXiv:2511.01844}. The method exploits the similarities between solutions at different parameter points to significantly reduce computational costs. In this companion paper, we provide a comprehensive description of our HH-based high-fidelity calculations and implementation of both variational-method-based and Galerkin-projection-based scattering emulators. We demonstrate the effectiveness of active learning in the form of greedy algorithms for selecting optimal training points in the parameter space, and the high accuracy and speed of the emulators, for two different nucleon forces and two scattering channels (${1/2}^+$ and ${1/2}^-$). For example, in a two-dimensional parameter space, the relative emulation errors can be reduced to $10^{-7}$ with fewer than 10 training points. Our work paves the way for the efficient calibration of $χ$EFT\xspace nucleon interactions using Bayesian statistics, and the methodology can be applied to other nuclear scattering processes (including neutron-deuteron scattering), as well as other finite quantum systems. △ Less

Submitted 13 November, 2025; originally announced November 2025.

Comments: 24 page, 16 figures, 1 table

Accurate and Efficient Emulation of Proton-Deuteron Scattering via the Reduced Basis Method and Active Learning

Authors: Alex Gnech, Xilin Zhang, Christian Drischler, R. J. Furnstahl, Alessandro Grassi, Alejandro Kievsky, Laura E. Marcucci, Michele Viviani

Abstract: We introduce highly accurate and efficient emulators for proton-deuteron scattering below the deuteron breakup threshold. We explore two different reduced-basis method strategies: one based on the Kohn variational principle and another on Galerkin projections of the underlying system of linear equations. We use the adaptive greedy algorithm previously developed for two-body scattering for optimal… ▽ More We introduce highly accurate and efficient emulators for proton-deuteron scattering below the deuteron breakup threshold. We explore two different reduced-basis method strategies: one based on the Kohn variational principle and another on Galerkin projections of the underlying system of linear equations. We use the adaptive greedy algorithm previously developed for two-body scattering for optimal selection of high-fidelity training points in the input parameter space. We demonstrate that these emulators reproduce ab initio hyperspherical harmonics calculations of $R$-matrix elements with remarkable precision, achieving relative errors as low as $10^{-7}$ with a small number of training points, even in regions of strong nonlinear parameter dependence. They also dramatically accelerate the exploration of the scattering predictions in the parameter space, a capability highly desired for calibrating (chiral) three-nucleon forces against scattering measurements. Our formalism can be further generalized to handle nucleon-deuteron scattering above the breakup threshold. These emulator developments will provide valuable tools to accelerate uncertainty quantification and rigorous parameter inference in the study of nuclear forces. △ Less

Submitted 3 November, 2025; originally announced November 2025.

Comments: 7 pages, 2 figures

$A=2,3,4$ nuclear contact coefficients in the generalized contact formalism

Authors: E. Proietti, L. E. Marcucci, M. Viviani

Abstract: We present a theoretical calculation for the $A = 2, 3$ and 4 nuclear contact coefficients within the generalized contact formalism, using both local and non-local chiral potentials. The Hyperspherical Harmonics method is employed to calculate the nuclear wave functions, from which we derive two-body momentum distributions and density functions to extract the contact coefficients. We have verified… ▽ More We present a theoretical calculation for the $A = 2, 3$ and 4 nuclear contact coefficients within the generalized contact formalism, using both local and non-local chiral potentials. The Hyperspherical Harmonics method is employed to calculate the nuclear wave functions, from which we derive two-body momentum distributions and density functions to extract the contact coefficients. We have verified that the contact coefficients, extracted from two-body momentum distributions or from density functions, are consistent for a given nucleus and potential. We have also analyzed the model-independence of the ratios between the contact coefficients. This study extends previous works based on local interaction models only and explores the impact of non-local potentials on the consistency of contact coefficient ratios across different nuclei. △ Less

Submitted 4 August, 2025; originally announced August 2025.

Comments: 24 pages, 25 figures and 4 tables. Submitted for publication

Convergence of the $ppp$ correlation function within the hyperspherical adiabatic basis

Authors: E. Garrido, A. Kievsky, R. Del Grande, L. Serksnyte, M. Viviani, L. E. Marcucci

Abstract: The computation of the three-particle correlation function involving three hadrons started just recently after the first publications of ALICE measurements. Key elements to be considered are the correct description of the asymptotics, antisymmetrization issues and, in most cases, the treatment of the Coulomb interaction. In the case of the $ppp$ correlation function, a first analysis was done wher… ▽ More The computation of the three-particle correlation function involving three hadrons started just recently after the first publications of ALICE measurements. Key elements to be considered are the correct description of the asymptotics, antisymmetrization issues and, in most cases, the treatment of the Coulomb interaction. In the case of the $ppp$ correlation function, a first analysis was done where the hyperspherical adiabatic method was used to determine the $ppp$ wave function at different energies. Although the asymptotic behavior, antisymmetrization issues and the treatment of the Coulomb interaction were discussed in detail, the convergence properties of the adiabatic basis were studied at low energies around the formation of the correlation peak determined mainly by the $J^π=1/2^-$ and $3/2^-$ three-body states. Since many and very precise data have been taken or are planned to be measured at energies beyond the peak, we present an analysis of the convergence characteristics of the basis as the energy of the process increases. We show that in order to describe correctly the correlation tail it is necessary to consider three-body states up to $J^π=21/2^-$ whereas higher states can be considered as free. Once those states are incorporated solving the associate dynamical equations, the agreement with the experimental data is found to be excellent. △ Less

Submitted 28 May, 2025; originally announced May 2025.

Comments: Submitted for publication, six pages, three figures

ToMCCA-3: A realistic 3-body coalescence model

Authors: Maximilian Mahlein, Bhawani Singh, Michele Viviani, Francesca Bellini, Laura Fabbietti, Alejandro Kievsky, Laura Elisa Marcucci

Abstract: The formation of light nuclei in high-energy collisions provides valuable insights into the underlying dynamics of the strong interaction and the structure of the particle-emitting source. Understanding this process is crucial not only for nuclear physics but also for astrophysical studies, where the production of rare antinuclei could serve as a probe for new physics. This work presents a three-b… ▽ More The formation of light nuclei in high-energy collisions provides valuable insights into the underlying dynamics of the strong interaction and the structure of the particle-emitting source. Understanding this process is crucial not only for nuclear physics but also for astrophysical studies, where the production of rare antinuclei could serve as a probe for new physics. This work presents a three-body coalescence model based on the Wigner function formalism, offering a refined description of light-nucleus production. By incorporating realistic two- and three-body nuclear interaction potentials constrained by modern scattering and femtoscopic correlation data, our approach improves on traditional coalescence models. The framework is validated using event generators applied to proton-proton collisions at $\sqrt{s}=13$ TeV to predict the momentum spectra of light (anti) nuclear nuclei with mass number $A=3$, which are then compared with the experimental data from ALICE. Our results demonstrate the sensitivity of light nucleus yields to the choice of nuclear wave functions, emphasizing the importance of an accurate description of the coalescence process. This model lays the foundation for the extension of coalescence studies of $A=3$ light nuclei to a wider range of collision systems and energies. △ Less

Submitted 3 April, 2025; originally announced April 2025.

Comments: 23 pages, 4 Figures

$A=2,3$ nuclear contact coefficients in the Generalized Contact Formalism

Authors: Eleonora Proietti, Laura Elisa Marcucci, Michele Viviani

Abstract: This work focuses on extracting nuclear contact coefficients for \( A = 2 \), \( A = 3 \) and \( A = 4 \) nuclei within the Generalized Contact Formalism framework. We investigate the universality of these coefficients across different nuclear systems and interaction models, using both local (in \( r \)-space) and non-local (in \( k \)-space) chiral potentials. The Hyperspherical Harmonics method… ▽ More This work focuses on extracting nuclear contact coefficients for \( A = 2 \), \( A = 3 \) and \( A = 4 \) nuclei within the Generalized Contact Formalism framework. We investigate the universality of these coefficients across different nuclear systems and interaction models, using both local (in \( r \)-space) and non-local (in \( k \)-space) chiral potentials. The Hyperspherical Harmonics method is employed to calculate the nuclear wave functions from which we obtain the two-body momentum distributions and the two-body density functions, which are essential for extracting the contact coefficients. The adopted method is a rigorous ab-initio approach that can be applied to virtually any potential. We present ratios of contact coefficients across various spin and isospin channels, highlighting their independence from the used nuclear potential. This study extends previous work where only local interaction models were employed. Furthermore, we verify whether the contact coefficient ratio between different nuclei remains consistent even when non-local potentials are considered. Future work will extend this analysis to heavier nuclei, such as \( A = 4 \) and \( A = 6 \) nuclei. △ Less

Submitted 30 January, 2025; originally announced January 2025.

Comments: Proceedings of the 11th International Workshop on Chiral Dynamics (CD2024)

The 3-$α$ and 4-$α$ particle systems within short-range Effective Field Theory

Authors: E. Filandri, M. Viviani, L. Girlanda, A. Kievsky, L. E. Marcucci

Abstract: ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei represent essential elements for life on Earth. The study of their formation plays a key role in understanding heavy element nucleosynthesis and stellar evolution. In this paper we present the study of ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei as systems composed of $α… ▽ More ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei represent essential elements for life on Earth. The study of their formation plays a key role in understanding heavy element nucleosynthesis and stellar evolution. In this paper we present the study of ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei as systems composed of $α$-particle clusters using the short-range effective field theory approach. The fundamental and excited states of the studied nuclei are calculated within an ab-initio approach, using the Hyperspherical Harmonics method. Thanks to the two-body potential and fine-tuning of the three-body force, we have found the ${}^{12}{\rm C}$ system nicely reproduced by theory. However, for the ${}^{16}{\rm O}$ case, it is necessary to include a 4-body force in order to achieve agreement with the experimental data. △ Less

Submitted 24 January, 2025; originally announced January 2025.

The X17 boson and the d(p,e+ e-)3He and d(n,e+ e-)3H processes: a theoretical analysis

Authors: M. Viviani, E. Filandri, L. Girlanda, C. Gustavino, A. Kievsky, L. E. Marcucci

Abstract: The present work deals with the e+ e- pair production in the d(p,e+e-)3He and d(n,e+ e-)3H processes, in order to evidentiate possible effects due to the exchange of a hypothetical low-mass boson, the so-called X17. These processes are studied for energies of the incident beams in the range 18-30 MeV, in order to have a sufficient energy to produce such a boson, whose mass is estimated to be aroun… ▽ More The present work deals with the e+ e- pair production in the d(p,e+e-)3He and d(n,e+ e-)3H processes, in order to evidentiate possible effects due to the exchange of a hypothetical low-mass boson, the so-called X17. These processes are studied for energies of the incident beams in the range 18-30 MeV, in order to have a sufficient energy to produce such a boson, whose mass is estimated to be around 17 MeV. We first analyze them as a purely electromagnetic processes, in the context of a state-of-the-art approach to nuclear strong-interaction dynamics and nuclear electromagnetic currents, derived from chiral effective field theory chiEFT. Next, we examine how the exchange of a hypothetical low-mass boson would impact the cross sections for such processes. We consider several possibilities, that this boson is either a scalar, pseudoscalar, vector, or axial particle. The main aim of the study is to exploit the specular structure of the 3He and 3H nuclei to investigate the isospin dependency of the X17-nucleon interaction, as the alleged "proto-phobicity". △ Less

Submitted 15 April, 2025; v1 submitted 29 August, 2024; originally announced August 2024.

Comments: 19 pages, 15 figures, new version with more details, added two appendices. arXiv admin note: text overlap with arXiv:2104.07808

Journal ref: Phys. Rev. C 111, 034002 (2025)

The $pΛ$ and $ppΛ$ correlation functions

Authors: E. Garrido, A. Kievsky, M. Gattobigio, M. Viviani, L. E. Marcucci, R. Del Grande, L. Fabbietti, D. Melnichenko

Abstract: In this work we present the study of $pΛ$ and $ppΛ$ scattering processes using femtoscopic correlation functions. This observable has been recently used to access the low-energy interaction of hadrons emitted in the final state of high-energy collisions, delivering unprecedented precision information of the interaction among strange hadrons. The formalism for particle pairs is well established and… ▽ More In this work we present the study of $pΛ$ and $ppΛ$ scattering processes using femtoscopic correlation functions. This observable has been recently used to access the low-energy interaction of hadrons emitted in the final state of high-energy collisions, delivering unprecedented precision information of the interaction among strange hadrons. The formalism for particle pairs is well established and it relates the measured correlation functions with the scattering wave function and the emission source. In the present work we analyze the $NNΛ$ scattering in free space and relate the corresponding wave function to the $ppΛ$ correlation measurement performed by the ALICE collaboration. The three-body problem is solved using the hyperspherical adiabatic basis. Regarding the $pΛ$ and $ppΛ$ interactions, different models are used and their impact on the correlation function is studied. The three body force considered in this work is anchored to describe the binding energy of the hypertriton and to give a good description of the two four-body hypernuclei. As a main result we have observed a huge, low-energy peak in the $ppΛ$ correlation function, mainly produced by the $J^π=1/2^+$ three-body state. The study of this peak from an experimental as well as a theoretical point of view will provide important constraints to the two- and three-body interactions. △ Less

Submitted 3 August, 2024; originally announced August 2024.

Comments: Submitted for publication

Study of the alpha-particle monopole transition form factor

Authors: M. Viviani, A. Kievsky, L. E. Marcucci, L. Girlanda

Abstract: The 4He monopole form factor is studied by computing the transition matrix element of the electromagnetic charge operator between the 4He ground-state and the p+3H and n+3He scattering states. The nuclear wave functions are calculated using the hyperspherical harmonic method, by starting from Hamiltonians including two- and three-body forces derived in chiral effective field theory. The electromag… ▽ More The 4He monopole form factor is studied by computing the transition matrix element of the electromagnetic charge operator between the 4He ground-state and the p+3H and n+3He scattering states. The nuclear wave functions are calculated using the hyperspherical harmonic method, by starting from Hamiltonians including two- and three-body forces derived in chiral effective field theory. The electromagnetic charge operator retains, beyond the leading order (impulse approximation) term, also higher order contributions, as relativistic corrections and meson-exchange currents. The results for the monopole form factor are in fairly agreement with recent MAMI data. Comparison with other theoretical calculations are also provided. △ Less

Submitted 2 June, 2024; originally announced June 2024.

Comments: 22 pages, 6 figures

The 3He(\vec n,p)3H parity-conserving asymmetry

Authors: M. Viviani, S. Baeßler, L. Barrón-Palos, N. Birge, J. D. Bowman, J. Calarco, V. Cianciolo, C. E. Coppola, C. B. Crawford, G. Dodson, N. Fomin, I. Garishvili, M. T. Gericke, L. Girlanda, G. L. Greene, G. M. Hale, J. Hamblen, C. Hayes, E. B. Iverson, M. L. Kabir, A. Kievsky, L. E. Marcucci, M. McCrea, E. Plemons, A. Ramírez-Morales , et al. (6 additional authors not shown)

Abstract: Recently, the n$^3$He collaboration reported a measurement of the parity-violating (PV) proton directional asymmetry $A_{\mathrm {PV}} = (1.55\pm 0.97~\mathrm {(st\ at)} \pm 0.24~\mathrm {(sys)})\times 10^{-8}$ in the capture reaction of ${}^3$He$(\vec {n},{\mathrm p}){}^3$H at meV incident neutron energies. The result increased the limited inventory of precisely measured and calculable PV observa… ▽ More Recently, the n$^3$He collaboration reported a measurement of the parity-violating (PV) proton directional asymmetry $A_{\mathrm {PV}} = (1.55\pm 0.97~\mathrm {(st\ at)} \pm 0.24~\mathrm {(sys)})\times 10^{-8}$ in the capture reaction of ${}^3$He$(\vec {n},{\mathrm p}){}^3$H at meV incident neutron energies. The result increased the limited inventory of precisely measured and calculable PV observables in few-body systems required to further understand the structure of hadronic weak interaction. In this letter, we report the experimental and theoretical investigation of a parity conserving (PC) asymmetry $A_{\mathrm {PC}}$ in the same reaction (the first ever measured PC observable at meV neutron energies). As a result of S- and P-wave mixing in the reaction, the $A_{\mathrm {PC}}$ is inversely proportional to the neutron wavelength $λ$. The experimental value is $(λ\times A_{\mathrm {PC}})\equivβ= (-1.97 \pm 0.28~\mathrm{(stat)}\pm 0.12~\mathrm{(sys)}) \times 10^{-6}$ Amstrongs. We present results for a theoretical analysis of this reaction by solving the four-body scattering problem within the hyperspherical harmonic method. We find that in the ${}^3$He$(\vec {n},{\mathrm p}){}^3$H reaction, $A_{\mathrm {PC}}$ depends critically on the energy and width of the close $0^-$ resonant state of ${}^4$He, resulting in a large sensitivity to the spin-orbit components of the nucleon-nucleon force and even to the three-nucleon force. The analysis of the accurately measured $A_{\mathrm {PC}}$ and $A_{\mathrm {PV}}$ using the same few-body theoretical models gives essential information needed to interpret the PV asymmetry in the ${}^3$He$(\vec {n}, {\mathrm p}){}^3$H reaction. △ Less

Submitted 16 May, 2024; originally announced May 2024.

Comments: 8 pages, 3 figures

Solar fusion III: New data and theory for hydrogen-burning stars

Authors: B. Acharya, M. Aliotta, A. B. Balantekin, D. Bemmerer, C. A. Bertulani, A. Best, C. R. Brune, R. Buompane, F. Cavanna, J. W. Chen, J. Colgan, A. Czarnecki, B. Davids, R. J. deBoer, F. Delahaye, R. Depalo, A. García, M. Gatu Johnson, D. Gazit, L. Gialanella, U. Greife, D. Guffanti, A. Guglielmetti, K. Hambleton, W. C. Haxton , et al. (25 additional authors not shown)

Abstract: In stars that lie on the main sequence in the Hertzsprung-Russel diagram, like our sun, hydrogen is fused to helium in a number of nuclear reaction chains and series, such as the proton-proton chain and the carbon-nitrogen-oxygen cycles. Precisely determined thermonuclear rates of these reactions lie at the foundation of the standard solar model. This review, the third decadal evaluation of the nu… ▽ More In stars that lie on the main sequence in the Hertzsprung-Russel diagram, like our sun, hydrogen is fused to helium in a number of nuclear reaction chains and series, such as the proton-proton chain and the carbon-nitrogen-oxygen cycles. Precisely determined thermonuclear rates of these reactions lie at the foundation of the standard solar model. This review, the third decadal evaluation of the nuclear physics of hydrogen-burning stars, is motivated by the great advances made in recent years by solar neutrino observatories, putting experimental knowledge of the proton-proton chain neutrino fluxes in the few-percent precision range. The basis of the review is a one-week community meeting held in July 2022 in Berkeley, California, and many subsequent digital meetings and exchanges. The relevant reactions of solar and stellar hydrogen burning are reviewed here, from both theoretical and experimental perspectives. Recommendations for the state of the art of the astrophysical S-factor and its uncertainty are formulated for each of them. Several other topics of paramount importance for the solar model are reviewed, as well: recent and future neutrino experiments, electron screening, radiative opacities, and current and upcoming experimental facilities. In addition to reaction-specific recommendations, also general recommendations are formed. △ Less

Submitted 15 September, 2025; v1 submitted 10 May, 2024; originally announced May 2024.

Comments: 101 pages, 25 figures, including supplementary material. Final version published in Reviews of Modern Physics

Report number: N3AS-24-016

Journal ref: Rev. Mod. Phys. 97, 035002 (2025)

Momentum dependent nucleon-nucleon contact interactions and their effect on p-d scattering observables

Authors: E. Filandri, L. Girlanda, A. Kievsky, L. E. Marcucci, M. Viviani

Abstract: Starting from a complete set of relativistic nucleon-nucleon contact operators up to order $O(p^4)$ of the expansion in the soft (relative or nucleon) momentum $p$, we show that non-relativistic expansions of relativistic operators involve twenty-six independent combinations, two starting at $O(p^0)$, seven at order $O(p^2)$ and seventeen at order $O(p^4)$. This demonstrates the existence of two l… ▽ More Starting from a complete set of relativistic nucleon-nucleon contact operators up to order $O(p^4)$ of the expansion in the soft (relative or nucleon) momentum $p$, we show that non-relativistic expansions of relativistic operators involve twenty-six independent combinations, two starting at $O(p^0)$, seven at order $O(p^2)$ and seventeen at order $O(p^4)$. This demonstrates the existence of two low-energy free constants that parameterize interactions dependent on the total momentum of the pair of nucleons $P$. The latter, through the use of a unitary transformation, can be removed in the two-nucleon fourth-order contact interaction of the Chiral Effective Field Theory, generating a three-nucleon interaction at the same order. Within a hybrid approach in which this interaction is considered together with the phenomenological potential AV18, we show that the LECs involved can be used to fit very accurate data on the polarization observables of the low-energy $p-d$ scattering, in particular the $A_y$ asymmetry. △ Less

Submitted 17 April, 2024; originally announced April 2024.

Comments: arXiv admin note: text overlap with arXiv:2302.03468

The $nnn$ and $ppp$ correlation functions

Authors: A. Kievsky, E. Garrido, M. Viviani, L. E. Marcucci, L. Serksnyte, R. Del Grande

Abstract: Scattering experiments with three free nucleons in the ingoing channel are extremely challenging in terrestrial laboratories. Recently, the ALICE Collaboration has successfully measured the scattering of three protons indirectly, by using the femtoscopy method in high-energy proton-proton collisions at the Large Hadron Collider. In order to establish a connection with current and future measuremen… ▽ More Scattering experiments with three free nucleons in the ingoing channel are extremely challenging in terrestrial laboratories. Recently, the ALICE Collaboration has successfully measured the scattering of three protons indirectly, by using the femtoscopy method in high-energy proton-proton collisions at the Large Hadron Collider. In order to establish a connection with current and future measurements of femtoscopic three-particle correlation functions, we analyse the scenarios involving $nnn$ and $ppp$ systems using the hyperspherical adiabatic basis. The correlation function is a convolution of the source function and the corresponding scattering wave function. The finite size of the source allows for the use of the free scattering wave function in most of the adiabatic channels except the lowest ones. The scattering wave function has been computed using two different potential models: $(i)$ a spin-dependent Gaussian potential with parameters fixed to reproduce the scattering length and effective range and $(ii)$ the Argonne $v_{18}$ nucleon-nucleon interaction. Moreover, in the case of three protons, the Coulomb interaction has been considered in its hypercentral form. The results presented here have to be considered as a first step in the description of three-particle correlation functions using the hyperspherical adiabatic basis, opening the door to the investigation of other systems, such as the $ppΛ$ system. For completeness, the comparison with the measurement by the ALICE Collaboration is shown assuming different values of the source radius. △ Less

Submitted 3 July, 2025; v1 submitted 16 October, 2023; originally announced October 2023.

Comments: 18 pages, 12 figures

Role of three-body dynamics in nucleon-deuteron correlation functions

Authors: M. Viviani, S. König, A. Kievsky, L. E. Marcucci, B. Singh, O. Vázquez Doce

Abstract: Correlation functions of hadrons can be accessed in high-energy collisions of atomic nuclei, revealing information about the underlying interaction. This work complements experimental efforts to study nucleon-deuteron $Nd$ -- with $N=p$ (proton) or $N=n$ (neutron) -- correlations with theory evaluations using different techniques. The correlation functions $C_{nd}$ and $C_{pd}$ are calculated base… ▽ More Correlation functions of hadrons can be accessed in high-energy collisions of atomic nuclei, revealing information about the underlying interaction. This work complements experimental efforts to study nucleon-deuteron $Nd$ -- with $N=p$ (proton) or $N=n$ (neutron) -- correlations with theory evaluations using different techniques. The correlation functions $C_{nd}$ and $C_{pd}$ are calculated based on scattering wave function, extending previous benchmarks for the $Nd$ scattering matrix to this new observable. We use hyperspherical harmonics and Faddeev techniques with one of the widely used nucleon-nucleon ($NN$) interactions, the Argonne $v_{18}$ potential. Moreover, in the low-energy region we perform additional calculations in the framework of pionless effective field theory. The $pd$ correlation function is computed in the large-energy region to make contact with a recent measurement by the ALICE Collaboration. We show that the scattering wave function has the proper dynamical input to describe an initial rise and subsequent oscillations of $C_{pd}$ as a function of the energy. Effects on the observables using different $NN$ and three-nucleon potentials are evaluated with the conclusion that variations of around $2\%$ are observed. Although these effects are small, future measurements can go beyond this accuracy allowing for new detailed studies of strong interaction in light nuclear systems. The present study supports the current efforts devoted to the measurement of correlation functions in systems dominated by the strong interactions, such as $pd$, $ppp$, $Λd$ and $ppΛ$. △ Less

Submitted 4 June, 2023; originally announced June 2023.

Comments: 23 pages, 8 figures

Bayesian analysis of muon capture on deuteron in chiral effective field theory

Authors: Alex Gnech, Laura Elisa Marcucci, Michele Viviani

Abstract: We compute the muon capture on deuteron in the doublet hyperfine state for a variety of nuclear interactions and consistent nuclear currents. Our analysis includes a detailed examination of the theoretical uncertainties coming from different sources: the single-nucleon axial form factor, the truncation of the interaction and current chiral expansion, and the model dependence. Moreover, we study th… ▽ More We compute the muon capture on deuteron in the doublet hyperfine state for a variety of nuclear interactions and consistent nuclear currents. Our analysis includes a detailed examination of the theoretical uncertainties coming from different sources: the single-nucleon axial form factor, the truncation of the interaction and current chiral expansion, and the model dependence. Moreover, we study the impact of the use of different power counting scheme for the electroweak currents on the truncation error. To estimate the truncation error of the chiral expansion of interactions and currents we use the most modern techniques based on Bayesian analysis. This method enables us to give a clear statistical interpretation of the computed theoretical uncertainties. Finally, we provide the differential capture rate as function of the kinetic energy of the outgoing neutron which may be measured in future experiments. Our recommended theoretical value for the total doublet capture rate is $Γ_{\rm th}=395\pm 10$ s$^{-1}$ ($68\%$ confidence level). We calculated also the capture rate in the quartet hyperfine state, which turns out to be in the range $[13.3-13.8]$ s$^{-1}$ depending on the adopted nuclear interaction. △ Less

Submitted 6 March, 2024; v1 submitted 12 May, 2023; originally announced May 2023.

Comments: 14 pages, 10 figures, Supplemental Materials available under request. Accepted version on PRC

Revisiting proton-proton fusion in chiral effective field theory

Authors: Bijaya Acharya, Laura Elisa Marcucci, Lucas Platter

Abstract: We calculate the $S$-factor for proton-proton fusion using chiral effective field theory interactions and currents. By performing order-by-order calculations with a variety of chiral interactions that are regularized and calibrated in different ways, we assess the uncertainty in the $S$-factor from the truncation of the effective field theory expansion and from the sensitivity of the $S$-factor to… ▽ More We calculate the $S$-factor for proton-proton fusion using chiral effective field theory interactions and currents. By performing order-by-order calculations with a variety of chiral interactions that are regularized and calibrated in different ways, we assess the uncertainty in the $S$-factor from the truncation of the effective field theory expansion and from the sensitivity of the $S$-factor to the short-distance axial current determined from three- and four-nucleon observables. We find that $S(0)=(4.100\pm0.019\mathrm{(syst)}\pm0.013\mathrm{(stat)}\pm0.008(g_A))\times10^{-23}~\mathrm{MeV\,fm}^2\,,$ where the three uncertainties arise, respectively, from the truncation of the effective field theory expansion, use of the two-nucleon axial current fit to few-nucleon observables and variation of the axial coupling constant within the recommended range. The increased value of $S(0)$ compared to previous calculations is mainly driven by an increase in the recommended value for the axial coupling constant and is in agreement with a recent analysis based on pionless effective field theory. △ Less

Submitted 15 June, 2023; v1 submitted 6 April, 2023; originally announced April 2023.

Journal ref: J. Phys. G: Nucl. Part. Phys. 50 (2023) 095102

Effect of the N3LO three-nucleon contact interaction on p-d scattering observables

Authors: L. Girlanda, E. Filandri, A. Kievsky, L. E. Marcucci, M. Viviani

Abstract: A unitary transformation allows to remove redundant terms in the two-nucleon (2N) contact interaction at the fourth order (N3LO) in the low-energy expansion of Chiral Effective Field Theory. In so doing a three-nucleon (3N) interaction is generated. We express its short-range component in terms of five combinations of low-energy constants (LECs) parametrizing the N3LO 2N contact Lagrangian. Within… ▽ More A unitary transformation allows to remove redundant terms in the two-nucleon (2N) contact interaction at the fourth order (N3LO) in the low-energy expansion of Chiral Effective Field Theory. In so doing a three-nucleon (3N) interaction is generated. We express its short-range component in terms of five combinations of low-energy constants (LECs) parametrizing the N3LO 2N contact Lagrangian. Within a hybrid approach, in which this interaction is considered in conjunction with the phenomenological AV18 2N potential, we show that the involved LECs can be used to fit very accurate data on polarization observables of low-energy $p-d$ scattering, in particular the $A_y$ asymmetry. The resulting interaction is of the right order of magnitude for a N3LO contribution. △ Less

Submitted 7 February, 2023; originally announced February 2023.

Comments: 9 pages, 2 figures

Muon capture on deuteron using local chiral potentials

Authors: L. Ceccarelli, A. Gnech, L. E. Marcucci, M. Piarulli, M. Viviani

Abstract: The muon capture reaction $μ^- + d \rightarrow n + n + ν_μ$ 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 es… ▽ More The muon capture reaction $μ^- + d \rightarrow n + n + ν_μ$ 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 $Γ^D(^1S_0)$ has been found to be $Γ^D(^1S_0)=255.8(0.6)(4.4)(2.9)$ s$^{-1}$, where the three errors come from the first three sources of uncertainty. The value for $Γ^D(^1S_0)$ obtained within this local chiral framework is compared with previous calculations and found in very good agreement. △ Less

Submitted 20 September, 2022; originally announced September 2022.

Comments: 33 pages, 3 figures

Journal ref: Front. Phys. 10, 1049919 (2023)

Theoretical study of the d(d,p)3H and d(d,n)3He processes at low energies

Authors: M. Viviani, L. Girlanda, A. Kievsky, D. Logoteta, L. E. Marcucci

Abstract: We present a theoretical study of the processes d(d,p)3H and d(d,n)3He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the ab-initio hyperspherical harmonic method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report… ▽ More We present a theoretical study of the processes d(d,p)3H and d(d,n)3He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the ab-initio hyperspherical harmonic method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical factor, the quintet suppression factor, and various single and double polarized observables. An estimate of the "theoretical uncertainty" for all these quantities is provided by varying the cutoff parameter used to regularize the chiral interactions at high momentum. △ Less

Submitted 4 July, 2022; originally announced July 2022.

Comments: 5 pages, 4 figures

Comparative study of ${}^6$He $β$-decay based on different similarity-renormalization-group evolved chiral interactions

Authors: A. Gnech, L. E. Marcucci, R. Schiavilla, M. Viviani

Abstract: We report on a study of the Gamow-Teller matrix element contributing to ${}^6$He $β$-decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory ($χ$EFT) -- without and with the explicit inclusion of $Δ$-isobars. We consider evolution paramet… ▽ More We report on a study of the Gamow-Teller matrix element contributing to ${}^6$He $β$-decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory ($χ$EFT) -- without and with the explicit inclusion of $Δ$-isobars. We consider evolution parameters $Λ_{\rm SRG}$ in the range between 1.2 and 2.0 fm$^{-1}$ and, for the $Δ$-less case, also the unevolved (bare) interaction. The axial current contains one- and two-body terms, consistently derived at tree level (no loops) in the two distinct $χ$EFT formulations we have adopted here. The ${}^6$He and ${}^6$Li ground-state wave functions are obtained from hyperspherical-harmonics (HH) solutions of the nuclear many-body problem. In $A\,$=$\,6$ systems, the HH method is limited at present to treat only two-body interactions and non-SRG evolved currents. Our results exhibit a significant dependence on $Λ_{\text{SRG}}$ of the contributions associated with two-body currents, suggesting that a consistent SRG-evolution of these is needed in order to obtain reliable estimates. We also show that the contributions from one-pion-exchange currents depend strongly on the model (chiral) interactions and on the momentum- or configuration-space cutoffs used to regularize them. These results might prove helpful in clarifying the origin of the sign difference recently found in No-Core-Shell-Model and Quantum Monte Carlo calculations of the ${}^6$He Gamow-Teller matrix element. △ Less

Submitted 10 September, 2021; v1 submitted 14 June, 2021; originally announced June 2021.

Comments: 16 pages, 4 figures, accepted for publication on Phys. Rev. C

Journal ref: Phys. Rev. C 104, 035501 (2021)

The X17 boson and the $^3$H$(p,e^+ e^-)^4$He and $^3$He$(n,e^+ e^-)^4$He processes: a theoretical analysis

Authors: M. Viviani, E. Filandri, L. Girlanda, C. Gustavino, A. Kievsky, L. E. Marcucci, R. Schiavilla

Abstract: The present work deals with $e^+$-$e^-$ pair production in the four-nucleon system. We first analyze the process as a purely electromagnetic one in the context of a state-of-the-art approach to nuclear strong-interaction dynamics and nuclear electromagnetic currents, derived from chiral effective field theory ($χ$EFT). Next, we examine how the exchange of a hypothetical low-mass boson would impact… ▽ More The present work deals with $e^+$-$e^-$ pair production in the four-nucleon system. We first analyze the process as a purely electromagnetic one in the context of a state-of-the-art approach to nuclear strong-interaction dynamics and nuclear electromagnetic currents, derived from chiral effective field theory ($χ$EFT). Next, we examine how the exchange of a hypothetical low-mass boson would impact the cross section for such a process. We consider several possibilities, that this boson is either a scalar, pseudoscalar, vector, or axial particle. The ab initio calculations use exact hyperspherical-harmonics methods to describe the bound state and low-energy spectrum of the $A\,$=$\,4$ continuum, and fully account for initial state interaction effects in the $3+1$ clusters. While electromagnetic interactions are treated to high orders in the chiral expansion, the interactions of the hypothetical boson with nucleons are modeled in leading-order $χ$EFT (albeit, in some instances, selected subleading contributions are also accounted for). We also provide an overview of possible future experiments probing pair production in the $A\,$=$\,4$ system at a number of candidate facilities.facilities. △ Less

Submitted 18 June, 2021; v1 submitted 15 April, 2021; originally announced April 2021.

Comments: 32 pages, 17 figures. Corrected version, having fixed a problem with a phase in the multipolar expansions. Only Figs. 4 and 10 change significantly, the rest only marginally. The conclusions are unchanged. We include also a number of improvements: 1) better wave functions, 2) the isoscalar pseudoscalar case, and 3) the comparison with the new ATOMKI data (see new Fig. 17)

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

Authors: R. Schiavilla, L. Girlanda, A. Gnech, A. Kievsky, A. Lovato, L. E. Marcucci, M. Piarulli, M. Viviani

Abstract: 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 intera… ▽ More 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 $χ^2$/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. △ Less

Submitted 3 February, 2021; originally announced February 2021.

Comments: 23 pages, 6 figures

Journal ref: Phys. Rev. C 103, 054003 (2021)

Unitary ambiguity of NN contact interactions and the 3N force

Authors: L. Girlanda, A. Kievsky, L. E. Marcucci, M. Viviani

Abstract: We identify a redundancy between two- and three-nucleon contact interactions at the fourth and fifth order of the chiral expansion respectively. In particular we show that tensor-type and spin-orbit three-nucleon contact interactions effectively account for that part of the two-nucleon interaction which depends on the total center-of-mass momentum and is unconstrained by relativity. This might giv… ▽ More We identify a redundancy between two- and three-nucleon contact interactions at the fourth and fifth order of the chiral expansion respectively. In particular we show that tensor-type and spin-orbit three-nucleon contact interactions effectively account for that part of the two-nucleon interaction which depends on the total center-of-mass momentum and is unconstrained by relativity. This might give the chiral effective field theory enough flexibility to successfully address $A=3$ scattering observables already at N3LO. △ Less

Submitted 10 November, 2020; v1 submitted 8 July, 2020; originally announced July 2020.

Comments: 9 pages, discussion extended to OPE 3NF

Journal ref: Phys. Rev. C 102, 064003 (2020)

Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis

Authors: Alex Gnech, Michele Viviani, Laura Elisa Marcucci

Abstract: We have studied the solution of the six-nucleon bound state problem using the hyperspherical harmonic (HH) approach. For this study we have considered only two-body nuclear forces. In particular we have used a chiral nuclear potential evolved with the similarity renormalization group unitary transformation. A restricted basis has been selected by performing a careful analysis of the convergence of… ▽ More We have studied the solution of the six-nucleon bound state problem using the hyperspherical harmonic (HH) approach. For this study we have considered only two-body nuclear forces. In particular we have used a chiral nuclear potential evolved with the similarity renormalization group unitary transformation. A restricted basis has been selected by performing a careful analysis of the convergence of different HH classes. Finally, the binding energy and other properties of ${}^6$Li ground state are calculated and compared with the results obtained by other techniques. Then, we present a calculation of matrix elements relevant for direct dark matter search involving ${}^6$Li. The results obtained demonstrate the feasibility of using the HH method to perform calculation beyond $A = 4$. △ Less

Submitted 13 April, 2020; originally announced April 2020.

Comments: 21 pages, 9 figures

Journal ref: Phys. Rev. C 102, 014001 (2020)

Study of $n+{}^3$H, $p+{}^3$He, $p+{}^3$H, and $n+{}^3$He scattering with the HH method

Authors: M. Viviani, L. Girlanda, A. Kievsky, L. E. Marcucci

Abstract: The $n+{}^3$H, $p+{}^3$He, $p+{}^3$H, and $n+{}^3$He elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interact… ▽ More The $n+{}^3$H, $p+{}^3$He, $p+{}^3$H, and $n+{}^3$He elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interactions. A detailed study of the convergence and numerical stability of the method is presented. We have found that the effect the 3N force is in general tiny except for $p+{}^3$H scattering below the opening of the $n+{}^3$He channel. In such a case, the effect of 3N forces is appreciable and a clear dependence on the cutoff used to regularize the high-momentum tail of the interactions is observed. Such a dependence is related to the presence of the poorly known sharp $0^+$ resonance, considered to be the first excited state of ${}^4$He. △ Less

Submitted 31 March, 2020; originally announced March 2020.

Comments: 33 pages, 15 figures

The Hyperspherical Harmonics method: a tool for testing and improving nuclear interaction models

Authors: L. E. Marcucci, J. Dohet-Eraly, L. Girlanda, A. Gnech, A. Kievsky, M. Viviani

Abstract: The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two- and… ▽ More The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two- and three-nucleon components of the nuclear interaction. In the present review we introduce the formalism of the HH method, both for bound and scattering states. In particular, we describe the implementation of the method to study the $A=3$ and $4$ scattering problem. Second, we present a selected choice of results of the last decade, most representative of the latest achievements. Finally, we conclude with a discussion of what we believe will be the most significant developments within the HH method for the next five-to-ten years. △ Less

Submitted 20 December, 2019; originally announced December 2019.

Comments: 25 pages, 9 figures, 4 tables, submitted to Frontiers in Physics (Research Topic) "The Long-Lasting Quest for Nuclear Interactions: The Past, the Present and the Future"

From response functions to cross sections in neutrino scattering off the deuteron and trinucleons

Authors: J. Golak, R. Skibinski, K. Topolnicki, H. Witala, A. Grassi, H. Kamada, L. E. Marcucci

Abstract: Response functions, differential cross sections and total cross sections for several (anti)neutrino induced reactions on 2H, 3He and 3H are calculated in momentum space for (anti)neutrino energies up to 160 MeV, using the AV18 nucleon-nucleon potential and a single-nucleon weak current operator. This work is a continuation of our investigations presented in J. Golak et al. [Phys. Rev. C 98, 015501… ▽ More Response functions, differential cross sections and total cross sections for several (anti)neutrino induced reactions on 2H, 3He and 3H are calculated in momentum space for (anti)neutrino energies up to 160 MeV, using the AV18 nucleon-nucleon potential and a single-nucleon weak current operator. This work is a continuation of our investigations presented in J. Golak et al. [Phys. Rev. C 98, 015501 (2018)]. △ Less

Submitted 22 August, 2019; originally announced August 2019.

Comments: 23 pages, 16 figures in 60 files

Journal ref: Phys. Rev. C 100, 064003 (2019)

Comparing proton momentum distributions in $A=2$ and 3 nuclei via $^2$H $^3$H and $^3$He $(e, e'p)$ measurements

Authors: R. Cruz-Torres, S. Li, F. Hauenstein, A. Schmidt, D. Nguyen, D. Abrams, H. Albataineh, S. Alsalmi, D. Androic, K. Aniol, W. Armstrong, J. Arrington, H. Atac, T. Averett, C. Ayerbe Gayoso, X. Bai, J. Bane, S. Barcus, A. Beck, V. Bellini, H. Bhatt, D. Bhetuwal, D. Biswas, D. Blyth, W. Boeglin , et al. (103 additional authors not shown)

Abstract: We report the first measurement of the $(e,e'p)$ reaction cross-section ratios for Helium-3 ($^3$He), Tritium ($^3$H), and Deuterium ($d$). The measurement covered a missing momentum range of $40 \le p_{miss} \le 550$ MeV$/c$, at large momentum transfer ($\langle Q^2 \rangle \approx 1.9$ (GeV$/c$)$^2$) and $x_B>1$, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The… ▽ More We report the first measurement of the $(e,e'p)$ reaction cross-section ratios for Helium-3 ($^3$He), Tritium ($^3$H), and Deuterium ($d$). The measurement covered a missing momentum range of $40 \le p_{miss} \le 550$ MeV$/c$, at large momentum transfer ($\langle Q^2 \rangle \approx 1.9$ (GeV$/c$)$^2$) and $x_B>1$, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The data is compared with plane-wave impulse approximation (PWIA) calculations using realistic spectral functions and momentum distributions. The measured and PWIA-calculated cross-section ratios for $^3$He$/d$ and $^3$H$/d$ extend to just above the typical nucleon Fermi-momentum ($k_F \approx 250$ MeV$/c$) and differ from each other by $\sim 20\%$, while for $^3$He/$^3$H they agree within the measurement accuracy of about 3\%. At momenta above $k_F$, the measured $^3$He/$^3$H ratios differ from the calculation by $20\% - 50\%$. Final state interaction (FSI) calculations using the generalized Eikonal Approximation indicate that FSI should change the $^3$He/$^3$H cross-section ratio for this measurement by less than 5\%. If these calculations are correct, then the differences at large missing momenta between the $^3$He/$^3$H experimental and calculated ratios could be due to the underlying $NN$ interaction, and thus could provide new constraints on the previously loosely-constrained short-distance parts of the $NN$ interaction. △ Less

Submitted 24 September, 2019; v1 submitted 17 February, 2019; originally announced February 2019.

Comments: 8 pages, 3 figures (4 panels)

Report number: JLAB-PHY-19-2893; LA-UR-18-31091

Journal ref: Physics Letters B 797 (2019) 134890

Theoretical calculation of the $p-{}^6{\rm Li}$ radiative capture reaction

Authors: Alex Gnech, Laura Elisa Marcucci

Abstract: We present a new calculation of the ${}^6{\rm Li}(p,γ){}^7{\rm Be}$ radiative capture astrophysical $S$-factor in a cluster model framework. We consider several intercluster potentials, adjusted to reproduce the ${}^7{\rm Be}$ bound state properties and the $p-{}^6{\rm Li}$ elastic scattering phase shifts. Using these potentials, we calculate the astrophysical $S$-factor, obtaining a good agreemen… ▽ More We present a new calculation of the ${}^6{\rm Li}(p,γ){}^7{\rm Be}$ radiative capture astrophysical $S$-factor in a cluster model framework. We consider several intercluster potentials, adjusted to reproduce the ${}^7{\rm Be}$ bound state properties and the $p-{}^6{\rm Li}$ elastic scattering phase shifts. Using these potentials, we calculate the astrophysical $S$-factor, obtaining a good agreement with available data, and the photon angular distribution. Finally, we discuss the consequences of a hypothetical resonance-like structure on the $S$-factor. △ Less

Submitted 15 February, 2019; originally announced February 2019.

Comments: 27 pages, 9 figures

Short-range three-nucleon interaction from A=3 data and its hierarchical structure

Authors: L. Girlanda, A. Kievsky, M. Viviani, L. E. Marcucci

Abstract: We construct accurate models of three-nucleon (3N) interaction by fitting, in a hybrid phenomenological approach, the low-energy constants parametrizing the subleading 3N contact operators to the triton binding energy, n-d scattering lengths, cross section and polarization observables of p-d scattering at 2 MeV center-of-mass energy. These models lead to a satisfactory description of polarized p-d… ▽ More We construct accurate models of three-nucleon (3N) interaction by fitting, in a hybrid phenomenological approach, the low-energy constants parametrizing the subleading 3N contact operators to the triton binding energy, n-d scattering lengths, cross section and polarization observables of p-d scattering at 2 MeV center-of-mass energy. These models lead to a satisfactory description of polarized p-d scattering data in the whole energy range below the deuteron breakup threshold. In particular, the long-standing $A_y$ puzzle seems to be solved thanks to the new terms considered in the 3N force. Two types of hierarchies among the subleading contact operators are also derived, based on the large-$N_c$ counting and on a recently proposed relativistic counting. We test these hierarchies against the same experimental data and show that they are respected at a reasonable level. △ Less

Submitted 23 November, 2018; originally announced November 2018.

Comments: 35 pages, 9 figures

Journal ref: Phys. Rev. C 99, 054003 (2019)

Local chiral interactions and magnetic structure of few-nucleon systems

Authors: R. Schiavilla, A. Baroni, S. Pastore, M. Piarulli, L. Girlanda, A. Kievsky, A. Lovato, L. E. Marcucci, Steven C. Pieper, M. Viviani, R. B. Wiringa

Abstract: 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 spa… ▽ More 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. △ Less

Submitted 26 September, 2018; originally announced September 2018.

Comments: 24 pages, 13 figures

Journal ref: Phys. Rev. C 99, 034005 (2019)

Non-Symmetrized Hyperspherical Harmonics Method for Non-Equal Mass Three-Body Systems

Authors: A. Nannini, L. E. Marcucci

Abstract: The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and $^3_Λ$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NNΛ$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. T… ▽ More The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and $^3_Λ$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NNΛ$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between $^3$H and $^3$He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the $^3_Λ$H hypernucleus binding energy is calculated using different $NN$ and $ΛN$ potential models. The results have been compared with those present in the literature, finding a very nice agreement. △ Less

Submitted 19 October, 2018; v1 submitted 6 September, 2018; originally announced September 2018.

Comments: 15 pages, 1 figure and 14 tables, version revisited according to referees suggestions

Momentum distributions and short-range correlations in the deuteron and $^3$He with modern chiral potentials

Authors: L. E. Marcucci, F. Sammarruca, M. Viviani, R. Machleidt

Abstract: We study momentum distributions and short-range correlation probabilities in $A$=2 and $A$=3 systems. First, we show results with phenomenological and meson-theoretic two- and three-nucleon forces to verify consistency with previous similar studies. We then apply most recent high-quality chiral nucleon-nucleon potentials up to fifth order in the chiral expansion together with the leading chiral th… ▽ More We study momentum distributions and short-range correlation probabilities in $A$=2 and $A$=3 systems. First, we show results with phenomenological and meson-theoretic two- and three-nucleon forces to verify consistency with previous similar studies. We then apply most recent high-quality chiral nucleon-nucleon potentials up to fifth order in the chiral expansion together with the leading chiral three-nucleon force. Predictions are examined in the context of a broader discussion of short-range correlation probabilities extracted from analyses of inclusive electron scattering data, addressing the question of whether modern interactions can be reconciled with the latter. △ Less

Submitted 6 September, 2018; originally announced September 2018.

Comments: 20 pages, 18 figures and 8 tables

Journal ref: Phys. Rev. C 99, 034003 (2019)

Radiative pion capture in 2H, 3He and 3H

Authors: J. Golak, R. Skibinski, K. Topolnicki, H. Witala, A. Grassi, H. Kamada, A. Nogga, L. E. Marcucci

Abstract: The $π^- + {^2{\rm H}} \rightarrow γ+ n + n$, $π^- + {^3{\rm He}} \rightarrow γ+ {^3{\rm H}}$, $π^- + {^3{\rm He}} \rightarrow γ+ n + d$, $π^- + {^3{\rm He}} \rightarrow γ+ n + n + p$ and $π^- + {^3{\rm H}} \rightarrow γ+ n + n + n$ capture reactions are studied with the AV18 two-nucleon potential and the Urbana~IX three-nucleon potential. We provide for the first time realistic predictions for th… ▽ More The $π^- + {^2{\rm H}} \rightarrow γ+ n + n$, $π^- + {^3{\rm He}} \rightarrow γ+ {^3{\rm H}}$, $π^- + {^3{\rm He}} \rightarrow γ+ n + d$, $π^- + {^3{\rm He}} \rightarrow γ+ n + n + p$ and $π^- + {^3{\rm H}} \rightarrow γ+ n + n + n$ capture reactions are studied with the AV18 two-nucleon potential and the Urbana~IX three-nucleon potential. We provide for the first time realistic predictions for the differential and total capture rates for all these processes, treating consistently the initial and final nuclear states. Our results are based on the single nucleon Kroll-Ruderman-type transition operator and concentrate on the full treatment of the nuclear final state interactions. They are compared with older theoretical predictions and experimental data. △ Less

Submitted 19 July, 2018; originally announced July 2018.

Comments: 23 pages, 13 eps figures

Journal ref: Phys. Rev. C 98, 054001 (2018)

Nuclear and neutron matter equations of state from high-quality potentials up to fifth order of the chiral expansion

Authors: F. Sammarruca, L. E. Marcucci, L. Coraggio, J. W. Holt, N. Itaco, R. Machleidt

Abstract: We present predictions for the equation of state of symmetric nuclear and pure neutron matter based on recent high-quality nucleon-nucleon potentials from leading order to fifth order in the chiral expansion. We include as well the next-to-next-to-leading order (N2LO) chiral three-nucleon force whose low-energy constants cD and cE are fitted to the binding energies of 3H and 3He as well as the \b{… ▽ More We present predictions for the equation of state of symmetric nuclear and pure neutron matter based on recent high-quality nucleon-nucleon potentials from leading order to fifth order in the chiral expansion. We include as well the next-to-next-to-leading order (N2LO) chiral three-nucleon force whose low-energy constants cD and cE are fitted to the binding energies of 3H and 3He as well as the \b{eta}-decay lifetime of 3H. The ground state energy per particle is computed in the particle- particle ladder approximation up to a few times saturation density. Due to the soft character of the interactions, uncertainties due to the convergence in many-body perturbation theory are small. We find that nuclear matter saturation is reproduced quantitatively at N3LO and N4LO, and therefore we encourage the application of these interactions in finite nuclei, where the description of ground- state energies and charge radii of medium-mass nuclei may be improved. △ Less

Submitted 17 July, 2018; originally announced July 2018.

Comments: 11 pages, 12 figures

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

Authors: A. Baroni, R. Schiavilla, L. E. Marcucci, L. Girlanda, A. Kievsky, A. Lovato, S. Pastore, M. Piarulli, Steven C. Pieper, M. Viviani, R. B. Wiringa

Abstract: 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 c… ▽ More 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. △ Less

Submitted 26 June, 2018; originally announced June 2018.

Comments: 16 pages, 3 figures

Journal ref: Phys. Rev. C 98, 044003 (2018)

Momentum space treatment of inclusive neutrino scattering off the deuteron and trinucleons

Authors: J. Golak, R. Skibinski, K. Topolnicki, H. Witala, A. Grassi, H. Kamada, L. E. Marcucci

Abstract: The $\barν_e + {^2{\rm H}} \rightarrow e^+ + n + n$, $ν_e + {^2{\rm H}} \rightarrow e^- + p + p$, $\barν_l + {^2{\rm H}} \rightarrow \barν_l + {^2{\rm H}}$, $ν_l + {^2{\rm H}} \rightarrow ν_l + {^2{\rm H}}$, $\barν_l + {^2{\rm H}} \rightarrow \barν_l + p + n$, $ν_l + {^2{\rm H}} \rightarrow ν_l + p + n$, $\barν_e + {^3{\rm He}} \rightarrow e^+ + {^3{\rm H}}$,… ▽ More The $\barν_e + {^2{\rm H}} \rightarrow e^+ + n + n$, $ν_e + {^2{\rm H}} \rightarrow e^- + p + p$, $\barν_l + {^2{\rm H}} \rightarrow \barν_l + {^2{\rm H}}$, $ν_l + {^2{\rm H}} \rightarrow ν_l + {^2{\rm H}}$, $\barν_l + {^2{\rm H}} \rightarrow \barν_l + p + n$, $ν_l + {^2{\rm H}} \rightarrow ν_l + p + n$, $\barν_e + {^3{\rm He}} \rightarrow e^+ + {^3{\rm H}}$, $\barν_l + {^3{\rm He}} \rightarrow \barν_l + {^3{\rm He}}$, $ν_l + {^3{\rm He}} \rightarrow ν_l + {^3{\rm He}}$, $\barν_l + {^3{\rm H}} \rightarrow \barν_l + {^3{\rm H}}$, $ν_l + {^3{\rm H}} \rightarrow ν_l + {^3{\rm H}}$, $\barν_e + {^3{\rm He}} \rightarrow e^+ + n + d$, $\barν_e + {^3{\rm He}} \rightarrow e^+ + n + n + p$, $\barν_l + {^3{\rm He}} \rightarrow \barν_l + p + d$, $\barν_l + {^3{\rm He}} \rightarrow \barν_l + p + p +n$, $ν_l + {^3{\rm H}} \rightarrow ν_l + n + d$ and $ν_l + {^3{\rm H}} \rightarrow ν_l + n + n + p$ reactions ($l= e, μ, τ$) are studied consistently in momentum space for (anti)neutrino energies up to 300 MeV. For most of these processes we provide predictions for the total cross sections and in the case of the (anti)neutrino-$^3$He and (anti)neutrino-$^3$H inelastic scattering we compute examples of essential response functions, using the AV18 nucleon-nucleon potential and a single-nucleon weak current operator. For the reactions with the deuteron we study relativistic effects in the final state kinematics and compare two-nucleon scattering states obtained in momentum and coordinate spaces. Our results from momentum space are compared with the theoretical predictions by G.Shen et al., Phys. Rev. C 86, 035503 (2012). The observed disagreement can be attributed to the differences in kinematics and in the weak current operator. △ Less

Submitted 30 April, 2018; originally announced May 2018.

Comments: 31 pages, 18 figures in 49 eps files

Journal ref: Phys. Rev. C 98, 015501 (2018)

The $α+ d \rightarrow ~ ^6\mathrm{Li} + γ$ astrophysical $S$-factor and its implications for Big Bang Nucleosynthesis

Authors: A. Grassi, G. Mangano, L. E. Marcucci, O. Pisanti

Abstract: The $α+d\rightarrow\, ^6{\rm Li}+γ$ radiative capture is studied in order to predict the $^6$Li primordial abundance. Within a two-body framework, the $α$ particle and the deuteron are considered the structureless constituents of $^6$Li. Five $α+d$ potentials are used to solve the two-body problem: four of them are taken from the literature, only one having also a tensor component. A fifth model i… ▽ More The $α+d\rightarrow\, ^6{\rm Li}+γ$ radiative capture is studied in order to predict the $^6$Li primordial abundance. Within a two-body framework, the $α$ particle and the deuteron are considered the structureless constituents of $^6$Li. Five $α+d$ potentials are used to solve the two-body problem: four of them are taken from the literature, only one having also a tensor component. A fifth model is here constructed in order to reproduce, besides the $^6$Li static properties as binding energy, magnetic dipole and electric quadrupole moments, also the $S$-state asymptotic normalization coefficient (ANC). The two-body bound and scattering problem is solved with different techniques, in order to minimize the numerical uncertainty of the present results. The long-wavelength approximation is used, and therefore only the electric dipole and quadrupole operators are retained. The astrophysical $S$-factor is found to be significantly sensitive to the ANC, but in all the cases in good agreement with the available experimental data. The theoretical uncertainty has been estimated of the order of few % when the potentials which reproduce the ANC are considered, but increases up to $\simeq 20$ % when all the five potential models are retained. The effect of this $S$-factor prediction on the $^6$Li primordial abundance is studied, using the public code PArthENoPE. For the five models considered here we find $^6{\rm Li}/$H$ = (0.9 - 1.8) \times 10^{-14}$, with the baryon density parameter in the 3-$σ$ range of Planck 2015 analysis, $Ω_b h^2= 0.02226 \pm 0.00023$. △ Less

Submitted 28 July, 2017; originally announced July 2017.

Comments: 26 pages, 9 figures

Journal ref: Phys. Rev. C 96, 045807 (2017)

Light-nuclei spectra from chiral dynamics

Authors: M. Piarulli, A. Baroni, L. Girlanda, A. Kievsky, A. Lovato, Ewing Lusk, L. E. Marcucci, Steven C. Pieper, R. Schiavilla, M. Viviani, R. B. Wiringa

Abstract: A major goal of nuclear theory is to explain the spectra and stability of nuclei in terms of effective many-body interactions amongst the nucleus' constituents-the nucleons, i.e., protons and neutrons. Such an approach, referred to below as the basic model of nuclear theory, is formulated in terms of point-like nucleons, which emerge as effective degrees of freedom, at sufficiently low energy, as… ▽ More A major goal of nuclear theory is to explain the spectra and stability of nuclei in terms of effective many-body interactions amongst the nucleus' constituents-the nucleons, i.e., protons and neutrons. Such an approach, referred to below as the basic model of nuclear theory, is formulated in terms of point-like nucleons, which emerge as effective degrees of freedom, at sufficiently low energy, as a result of a decimation process, starting from the fundamental quarks and gluons, described by Quantum Chromodynamics (QCD). A systematic way to account for the constraints imposed by the symmetries of QCD, in particular chiral symmetry, is provided by chiral effective field theory, in the framework of a low-energy expansion. Here we show, in quantum Monte Carlo calculations accurate to $\leq\!2\%$ of the binding energy, that two- and three-body chiral interactions fitted {\sl only} to bound- and scattering-state observables in, respectively, the two- and three-nucleon sectors, lead to predictions for the energy levels and level ordering of nuclei in the mass range $A\,$=$\,$4-12 in very satisfactory agreement with experimental data. Our findings provide strong support for the fundamental assumptions of the basic model, and pave the way to its systematic application to the electroweak structure and response of these systems as well as to more complex nuclei. △ Less

Submitted 10 July, 2017; originally announced July 2017.

Comments: 21 pages, 3 figures

Journal ref: Phys. Rev. Lett. 120, 052503 (2018)

Benchmark calculation of p-3H and n-3He scattering

Authors: M. Viviani, A. Deltuva, R. Lazauskas, A. C. Fonseca, A. Kievsky, L. E. Marcucci

Abstract: p-3H and n-3He scattering in the energy range above the n-3He but below the d-d thresholds is studied by solving the 4-nucleon problem with a realistic nucleon-nucleon interaction. Three different methods -- Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev-Yakubovsky -- have been employed and their results for both elastic and charge-exchange processes are compared. We observe a… ▽ More p-3H and n-3He scattering in the energy range above the n-3He but below the d-d thresholds is studied by solving the 4-nucleon problem with a realistic nucleon-nucleon interaction. Three different methods -- Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev-Yakubovsky -- have been employed and their results for both elastic and charge-exchange processes are compared. We observe a good agreement between the three different methods, thus the obtained results may serve as a benchmark. A comparison with the available experimental data is also reported and discussed. △ Less

Submitted 28 October, 2016; originally announced October 2016.

Comments: 13 pages, 6 figures. arXiv admin note: text overlap with arXiv:1109.3625

Journal ref: Phys. Rev. C 95, 034003 (2017)

Local chiral potentials and the structure of light nuclei

Authors: Maria Piarulli, Luca Girlanda, Rocco Schiavilla, Alejandro Kievsky, Alessandro Lovato, Laura E. Marcucci, Steven C. Pieper, Michele Viviani, Robert B. Wiringa

Abstract: We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes… ▽ More We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $Δ$-isobars in the intermediate states up to order $Q^3$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order $Q^4$. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential. △ Less

Submitted 20 June, 2016; originally announced June 2016.

Comments: 29 pages, 3 figures

Journal ref: Phys. Rev. C 94, 054007 (2016)

Muon capture on 3H

Authors: J. Golak, R. Skibinski, H. Witala, K. Topolnicki, H. Kamada, A. Nogga, L. E. Marcucci

Abstract: The muon capture on 3H leading to muonic neutrino and three neutrons in the final state is studied under full inclusion of final state interactions. Predictions for the three-body break-up of 3H are calculated with the AV18 potential, augmented by the Urbana IX three-nucleon force. Our results are based on the single nucleon weak current operator comprising the dominant relativistic corrections. T… ▽ More The muon capture on 3H leading to muonic neutrino and three neutrons in the final state is studied under full inclusion of final state interactions. Predictions for the three-body break-up of 3H are calculated with the AV18 potential, augmented by the Urbana IX three-nucleon force. Our results are based on the single nucleon weak current operator comprising the dominant relativistic corrections. This work is a natural extension of our investigations of the muon capture on 3He leading to 3H or n+d or n+n+p and muonic neutrino in the final state, presented in Phys. Rev. C90, 024001 (2014). △ Less

Submitted 18 May, 2016; originally announced May 2016.

Comments: 18 pages, 6 eps figures. arXiv admin note: text overlap with arXiv:1406.6781

Journal ref: Phys. Rev. C 94, 034002 (2016)

Tritium $β$-decay in chiral effective field theory

Authors: A. Baroni, L. Girlanda, A. Kievsky, L. E. Marcucci, R. Schiavilla, M. Viviani

Abstract: We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $β$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($χ$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to ei… ▽ More We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $β$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($χ$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either $χ$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations. △ Less

Submitted 4 January, 2017; v1 submitted 5 May, 2016; originally announced May 2016.

Comments: 19 pages,6 figures, corrections to Text as suggested by Referee added; Erratum: 4 pages, 3 figures, corrections to Eq.(20), Tables I, II, III, Figures 4, 5, conclusions unchanged

Chiral nucleon-nucleon forces in nuclear structure calculations

Authors: L. Coraggio, A. Gargano, J. W. Holt, N. Itaco, R. Machleidt, L. E. Marcucci, F. Sammarruca

Abstract: Realistic nuclear potentials, derived within chiral perturbation theory, are a major breakthrough in modern nuclear structure theory, since they provide a direct link between nuclear physics and its underlying theory, namely the QCD. As a matter of fact, chiral potentials are tailored on the low-energy regime of nuclear structure physics, and chiral perturbation theory provides on the same footing… ▽ More Realistic nuclear potentials, derived within chiral perturbation theory, are a major breakthrough in modern nuclear structure theory, since they provide a direct link between nuclear physics and its underlying theory, namely the QCD. As a matter of fact, chiral potentials are tailored on the low-energy regime of nuclear structure physics, and chiral perturbation theory provides on the same footing two-nucleon forces as well as many-body ones. This feature fits well with modern advances in ab-initio methods and realistic shell-model. Here, we will review recent nuclear structure calculations, based on realistic chiral potentials, for both finite nuclei and infinite nuclear matter. △ Less

Submitted 10 February, 2016; originally announced February 2016.

Comments: 10 pages, 8 figures, plenary talk presented at "Nucleus-Nucleus 2015" Conference, 21-26 June 2015, Catania, to be published in the "Conference Proceedings" Series of the Italian Physical Society

Implication of the proton-deuteron radiative capture for Big Bang Nucleosynthesis

Authors: L. E. Marcucci, G. Mangano, A. Kievsky, M. Viviani

Abstract: The astrophysical $S$-factor for the radiative capture $d(p,γ)^3$He in the energy-range of interest for Big Bang Nucleosynthesis (BBN) is calculated using an {\it ab-initio} approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions - the Argonne $v_{18}$ and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The… ▽ More The astrophysical $S$-factor for the radiative capture $d(p,γ)^3$He in the energy-range of interest for Big Bang Nucleosynthesis (BBN) is calculated using an {\it ab-initio} approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions - the Argonne $v_{18}$ and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the $1/m$ leading order contribution ($m$ is the nucleon mass), also the next-to-leading order term, proportional to $1/m^3$. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the $A=3$ bound and scattering states. A particular attention is used in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical $S$-factor of the order or below $\sim$1 %. Then, in this energy range, the $S$-factor is found to be $\sim$10 % larger than the currently adopted values.Part of this increase (1-3 %) is due to the $1/m^3$ one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the $d(p,γ)^3$He $S$-factor on deuterium primordial abundance. We find that the predicted theoretical value for $^2$H/H is in excellent agreement with its experimental determination, using the most recent determination of baryon density of Planck experiment, and with a standard number of relativistic degrees of freedom $N_{\rm eff}=3.046$ during primordial nucleosynthesis. △ Less

Submitted 27 October, 2015; originally announced October 2015.

Comments: 5 pages, 2 figures, submitted to Phys. Rev. Lett

Journal ref: Phys. Rev. Lett. 116, 102501 (2016)

Electromagnetic Structure of Few-Nucleon Ground States

Authors: L. E. Marcucci, F. Gross, M. T. Pena, M. Piarulli, R. Schiavilla, I. Sick, A. Stadler, J. W. Van Orden, M. Viviani

Abstract: Experimental form factors of the hydrogen and helium isotopes, extracted from an up-to-date global analysis of cross sections and polarization observables measured in elastic electron scattering from these systems, are compared to predictions obtained in three different theoretical approaches: the first is based on realistic interactions and currents, including relativistic corrections (labeled as… ▽ More Experimental form factors of the hydrogen and helium isotopes, extracted from an up-to-date global analysis of cross sections and polarization observables measured in elastic electron scattering from these systems, are compared to predictions obtained in three different theoretical approaches: the first is based on realistic interactions and currents, including relativistic corrections (labeled as the conventional approach); the second relies on a chiral effective field theory description of the strong and electromagnetic interactions in nuclei (labeled $χ$EFT); the third utilizes a fully relativistic treatment of nuclear dynamics as implemented in the covariant spectator theory (labeled CST). For momentum transfers below $Q \lesssim 5$ fm$^{-1}$ there is satisfactory agreement between experimental data and theoretical results in all three approaches. However, at $Q \gtrsim 5$ fm$^{-1}$, particularly in the case of the deuteron, a relativistic treatment of the dynamics, as is done in the CST, is necessary. The experimental data on the deuteron $A$ structure function extend to $Q \simeq 12$ fm$^{-1}$, and the close agreement between these data and the CST results suggests that, even in this extreme kinematical regime, there is no evidence for new effects coming from quark and gluon degrees of freedom at short distances. △ Less

Submitted 20 April, 2015; originally announced April 2015.

Comments: 66 pages, 23 figures, topical review submitted to J. Phys. G: Nucl. Part. Phys

Report number: JLAB-THY-15-2030

Astrophysical implications of the proton-proton cross section updates

Authors: E. Tognelli, S. Degl'Innocenti, L. E. Marcucci, P. G. Prada Moroni

Abstract: The p(p,e^+ ν_e)^2H reaction rate is an essential ingredient for theoretical computations of stellar models. In the past several values of the corresponding S-factor have been made available by different authors. Prompted by a recent evaluation of S(E), we analysed the effect of the adoption of different proton-proton reaction rates on stellar models, focusing, in particular, on the age of mid and… ▽ More The p(p,e^+ ν_e)^2H reaction rate is an essential ingredient for theoretical computations of stellar models. In the past several values of the corresponding S-factor have been made available by different authors. Prompted by a recent evaluation of S(E), we analysed the effect of the adoption of different proton-proton reaction rates on stellar models, focusing, in particular, on the age of mid and old stellar clusters (1-12 Gyr) and on standard solar model predictions. By comparing different widely adopted p(p,e^+ ν_e)^2H reaction rates, we found a maximum difference in the temperature regimes typical of main sequence hydrogen-burning stars (5x10^6 - 3x10^7 K) of about 3%. Such a variation translates into a change of cluster age determination lower than 1%. A slightly larger effect is observed in the predicted solar neutrino fluxes with a maximum difference, in the worst case, of about 8%. Finally we also notice that the uncertainty evaluation of the present proton-proton rate is at the level of few \permil, thus the p(p,e^+ ν_e)^2H reaction rate does not constitute anymore a significant uncertainty source in stellar models. △ Less

Submitted 2 February, 2015; v1 submitted 20 November, 2014; originally announced November 2014.

Comments: accepted

Towards order-by-order calculations of the nuclear and neutron matter equations of state in chiral effective field theory

Authors: F. Sammarruca, L. Coraggio, J. W. Holt, N. Itaco, R. Machleidt, L. E. Marcucci

Abstract: We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically w… ▽ More We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically we study the equations of state using consistent NLO and N2LO (next-to-next-to-leading order) chiral potentials where the low-energy constants cD and cE associated with contact vertices in the N2LO chiral three-nucleon force are fitted to reproduce the binding energies of 3H and 3He as well as the beta-decay lifetime of 3H. At these low orders in the chiral expansion there is little sign of convergence, while an exploratory study employing the N3LO two-nucleon force together with the N2LO three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and N2LO potentials described in the present work provide the basis for estimating theoretical uncertainties associated with the order-by-order convergence of nuclear many-body calculations in chiral effective field theory. △ Less

Submitted 17 April, 2015; v1 submitted 1 November, 2014; originally announced November 2014.

Comments: 9 pages, 6 figures. Accepted for publication in Physical Review C

Journal ref: Phys. Rev. C 91, 054311 (2015)

Muon capture on deuteron and the neutron-neutron scattering length

Authors: L. E. Marcucci, R. Machleidt

Abstract: We study the capture rate in the doublet hyperfine initial state for the muon capture reaction $μ^- + \,^2{\rm H} \rightarrow ν_μ+ n + n$ ($Γ^D$) and the total capture rate for the reaction $ μ^- + \,^3{\rm He} \rightarrow ν_μ+ \,^3{\rm H}$ ($Γ_0$). We investigate whether $Γ^D$ and $Γ_0$ could be sensitive to the $nn$ $S$-wave scattering length ($a_{nn}$). To this aim, we consider nuclear potentia… ▽ More We study the capture rate in the doublet hyperfine initial state for the muon capture reaction $μ^- + \,^2{\rm H} \rightarrow ν_μ+ n + n$ ($Γ^D$) and the total capture rate for the reaction $ μ^- + \,^3{\rm He} \rightarrow ν_μ+ \,^3{\rm H}$ ($Γ_0$). We investigate whether $Γ^D$ and $Γ_0$ could be sensitive to the $nn$ $S$-wave scattering length ($a_{nn}$). To this aim, we consider nuclear potentials and weak currents derived within $χ$EFT. We employ the N3LO chiral potential with cutoff $Λ$=500 MeV, but the low-energy constant (LEC) determining $a_{nn}$ is varied so as to obtain $a_{nn}$=-18.95 (the present empirical value), -16.0, -22.0, and +18.22 fm. The last value leads to a $nn$ bound state with a binding energy of 139 keV. The LECs $c_D$ and $c_E$, present in the three-nucleon potential and axial-vector current, are fitted to reproduce the $A=3$ binding energies and the triton Gamow-Teller matrix element. The capture rate $Γ^D$ is found to be 399(3) s$^{-1}$ for $a_{nn}$=-18.95 and -16.0 fm; and 400(3) s$^{-1}$ for $a_{nn}$=-22.0 fm. For $a_{nn}$=+18.22 fm, we obtain 275(3) s$^{-1}$ (135(3) s$^{-1}$), when the final $nn$ system is unbound (bound). The rate $Γ_0$ is found to be 1494(15), 1491(16), 1488(18), and 1475(16) s$^{-1}$ for $a_{nn}$=-18.95, -16.0, -22.0, and +18.22 fm, respectively. The theoretical uncertainties are due to the fitting procedure and radiative corrections. Our results seem to exclude the possibility of constraining a negative $a_{nn}$ with an uncertainty of less than $\sim \pm$ 3 fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forth-coming) experimental results for $Γ^D$. Finally, a comparison with the already available experimental data discourages the possibility of a bound $nn$ state. △ Less

Submitted 12 November, 2014; v1 submitted 15 September, 2014; originally announced September 2014.

Comments: 5 pages, 2 figures; revisited version accepted for publication on Phys. Rev. C

Journal ref: Phys. Rev. C 90, 054001 (2014)