Few-nucleon Systems Research Articles

Toward a unified treatment of ΔS=0 parity violation in low-energy nuclear processes

We revisit the unified treatment of low-energy hadronic parity violation espoused by Desplanques, Donoghue, and Holstein to the end of an ab initio treatment of parity violation in low-energy nuclear processes within the standard model. We use our improved effective Hamiltonian and precise nonperturbative assessments of the quark charges of the nucleon within lattice quantum chromodynamics (QCD) to make new assessments of the parity-violating meson-nucleon coupling constants. Comparing with recent, precise measurements of hadronic parity violation in few-body nuclear reactions, we find improved agreement with these experimental results, though some tensions remain. We thus note the broader problem of comparing low-energy constants from nuclear and few-nucleon systems, considering, too, unresolved theoretical issues in connecting an ab initio, effective Hamiltonian approach to chiral effective theories. We note how future experiments and lattice QCD studies could sharpen the emerging picture, promoting the study of hadronic parity violation as a laboratory for testing ``end-to-end'' theoretical descriptions of weak processes in hadrons and nuclei at low energies.

“Renormalization-group-invariant effective field theory” for few-nucleon systems is cutoff dependent

We consider nucleon-nucleon scattering using the formulation of chiral effective field theory which is claimed to be renormalization group invariant. The cornerstone of this framework is the existence of a well-defined infinite-cutoff limit for the scattering amplitude at each order of the expansion, which should not depend on a particular regulator form. Focusing on the ${}^{3}{P}_{0}$ partial wave as a representative example, we show that this requirement can in general not be fulfilled beyond the leading order, in spite of the perturbative treatment of subleading contributions to the amplitude. Several previous studies along these lines, including the next-to-leading order calculation by B. Long and C. J. Yang [Phys. Rev. C 84, 057001 (2011)] and a toy model example with singular long-range potentials by B. Long and U. van Kolck [Ann. Phys. 323, 1304 (2008)], are critically reviewed and scrutinized in detail.

Study of fundamental symmetries in the few-nucleon systems

In this contribution we present two studies of fundamental symmetries in light nuclei: the investigation of CP violation via the calculation of the electric dipole moments (EDMs) of the deuteron, 3H and 3He, and the possible existence of a new bosonic particle, the so-called X17, in the 3H(p, e + e −)4He and 3He(n, e + e −)4He reactions. The advantage to perform these investigations in few-nucleon systems is related to the possibility to compute accurate ab initio bound- and continuum-states wave functions using well established nuclear interactions. Therefore, if these effects are observed, they can be unambiguously related to underlying beyond Standard Model theories.

From correlations to universal behavior in few-nucleon systems

The deuteron, the only two-nucleon bound state, has a shallow character: its binding energy is strictly related to zero-energy parameters, the triplet scattering length 3anp and triplet effective range 3rnp. This fact places the deuteron inside the universal window, a region in which systems having a large value of the two- body scattering length are located. When the scattering length is large compared to the interaction range certain types of correlations can be observed. Increasing the number of nucleons these correlations are responsible for the particular spectrum of light nuclei as for example the lack of excited states in three- and four-nucleon systems. In this presentation some constraints imposed by the large values of the singlet and triplet scattering lengths in the spectrum of light nuclear systems are discussed.

Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N2LO

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to $A=48$ using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (${\mathrm{N}}^{2}\mathrm{LO}$) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A\ensuremath{\approx}10$ found in our earlier study utilizing the ${\mathrm{N}}^{2}\mathrm{LO}$ two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. The resulting Hamiltonian can be completely determined using the $A=3$ binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light $p$-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from $^{14}\mathrm{O}$ to $^{26}\mathrm{O}$ as well as $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$ show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the $A\ensuremath{\le}3$ data, once the fourth-order (${\mathrm{N}}^{3}\mathrm{LO}$) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by $\ensuremath{\approx}10%$ for the oxygen isotopes and by almost $20%$ for $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$.

Magnetic structure of few-nucleon systems at high momentum transfers in a chiral effective field theory approach

The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($\chi$EFT) up to one loop are determined by a simultaneous fit to the $A\,$=$\,2$--3 nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the $^3$He/$^3$H magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to $\approx 0.8$ GeV/c, beyond the expected regime of validity of the $\chi$EFT approach. The calculations are based on last-generation two-nucleon interactions including high orders in the chiral expansion and derived by Entem, Macheleidt, and Nosyk [Phys.\ Rev.\ C {\bf 96}, 024004 (2017)] and by Piarulli {\it et al.} [Phys.\ Rev.\ C {\bf 94}, 054007 (2016)], using different $\chi$EFT formulations. In the $A\,$=$\,3$ calculations, (chiral) three-nucleon interactions are also accounted for. The model dependence resulting from these different formulations of the interactions is found to be mild for momentum transfer below $\approx0.8$ GeV/c. An analysis of the convergence of the chiral expansion is also provided.

Data on the Neutron–Neutron Scattering Length from the nd-Breakup Reaction at En = 8 MeV and En = 11 MeV

A kinematically complete experiment devoted to studying the nd-breakup reaction at energies of 8 and 11 MeV via detecting all three secondary particles was performed. The {}^{1}S_{0} neutron–neutron (nn) scattering-length values of a_{nn}={-}19.8pm 0.4 and {-}19.0pm 0.5 fm at, respectively, E_{n}=8 and 11 MeV were obtained from a comparison of the experimental dependence of the yield of the nd-breakup reaction on the relative energy of the nn pair with the results of a simulation. An analysis of the values obtained for the nn scattering length, together with data from other experiments, confirms the hypothesis that three-nucleon forces affect the parameters of nn interaction that are extracted from reactions involving few-nucleon systems and gives a new asymptotic nn scattering length, a_{nn}={-}16.1pm 0.1 fm.

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. The method is demonstrated through calculations of the binding energies of nuclei with atomic number $A\ensuremath{\in}{2,3,4}$ in finite volume, matched to lattice QCD calculations at quark masses corresponding to ${m}_{\ensuremath{\pi}}=806\text{ }\text{ }\mathrm{MeV}$, and infinite-volume effective field theory calculations of $A\ensuremath{\in}{2,3,4,5,6}$ systems based on this matching.

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

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

Light nuclei with semilocal momentum-space regularized chiral interactions up to third order

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$.

Precision measurements of differential cross sections and analyzing powers in elastic deuteron-deuteron scattering at 65 MeV/nucleon

We present measurements of differential cross sections and analyzing powers for the elastic ^{2}mathrm{H}(mathbf {d},d){d} scattering process. The data were obtained using a 130 MeV polarized deuteron beam. Cross sections and spin observables of the elastic scattering process were measured at the AGOR facility at KVI using two independent setups, namely BINA and BBS. The data harvest at setups are in excellent agreement with each other and allowed us to carry out a thorough systematic analysis to provide the most accurate data in elastic deuteron-deuteron scattering at intermediate energies. The results can be used to confront upcoming state-of-the-art calculations in the four-nucleon scattering domain, and will, thereby, provide further insights in the dynamics of three- and four-nucleon forces in few-nucleon systems.

Magnetic structure and radiative captures of few-nucleon systems: status and prospects

We review the main ingredients for an ab-initio study of few-nucleon reactions of astrophysical interest within the chiral effective field theory approach, with particular attention to radiative captures relevant for Big Bang Nucleosynthesis and stellar evolution. We conclude with an outlook for ongoing and future work.

Hadrons and Few-Body Physics

We present a selection of topics with an interplay of hadron and few-body physics. This includes few-nucleon systems, light hypernuclei and quark dynamics for baryons and multiquarks. It is stressed that standard quark models predict very few stable multiquarks.

Comprehensive measurements of cross sections and spin observables of the three-body break-up channel in deuteron-deuteron scattering at 65\xa0MeV/nucleon

Detailed measurements of five-fold differential cross sections and a rich set of vector and tensor analyzing powers of the ^{2}mathrm{H}({varvec{d}},dp){n} break-up process using polarized deuteron-beam energy of 65 MeV/nucleon with a liquid-deuterium target are presented. The experiment was conducted at the AGOR facility at KVI using the BINA 4pi -detection system. We discuss the analysis procedure including a thorough study of the systematic uncertainties. The results can be used to examine upcoming state-of-the-art calculations in the four-nucleon scattering domain, and will, thereby, provide further insights into the dynamics of three- and four-nucleon forces in few-nucleon systems. The results of coplanar configurations are compared with the results of recent theoretical calculations based on the Single-Scattering Approximation (SSA). Through these comparisons, the validity of SSA approximation is investigated in the Quasi-Free (QF) region.

EMC effect, few-nucleon systems and Poincaré covariance

An approach for a Poincaré covariant description of nuclear structure and of lepton scattering off nuclei is proposed within the relativistic Hamiltonian dynamics in the light-front form. Indeed a high level of accuracy is needed for a comparison with the increasingly precise present and future experimental data at high momentum transfer. Therefore, to distinguish genuine QCD effects or effects of medium modified nucleon structure functions from conventional nuclear structure effects, the commutation rules between the Poincaré generators should be satisfied. For the first time in this paper a proper hadronic tensor for inclusive deep inelastic scattering of electrons off nuclei is derived in the impulse approximation in terms of the single nucleon hadronic tensor. Our approach is based : i) on a light-front spectral function for nuclei, obtained taking advantage of the successful non-relativistic knowledge of nuclear interaction, and ii) on the free current operator that, if defined in the Breit reference frame with the momentum transfer, , parallel to the z axis, fulfills Poincaré covariance and current conservation. Our results can be generalized : i) to exclusive processes or to semi-inclusive deep inelastic scattering processes; ii) to the case where the final state interaction is considered through a Glauber approximation; iii) to finite momentum transfer kinematics. As a first test, the hadronic tensor is applied to obtain the nuclear structure function and to evaluate the EMC effect for 3He in the Bjorken limit. Encouraging results including only the two-body part of the light-front spectral function are presented.

Analyzing powers in $$d(\vec {p}, pp)n$$ at intermediate and large scattering angles at 190 MeV

Understanding of the exact nature of three-nucleon forces is the most challenging topic in the field of nuclear physics. Three-nucleon break-up reaction is a good tool to look into the underlying dynamics of the nuclear force, thanks to its rich kinematical phase space which has different levels of sensitivity to three-nucleon force effects. The recent studies on few-nucleon systems have revealed that the current nuclear force models cannot describe nucleon-deuteron scattering data accurately. In the present work, the analyzing powers of the proton-deuteron break-up reaction obtained using a 190 MeV polarized proton beam will be discussed. We present for the first time the vector analyzing powers for the kinematics in which one of the protons scatters to intermediate and large scattering angles at this energy. The results show a fairly good agreement with various theoretical predictions for both intermediate and large scattering angles of the break-up phase space.

Few-nucleon system dynamics studied via deuteron-deuteron collisions at 160 MeV

Four nucleon scattering at intermediate energies provides unique opportunities to study effects of the two key ingredients of the nuclear dynamics, the nucleon-nucleon P-wave (NNP-wave) and the three-nucleon force (3NF). This is possible only with systematic and precise data, in conjunction with exact theoretical calculations. Using the BINA detector at KVI Groningen, the Netherlands, a rich set of differential cross section of the ^{2}2H(d,dp)n breakup reaction at 160 MeV deuteron beam energy has been measured. Besides the three-body breakup, also cross sections of the ^{2}2H(d, ^{3}3He)n proton transfer reaction have been obtained. The data are compared to the recent calculations for the three-cluster breakup.

Determination of phase space region for cross-check validation of the neutron detection in the BINA experiments

Deuteron breakup reactions are basic laboratories for testing nuclear force models. Recent improvements in the data analysis allow for direct identification of neutrons in the BINA detection setup. This opens up the opportunity to study new aspects of few-nucleon system dynamics like charge dependence of nuclear force or Coulomb interaction. In this paper we determine regions along the kinematical curves where differential cross section of deuteron-proton breakup reactions can be measured by the proton-neutron and proton-proton coincidences simultaneously. %In this paper we determine regions along the kinematical curves where differential cross section of $^1$H$(d,pp)n$ and $^1$H$(d,pn)p$ breakup reactions overlap. This is particularly useful for validation of the neutron detection technique.

Investigations of the few-nucleon systems within the LENPIC project

Results presented in this contribution are obtained within the Low Energy Nuclear Physics International Collaboration (LENPIC). LENPIC aims to develop chiral nucleon-nucleon and many-nucleon interactions complete through at least the fourth order in the chiral expansion. These interactions will be used together with consistently derived current operators to solve the structure and reactions of light and medium-mass nuclei including electroweak processes. In this contribution the current status of the chiral nuclear forces and current operators will be briefly discussed. A special role played by the calculations of nucleon-deuteron scattering will be explained.

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $\Delta$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schr\"odinger 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 $\Delta$ 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.