arXiv subjects

J. Golak

Publications and source records attributed to J. Golak.

At least 19 recordsLinked to original sources

arXiv2026

Challenging chiral EFT with tritium beta decay

We present a detailed investigation of tritium beta decay up to third order (N2LO) in chiral effective field theory (EFT) using the LENPIC interactions. Unlike existing studies, we use nucleon-deuteron scattering observables to fix the low-energy constant D that governs the strength of the short-range contributions to the exchange axial current operator and three-nucleon forces. Surprisingly, the resulting parameter-free predictions for the tritium Gamow-Teller reduced matrix element are found to considerably overestimate its empirical value. This result remains robust against reasonable variations of the pion-nucleon coupling constants and regularization scheme. A closer look at the size of the parameter-free long-range two-body contributions to the Gamow-Teller matrix element reveals the fine-tuned nature this observable in chiral EFT, which may partially explain the observed deviation. Our results indicate a considerable N2LO truncation uncertainty for tritium beta decay and point towards large higher-order two-body corrections. More definite conclusions await a complete fourth-order analysis of nucleon-deuteron scattering observables and tritium half-life.

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arXiv2026

Field-theoretical description of the deuteron breakup in the clothed particle representation

We present a field-theoretical description of the deuteron electrodisintegration reaction d(e,e'p)n induced by unpolarized and polarized electrons. The approach combines the Lehmann-Symanzik-Zimmermann in(out) formalism with the clothed particle representation in the instant form of relativistic dynamics, providing a fully relativistic and gauge-independent framework based on the Fock-Weyl criterion. Within the method of unitary clothing transformations, one and the same transformation that generates the relativistic nucleon-nucleon interaction (the Kharkiv potential) also induces a fresh family of electromagnetic current operators. As a result, one-body and two-body (meson-exchange) currents emerge on a common footing. We compute differential cross sections and polarization observables with the inclusion of final-state interaction effects and meson-exchange current contributions, and compare the results with Saclay and Jefferson Lab data as well as with earlier theoretical predictions. The role of relativistic ingredients (one- and two-body currents, Fermi-motion effects, etc.) and the interplay between them are analyzed in several kinematic regimes of the experiments at Saclay and Jefferson Lab.

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arXiv2026

Comparison of Relativistic and Non-relativistic Faddeev calculations for Proton-Deuteron Elastic Scattering

This investigation compares non-relativistic and relativistic nucleon-nucleon potentials in the context of proton-deuteron scattering. Conventional NN potentials (e.g., CDBonn, AV18, Nijmegen) rely on the nonrelativistic Schroedinger equation, whereas the Kharkiv potential is intrinsically relativistic. We employ the Coester-Pieper-Serduke (CPS) and Kamada-Gloeckle (KG) conversion methods to construct a phenomenological-relativistic potential (PRP) from a realistic NN potential, preserving the deuteron binding energy and phase shifts. Focusing on relativistic effects and not including Coulomb forces to avoid complexity, the solutions are compared by solving relativistic and nonrelativistic Faddeev equations. Calculations of the differential cross section using the relativistic Faddeev equation show that relativistic effects - particularly the deviation at the backward angle - become pronounced at 135 MeV. The differences in the forward angle were attributed to the characteristics of the Kharkiv potential itself. The reverse transformation of the Kharkiv potential into a pseudo-nonrelativistic potential (PNRP) confirms that the backward-angle relativistic effect increases with energy in the range from 100 MeV to 400 MeV. Comparisons of the polarization observables indicate that relativistic effects, as well as the discrepancy between the CPS and KG transformations, become significant above 300 MeV. However, for polarization observations below 300 MeV, the nonrelativistic results from PNRP do not deviate significantly from relativistic calculations.

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arXiv2025

Three-Nucleon Dynamics in the dp breakup collisions at 190 MeV/nucleon using the WASA detector at COSY-Jülich

The differential cross section for the $^{1}$H$(d,pp)n$ breakup reaction at deuteron beam energy of 380 MeV has been determined with high precision for 189 angular configurations of outgoing protons in the region of forward laboratory angles. The cross section data were compared to theoretical predictions based on the state-of-the-art nucleon-nucleon potentials, combined with a three-nucleon force, the Coulomb interaction or carried out in a relativistic approach. In the region of the lowest differential cross section, the discrepancy between the data and the theoretical predictions is observed, also in the case of relativistic calculations.

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arXiv2025

Searching for entanglement in final polarization states of the neutron-proton scattering

We investigate polarization states of the outgoing neutron-proton ($np$) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g. not only induced polarizations and correlations resulting from unpolarized $np$ scattering, but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons, and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states.The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at $E_{lab}=100$~MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.

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arXiv2025

Observability of modified threshold behavior near unitarity

A number of recent references have pointed out that an N-particle system having short-range interactions at S-wave and/or P-wave unitarity can exhibit modified threshold behavior for various reactive processes. But the question of how close to unitarity one must get in order to observe such modifications has not been addressed. The present study quantities this question by treating cases involving 3- or 4-neutrons, at the physical value of the neutron-neutron singlet scattering length a and at artificially altered values. One major conclusion is that the neutron-neutron scattering length is not yet sufficiently large for the 3n or 4n systems to demonstrate the unitarity threshold exponent.

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arXiv2025

Three-nucleon force effects in polarization transfers from the doubly spin-polarized initial neutron-deuteron state to the outgoing neutron in neutron-deuteron scattering

We discuss new spin observables presently accessible to measurement in the proton-deuteron (pd) system, namely polarization transfer coefficients from doubly spin-polarized initial state to the outgoing nucleon in the elastic nucleon-deuteron (Nd) scattering and in the nucleon-induced deuteron breakup reactions. The sensitivity of these observables to three-nucleon force (3NF) effects is investigated and compared to sensitivities of the constituent standard single polarization transfer coefficients in the neutron-deuteron (nd) system. $K_{y,y}^{y'}$ in elastic nd scattering, for which large 3NF effects, up to 40\%, have been found at higher energies, seems the most promising observable to measure.

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arXiv2025

Estimating theoretical uncertainties of the two-nucleon observables by using backpropagation

We present a novel approach to calculating theoretical uncertainties in few-nucleon calculations, making use of automatic differentiation via backpropagation, which is particularly efficient when there are many input variables but only a few outputs. The methods described in this paper constitute tools that can be used to investigate the properties of scalar functions used to define nuclear potentials and quantify their contribution to the uncertainty of few nucleon calculations. We demonstrate these methods in deuteron bound state and nucleon - nucleon scattering calculations. Backpropagation, implemented in the Python pytorch library, is used to calculate the gradients with respect to model parameters and propagate errors from these parameters to the deuteron binding energy and selected phase-shift parameters. The uncertainty values obtained using this approach are validated by directly sampling from the potential parameters. We find very good agreement between two ways of estimating that uncertainty.

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arXiv2024

Quasielastic $\overrightarrow{^{3}\mathrm{He}}(\overrightarrow{e},{e'})$ Asymmetry in the Threshold Region

A measurement of the double-spin asymmetry from electron-$^{3}$He scattering in the threshold region of two- and three-body breakup of $^{3}$He was performed at Jefferson Lab, for Q$^{2}$ values of 0.1 and 0.2 (GeV/$c$)$^{2}$. The results of this measurement serve as a stringent test of our understanding of few-body systems. When compared with calculations from plane wave impulse approximation and Faddeev theory, we found that the Faddeev calculations, which use modern nuclear potentials and prescriptions for meson-exchange currents, demonstrate an overall good agreement with data.

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arXiv2024

Experimental studies of the three nucleon system dynamics in the proton induced deuteron breakup at 108 MeV

The differential cross sections for the $^2$H(p,pp)n reaction have been measured for 84 angular configurations of the outgoing protons in the range of polar angles from 13 to 33 degrees with a proton beam of 108 MeV. Data have been collected in the Cyclotron Center Bronowice (CCB) at the Institute of Nuclear Physics PAS in Cracow, using the BINA detector setup. Analysis leading to determination of the breakup cross section values is described. Absolute normalization is obtained by normalization to the simultaneously measured $^2$H(p,d)p scattering events.Experimental results are compared to the state-of-the-art theoretical calculations. Global analysis shows significant influence of the Coulomb interaction and small effects of three nucleon force in the studied phase space region.

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arXiv2024

"To renormalize or not to renormalize ?'' in the proton-deuteron scattering calculations

We discuss two approaches which, by applying the screening method, permit one to include the long range proton-proton (pp) Coulomb force in proton-deuteron (pd) momentum-space scattering calculations. In the first one, based on Alt-Grassberger-Sandhas (AGS) equation, presented in Phys. Rev. C{\bf{71}}, 054005 (2005) and {\bf{73}}, 057001 (2006), one needs to renormalize elastic scattering amplitude before calculating observables. In the second treatment, proposed by us in Eur. Phys. Journal A {\bf{41}}, 369 (2009), {\bf{41}}, 385 (2009), and arXiv:2310.03433 [nucl.th], this renormalization is avoided. For the proton induced deuteron breakup reaction both approaches require renormalization of the corresponding transition amplitudes. We derive the basic equations underlying both methods under the assumption that all contributing partial wave states are included and explain why in our approach renormalization of the elastic scattering amplitude is superfluous. We show that in order to take into account in the screening limit all partial waves it is required that four additional terms, based on the 3-dimensional and partial-wave projected pp Coulomb t-matrices, identical for both approaches, must appear in transition amplitudes. We investigate importance of these terms for elastic pd scattering below the breakup threshold.

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arXiv2023

On inclusion of the long-range proton-proton Coulomb force in the three-nucleon scattering Faddeev calculations

We propose a simplified approach to incorporate the long-range proton-proton (pp) Coulomb force in the three-nucleon (3N) scattering calculations, based on exact formulation presented in Eur. Phys. Journal A {\bf{41}}, 369 (2009) and {\bf{41}}, 385 (2009). It permits us to get elastic proton-deuteron (pd) scattering and breakup observables relatively simply by performing standard Faddeev calculations as known for the neutron-deuteron (nd) system. The basic ingredient in that approach is a 3-dimensional screened pp Coulomb t-matrix obtained by numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. Based on this t-matrix pure Coulomb transition terms contributing to elastic scattering and breakup are calculated without any need for partial wave decomposition. For elastic scattering such a term removes the Rutherford amplitude for point deuteron proton-deuteron (pd) scattering. For breakup it has never been applied in spite of the fact that its contributions could become important in some regions of the breakup phase space. We demonstrate numerically that the pd elastic observables can be determined directly from the resulting 3N amplitudes without any renormalization, simply by increasing the screening radius in order to reach the existing screening limit. However,for pd breakup the renormalization of the contributing on-shell amplitudes is required. We apply our approach in a wide energy range of the incoming proton for pd elastic scattering as well as for pd breakup reaction.

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arXiv2022

Electron and neutrino scattering off the deuteron in a relativistic framework

We build a relativistic model to perform calculations of exclusive, semi-exclusive and inclusive unpolarized cross sections and various polarization observables in electron and neutrino scattering experiments with deuteron targets. The strong interaction dynamics is defined by an explicit dynamical unitary representation of the Poincaré group, where representations of space translations and rotations in the interacting and non-interacting representations are the same. The Argonne V18 potential is used to construct a relativistic nucleon-nucleon interaction reproducing the experimental deuteron binding energy and nucleon-nucleon scattering observables. Our formalism does not include the pion production channel and neglects two-body contributions in the electromagnetic as well as in the weak nuclear current operator. We show that it is applicable to processes at kinematics, where the internal two-nucleon energy remains below the pion production threshold but the magnitude of the three-momentum transfer extends at least to several GeV.

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arXiv2022

Pion absorption from the lowest atomic orbital in 2H, 3H and 3He

The pi- + 2H -> n + n, pi- + 3H -> n + n + n, pi- + 3He -> n + d and pi- + 3He -> p + n + n capture reactions from the lowest atomic orbitals are studied under full inclusion of final state interactions. Our results are obtained with the single-nucleon and two-nucleon transition operators derived at leading order in chiral effective field theory. The initial and final three-nucleon states are calculated with the chiral nucleon-nucleon SMS potential up to N4LO+ augmented by the consistently regularized chiral N2LO three-nucleon potential. We found that absorption rates depend strongly on the nuclear pion absorption operator used, and its two-body parts change the rates by a few orders of magnitude. The final state interactions between nucleons generated by the two-nucleon forces are also important, while the three-nucleon interaction plays a visible role only in the pi- + 3He -> n + d reaction. Our absorption rate for the pi- + 2H -> n + n process is in good agreement with the experimental data from the hadronic ground-state broadening in pionic deuterium. The capture rates on 3He are also generally consistent with the spectroscopic data within error bars, though our central values are found to be systematically below the data. We show that for the three-body breakup processes the dominant contributions to the absorption rates arise from the quasi-free scattering and final-state interaction kinematical configurations.

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arXiv2022

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 (N$^2$LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A \sim 10$ found in our earlier study utilizing the N$^2$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 $^{14}$O to $^{26}$O as well as $^{40}$Ca and $^{48}$Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the $A \leq 3$ data, once the fourth-order (N$^3$LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by $\sim 10\%$ for the oxygen isotopes and by almost $20\%$ for $^{40}$Ca and $^{48}$Ca.

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arXiv2022

Correlations among neutron-proton and neutron-deuteron elastic scattering observables

We employ two models of the nucleon-nucleon force: the OPE-Gaussian as well as the chiral N4LO and N4LO+ interactions with semilocal regularization in momentum space to study correlations among two-nucleon and three-nucleon elastic scattering observables. These models contain a number of free parameters whose values and covariance matrices are evaluated from a fit to the two-nucleon data. Such detailed knowledge of parameters allows us to create, using various sets of statistically generated parameters, numerous versions of these potentials and next apply them to two- and three-nucleon scattering to make predictions of various observables at the reaction energies up to 200 MeV. This permits a systematic analysis of correlations among two-nucleon and three-nucleon observables, basing on a relatively big sample of predictions. We found that most observables in neutron-proton and neutron-deuteron systems are uncorrelated, but there are exceptions revealing strong correlations, which depend on the reaction energy and scattering angle. This information may be useful for precise fixing free parameters of two-nucleon and three-nucleon forces and for understanding dependencies and correlations between potential parameters and observables.

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arXiv2022

Significance of chiral three-nucleon force contact terms for understanding of elastic nucleon-deuteron scattering

We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected, the results calculated with the contact terms multiplied by the fitted strength parameters yield an improved description of the elastic Nd scattering observables in a wide range of incoming nucleon energies below the pion production threshold.

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arXiv2021

Efficient emulator for solving three-nucleon continuum Faddeev equations with chiral three-nucleon force comprising any number of contact terms

We demonstrate a computational scheme which drastically decreases the required time to get theoretical predictions based on chiral two- and three-nucleon forces for observables in three-nucleon continuum. For a three-nucleon force containing N short-range terms all workload is reduced to solving N+1 Faddeev-type integral equations. That done, computation of observables for any combination of strengths of the contact terms is done in a flash. We demonstrate on example of the elastic nucleon-deuteron scattering observables the high precision of the proposed emulator and its capability to reproduce exact results.

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