Background: By looking specifically at free nucleons (here protons), we present for the first time a comprehensive body of experimental results concerning the mean free path, the nucleon-nucleon cross-section and in-medium effects in nuclear matter.

Purpose: Using the large dataset of exclusive measurements provided by the $4\pi$ array INDRA, we determine the relative degree of stopping as a function of system mass and bombarding energy. We show that the stopping can be directly related to the transport properties in the nuclear medium.

Methods: We perform a systematic study of protons nuclear stopping in central collisions for heavy-ion induced reactions in the Fermi-energy domain, between $15A$ and $100A$ MeV.

Results: It is found that the mean free path exhibits a maximum at ${\lambda }_{NN}=9.5\pm 2$ fm, around $E_{\mathrm{inc}}=35A-40A$ MeV incident energy and decreases toward an asymptotic value ${\lambda }_{NN}=4.5\pm 1$ fm at $E_{\mathrm{inc}}=100A$ MeV.

Conclusions: After accounting for Pauli blocking of elastic nucleon-nucleon collisions, it is shown that the effective in-medium $NN$ cross section is further reduced compared to the free value in this energy range. Therefore, in-medium effects cannot be neglected in the Fermi-energy range. These results bring new fundamental inputs for microscopic descriptions of nuclear reactions in the Fermi-energy domain.

Background: Double-$\beta$ decay is a rare nuclear process in which two neutrons in the nucleus are converted to two protons with the emission of two electrons and two electron antineutrinos.

Purpose: We measured the half-life of the two-neutrino double-$\beta$ decay of ${}^{150}\mathrm{Nd}$ to excited final states of ${}^{150}\mathrm{Sm}$ by detecting the deexcitation $\gamma$ rays of the daughter nucleus.

Method: This study yields the first detection of the coincidence $\gamma$ rays from the $0{}_1^{+}$ excited state of ${}^{150}\mathrm{Sm}$. These $\gamma$ rays have energies of 333.97 and 406.52 keV and are emitted in coincidence through a $0_1^{+}\to 2_1^{+}\to 0_{\mathrm{gs}}^{+}$ transition.

Results: The enriched ${\mathrm{Nd}}_2{\mathrm{O}}_3$ sample consisted of 40.13 g ${}^{150}\mathrm{Nd}$ and was observed for 642.8 days at the Kimballton Underground Research Facility, producing 21.6 net events in the region of interest. This count rate gives a half-life of $T_{1/2}=[1.{07}_{-0.25}^{+0.45}\left(\mathrm{stat}\right)\pm 0.07\left(\mathrm{syst}\right)]\times {10}^{20}$ yr. The effective nuclear matrix element was found to be $0.0465{}_{-0.0054}^{+0.0098}$. Finally, lower limits were obtained for decays to higher excited final states.

Conclusions: Our half-life measurement agrees within uncertainties with another recent measurement in which no coincidence was employed. Our nuclear matrix element calculation may have an impact on a recent neutrinoless double-$\beta$ decay nuclear matrix element calculation which implies that the decay to the first excited state in ${}^{150}\mathrm{Sm}$ is favored over that to the ground state.

Background: The two-flavor color superconducting (2SC) phase of quark matter is a possible constituent of the core of neutron stars. To assess its impact on the observable behavior of the star one must analyze transport properties, which in 2SC matter are controlled by the scattering of gapless fermionic modes by each other and possibly also by color-magnetic flux tubes.

Purpose: We determine the electrical and thermal conductivities and the shear viscosity of 2SC matter.

Methods: We use a variational formulation of transport theory, treating the strong and electromagnetic interactions via a weak coupling expansion.

Results: We provide the leading order scaling of the transport coefficients with temperature and chemical potential as well as accurate fits to our numerical results. We also find that the scattering of fermions by color-magnetic flux tubes is insignificant for thermal conductivity, but may contribute to the electrical conductivity and shear viscosity in the limit of very low temperature or high magnetic field. We also estimate the transport coefficients in unpaired quark matter.

Conclusions: Our calculation has set the stage for exploration of possible signatures of the presence of 2SC quark matter in neutron stars.

Background: Neutrinoless double-$\beta \left(0\nu \beta \beta \right)$ decay is related to many fundamental concepts in nuclear and particle physics beyond the standard model. Currently there are many experiments searching for this weak process. An accurate knowledge of the nuclear matrix element for the $0\nu \beta \beta$ decay is essential for determining the effective neutrino mass once this process is eventually measured.

Purpose: We report the first full relativistic description of the $0\nu \beta \beta$ decay matrix element based on a state-of-the-art nuclear structure model.

Methods: We adopt the full relativistic transition operators which are derived with the charge-changing nucleonic currents composed of the vector coupling, axial-vector coupling, pseudoscalar coupling, and weak-magnetism coupling terms. The wave functions for the initial and final nuclei are determined by the multireference covariant density functional theory (MR-CDFT) based on the point-coupling functional PC-PK1. Correlations beyond the mean field are introduced by configuration mixing of both angular momentum and particle number projected quadrupole deformed mean-field wave functions.

Results: The low-energy spectra and electric quadrupole transitions in ${}^{150}\mathrm{Nd}$ and its daughter nucleus ${}^{150}\mathrm{Sm}$ are well reproduced by the MR-CDFT calculations. The $0\nu \beta \beta$ decay matrix elements for both the $0_1^{+}\to 0_1^{+}$ and $0_1^{+}\to 0_2^{+}$ decays of ${}^{150}\mathrm{Nd}$ are evaluated. The effects of particle number projection, static and dynamic deformations, and the full relativistic structure of the transition operators on the matrix elements are studied in detail.

Conclusions: The resulting $0\nu \beta \beta$ decay matrix element for the $0_1^{+}\to 0_1^{+}$ transition is $5.60$, which gives the most optimistic prediction for the next generation of experiments searching for the $0\nu \beta \beta$ decay in ${}^{150}\mathrm{Nd}$.

We study the nuclear parton distribution functions on the basis of our recently developed semimicroscopic model, which takes into account a number of nuclear effects including nuclear shadowing, Fermi motion and nuclear binding, nuclear meson-exchange currents, and off-shell corrections to bound nucleon distributions. We discuss in detail the dependencies of nuclear effects on the type of parton distribution (nuclear sea vs valence), as well as on the parton flavor (isospin). We apply the resulting nuclear parton distributions to calculate ratios of cross sections for proton-induced Drell-Yan production off different nuclear targets. We obtain a good agreement on the magnitude, target and projectile $x$, and the dimuon mass dependence of proton-nucleus Drell-Yan process data from the E772 and E866 experiments at Fermilab. We also provide nuclear corrections for the Drell-Yan data from the E605 experiment.

Background: Microscopic calculations of four-body collisions become very challenging in the energy regime above the threshold for four free particles. The neutron-${}^3\mathrm{He}$ scattering is an example of such processes with elastic, rearrangement, and breakup channels.

Purpose: We aim to calculate observables for elastic and inelastic neutron-${}^3\mathrm{He}$ reactions up to 30 MeV neutron energy using realistic nuclear force models.

Methods: We solve the Alt, Grassberger, and Sandhas (AGS) equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations.

Results: We obtain fully converged results for the differential cross section and neutron analyzing power in the neutron-${}^3\mathrm{He}$ elastic scattering as well as the total cross sections for inelastic reactions. Several realistic potentials are used, including one with an explicit $\Delta$ isobar excitation.

Conclusions: There is reasonable agreement between the theoretical predictions and experimental data for the neutron-${}^3\mathrm{He}$ scattering in the considered energy regime. The most remarkable disagreements are seen around the minimum of the differential cross section and the extrema of the neutron analyzing power. The breakup cross section increases with energy exceeding rearrangement channels above 23 MeV.

Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars.

Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables.

Methods: We implement the model optimization by minimizing a suitably constructed ${\chi }^2$ objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients.

Results: A new model, “FSUGold2,” is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in ${}^{208}\mathrm{Pb}$ and a moderate value of the nuclear incompressibility.

Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.

Since the pioneering experiment E89-009 studying hypernuclear spectroscopy using the $(e,e^{\prime }{K}^{+})$ reaction was completed, two additional experiments, E01-011 and E05-115, were performed at Jefferson Lab. These later experiments used a modified experimental design, the “tilt method,” to dramatically suppress the large electromagnetic background, and allowed for a substantial increase in luminosity. Additionally, a new kaon spectrometer, HKS (E01-011), a new electron spectrometer, HES, and a new splitting magnet (E05-115) were added to produce new data sets of precision, high-resolution hypernuclear spectroscopy. All three experiments obtained a spectrum for ${}_{\Lambda }^{12}\mathrm{B}$, which is the most characteristic $p$-shell hypernucleus and is commonly used for calibration. Independent analyses of these different experiments demonstrate excellent consistency and provide the clearest level structure to date of this hypernucleus as produced by the $(e,e^{\prime }{K}^{+})$ reaction. This paper presents details of these experiments, and the extraction and analysis of the observed ${}_{\Lambda }^{12}\mathrm{B}$ spectrum.

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general $\beta$-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear $\beta$ decay are on the level of several percent.

Purpose: Extracting new information on tensor coupling constants by measuring the $\beta$-asymmetry parameter in the pure Gamow-Teller decay of ${}^{67}\mathrm{Cu}$, thereby testing the V-A structure of the weak interaction.

Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a ${}^3\mathrm{He}{\text{−}}^4\mathrm{He}$ dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic $\beta$ radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the $\beta$ asymmetry of ${}^{68}\mathrm{Cu}$ was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations.

Results: The experimental value, $\tilde{A}=0.587\left(14\right)$, is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are $-0.045<(C_T+C_T^{\prime })/C_A<0.159$ (90% C.L.).

Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear $\beta$ decay and contribute to further constraining tensor coupling constants.

Suppressions of light- and heavy-flavor observables are considered to be excellent probes of QCD matter created in ultrarelativistic heavy ion collisions. Suppression predictions of quark and gluon jets appear to suggest a clear hierarchy according to which neutral pions should be more suppressed than $D$ mesons, which in turn should be more suppressed than single electrons. However, joint comparison of neutral pion (light probe) and nonphotonic single-electron (heavy probe) suppression data at the BNL Relativistic Heavy Ion Collider (RHIC) unexpectedly showed similar jet suppression for these two probes, which presents the well-known heavy-flavor puzzle at RHIC. We here analyze which effects are responsible for this unexpected result by using the dynamical energy-loss formalism. We find that the main effect is a surprising reversal in the suppression hierarchy between neutral pions and $D$ mesons, which is due to the deformation of the suppression patterns of light partons by fragmentation functions. Furthermore, we find that, due to the decay functions, the single-electron suppression approaches the $D$-meson suppression. Consequently, we propose that these two effects, taken together, provide a clear intuitive explanation of this longstanding puzzle.

The half-life of ${}^{37}\mathrm{K}$ has been measured to be $1.23651\left(94\right)\mathrm{s}$, a value nearly an order of magnitude more precise than the best previously reported. The ${\beta }^{+}$ decay of ${}^{37}\mathrm{K}$ occurs mainly via a superallowed branch to the ground state of its $T=1/2$ mirror, ${}^{37}\mathrm{Ar}$. This transition has been used recently, together with similar transitions from four other nuclei, as a method for determining $V_{ud}$, but the precision of its $ft$ value was limited by the relatively large half-life uncertainty. Our result corrects that situation. Another motivation for improving the $ft$ value was to determine the standard-model prediction for the $\beta$-decay correlation parameters, which will be compared to those currently being measured by the TRINAT Collaboration at TRIUMF. The new $ft$ value, $4605\left(8\right)\mathrm{s}$, is now limited in precision by the $97.99\left(14\right)\%$ ground-state branching ratio.

The production of the prompt charmed mesons $D^0$, $D^{+}$, and $D^{*+}$ relative to the reaction plane was measured in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision of $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}$ with the ALICE detector at the CERN Large Hadron Collider. $D$ mesons were reconstructed via their hadronic decays at central rapidity in the transverse-momentum ($p_{\mathrm{T}}$) interval 2–16 $\mathrm{GeV}/c$. The azimuthal anisotropy is quantified in terms of the second coefficient $v_2$ in a Fourier expansion of the $D$-meson azimuthal distribution and in terms of the nuclear modification factor $R_{\mathrm{AA}}$, measured in the direction of the reaction plane and orthogonal to it. The $v_2$ coefficient was measured with three different methods and in three centrality classes in the interval 0%–50%. A positive $v_2$ is observed in midcentral collisions (30%–50% centrality class), with a mean value of $0.{204}_{-0.036}^{+0.099}$ (tot. unc.) in the interval $2<p_{\mathrm{T}}<6\mathrm{GeV}/c$, which decreases towards more central collisions (10%–30% and 0%–10% classes). The positive $v_2$ is also reflected in the nuclear modification factor, which shows a stronger suppression in the direction orthogonal to the reaction plane for midcentral collisions. The measurements are compared to theoretical calculations of charm-quark transport and energy loss in high-density strongly interacting matter at high temperature. The models that include substantial elastic interactions with an expanding medium provide a good description of the observed anisotropy. However, they are challenged to simultaneously describe the strong suppression of high-$p_{\mathrm{T}}$ yield of $D$ mesons in central collisions and their azimuthal anisotropy in noncentral collisions.

Background: The hexadecapole deformation ${\beta }_4$ is usually difficult to determine experimentally, especially its sign. The rapidly accumulated knowledge of ${\beta }_2$ inspires the desire of ${\beta }_4$ for radioactive nuclei, but the current low-quality beam is a severe experimental challenge. Therefore, a simple but sensitive method to extract ${\beta }_4$ in such a condition is urgently called for.

Purpose: To study the feasibility of extracting ${\beta }_4$ from the lower-energy backward quasi-elastic (QEL) scattering.

Methods: The QEL scattering at sub-barrier energy region is sensitive to the coupled-channels (CC) effect and consequently may be used to extract ${\beta }_4$. The QEL scattering excitation functions for ${}^{16}\mathrm{O}+{}^{152}\mathrm{Sm}$,${}^{170}\mathrm{Er}$, and ${}^{174}\mathrm{Yb}$ were measured at a backward angle with small energy intervals at energies near the Coulomb barrier. Experimental fusion barrier distributions were also derived. The lower-energy data were analyzed to extract ${\beta }_4$ with the help of the CC calculations.

Results: The obtained ${\beta }_4$ agrees with the available results reasonably well.

Conclusions: We have demonstrated that the QEL scattering at sub-barrier energies provides a feasible and sensitive method to extract the value of ${\beta }_4$, which is essentially meaningful for the radioactive nucleus because of its low beam intensity.

The Brussels-Montreal Skyrme functionals have been successful in describing properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab initio methods.

Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory.

Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions.

Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed.

Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the $B$-spline technique and a three-dimensional solver hfodd that is based on the harmonic-oscillator basis expansion. Several examples are considered, including the self-consistent HFB problem for spin-polarized trapped cold fermions and the Skyrme-Hartree-Fock ($+\text{BCS}$) problem for triaxial deformed nuclei.

Conclusions: The new madness-hfb framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are weakly bound nuclear configurations close to particle drip lines, strongly elongated and dinuclear configurations such as those present in fission and heavy-ion fusion, and exotic pasta phases that appear in neutron star crust.

The shape transition in the neutron-rich Os isotopes is studied by investigating the neutron-rich ${}^{196}\text{Os}$ nucleus through in-beam $\gamma$-ray spectroscopy using a two-proton transfer reaction from a ${}^{198}\text{Pt}$ target to a ${}^{82}\text{Se}$ beam. The beam-like recoils were detected and identified with the large-acceptance magnetic spectrometer PRISMA, and the coincident $\gamma$ rays were measured with the advanced gamma tracking array (AGATA) demonstrator. The de-excitation of the low-lying levels of the yrast-band of ${}^{196}\text{Os}$ were identified for the first time. The results are compared with state-of-the-art beyond-mean-field calculations, performed for the even-even ${}^{188-198}\mathrm{Os}$ isotopes. The new results suggest a smooth transition in the Os isotopes from a more axial rotational behavior towards predominately vibrational nuclei through triaxial configurations. An almost perfect $\gamma$-unstable/triaxial rotor yrast band is predicted for ${}^{196}\text{Os}$ which is in agreement with the experimentally measured excited states.

Background: The numerical solution of few-body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. This strongly limits the possibility of accurate treatments for many important few-particle problems in different branches of quantum physics.

Purpose: To develop a new general highly effective approach for the practical solution of few-body scattering equations that can be implemented on a graphics processing unit.

Methods: The general approach is realized in three steps: (i) the reformulation of the scattering equations using a convenient analytical form for the channel resolvent operator, (ii) a complete few-body continuum discretization and projection of all operators and wave functions onto an $L_2$ basis constructed from stationary wave packets, and (iii) the ultrafast solution of the resulting matrix equations using a graphics processor.

Results: The whole approach is illustrated by a calculation of the neutron-deuteron elastic scattering cross section below and above the three-body breakup threshold with a realistic $NN$ potential that is performed on a standard PC using a graphics processor with an extremely short runtime.

Conclusions: The general technique proposed in this paper opens a new way for a fast practical solution of quantum few-body scattering problems in both nonrelativistic and relativistic formulations in hadronic, nuclear, and atomic physics.

The reaction $\pi N\to \pi \pi N$ is studied at tree level up to next-to-leading order in the framework of manifestly covariant baryon chiral perturbation theory with explicit $\Delta \left(1232\right)$ degrees of freedom. Using total cross-section data to determine the relevant low-energy constants, predictions are made for various differential as well as total cross sections at higher energies. A detailed comparison of results based on the heavy-baryon and relativistic formulations of chiral perturbation theory with and without explicit $\Delta$ degrees of freedom is given.

Background: A model-independent formulation of weakly interacting massive particle (WIMP)-nucleon scattering was recently developed in Galilean-invariant effective field theory.

Purpose: Here we complete the embedding of this effective interaction in the nucleus, constructing the most general elastic nuclear cross section as a factorized product of WIMP and nuclear response functions. This form explicitly defines what can and cannot be learned about the low-energy constants of the effective theory—and consequently about candidate ultraviolet theories of dark matter—from elastic scattering experiments.

Results: We identify those interactions that cannot be reliably treated in a spin-independent/spin-dependent (SI/SD) formulation: For derivative- or velocity-dependent couplings, the SI/SD formulation generally mischaracterizes the relevant nuclear operator and its multipolarity (e.g., scalar or vector) and greatly underestimates experimental sensitivities. This can lead to apparent conflicts between experiments when, in fact, none may exist. The new nuclear responses appearing in the factorized cross section are related to familiar electroweak nuclear operators such as angular momentum $\vec{l}\left(i\right)$ and the spin-orbit coupling $\vec{\sigma }\left(i\right)·\vec{l}\left(i\right)$.

Conclusions: To unambiguously interpret experiments and to extract all of the available information on the particle physics of dark matter, experimentalists will need to (1) do a sufficient number of experiments with nuclear targets having the requisite sensitivities to the various operators and (2) analyze the results in a formalism that does not arbitrarily limit the candidate operators. In an appendix we describe a code that is available to help interested readers implement such an analysis.

Background: Weak interactions between quarks induce a parity-violating (PV) component in the nucleon-nucleon potential, whose effects are currently being studied in a number of experiments involving few-nucleon systems. In the present work, we reconsider the derivation of this PV component within a chiral effective field theory ($\chi$EFT) framework.

Purpose: The objectives of the present work are twofold. The first is to perform a detailed analysis of the PV nucleon-nucleon potential up to next-to-next-to-leading (N2LO) order in the chiral expansion, in particular, by determining the number of independent low-energy constants (LECs) at N2LO. The second objective is to investigate PV effects in a number of few-nucleon observables, including the $\vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $\vec{n}$-$p$ and $\vec{n}$-$d$ scattering, and the longitudinal asymmetry in the ${}^3$He${(\vec{n},p)}^3$H charge-exchange reaction.

Methods: The $\chi$EFT PV potential includes one-pion-exchange, two-pion-exchange, and contact terms as well as $1/M$ ($M$ being the nucleon mass) nonstatic corrections. Dimensional regularization is used to renormalize pion loops. The wave functions for the $A=2$–4 nuclei are obtained by using strong two- and three-body potentials also derived, for consistency, from $\chi$EFT. In the case of the $A=3$–4 systems, the wave functions are computed by expanding on a hyperspherical harmonics functions basis.

Results: We find that the PV potential at N2LO depends on six LECs: the pion-nucleon PV coupling constant $h_{\pi }^1$ and five parameters multiplying contact interactions. An estimate for the range of values of the various LECs is provided by using available experimental data, and these values are used to obtain predictions for the other PV observables.

Conclusions: The $\chi$EFT approach provides a very satisfactory framework to analyze PV effects in few-nucleon systems.