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Register a new userFast & rigorous constraints on chiral three-nucleon forces from few-body observables
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We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory ($chi$EFT) that are provided by bound-state observables in the $A=3$ and $A=4$ sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the $chi$EFT expansion at next-to-next-to-leading order. A consistent solution for the ${}^3$H binding energy, the ${}^4$He binding energy and radius, and the ${}^3$H $beta$-decay rate can only be obtained if $chi$EFT truncation errors are included in the analysis. All of these except the $beta$-decay rate give essentially degenerate constraints on the 3NF low-energy constants, so it is crucial for estimating these parameters. We use eigenvector continuation for fast and accurate emulation of No-Core Shell Model calculations of the considered few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the hyperparameters that quantify the truncation error. We find a $chi$EFT expansion parameter of $Q=0.33 pm 0.06$ for these observables.
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The operator structures that can contribute to three-nucleon forces are classified in the 1/Nc expansion. At leading order in 1/Nc a spin-flavor independent term is present, as are the spin-flavor structures associated with the Fujita-Miyazawa three-nucleon force. Modern phenomenological three-nucleon forces are thus consistent with this O(Nc) leading force, corrections to which are suppressed by a power series in 1/Nc^2. A complete basis of operators for the three-nucleon force, including all independent momentum structures, is given explicitly up to next-to-leading order in the 1/Nc expansion.
We present a complete calculation of nucleon-deuteron scattering as well as ground and low-lying excited states of light nuclei in the mass range A=3-16 up through next-to-next-to-leading order in chiral effective field theory using semilocal coordinate-space regularized two- and three-nucleon forces. It is shown that both of the low-energy constants entering the three-nucleon force at this order can be reliably determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. The inclusion of the three-nucleon force is found to improve the agreement with the data for most of the considered observables.
Using realistic wave functions, the proton-neutron and proton-proton momentum distributions in $^3He$ and $^4He$ are calculated as a function of the relative, $k_{rel}$, and center of mass, $K_{CM}$, momenta, and the angle between them. For large values of ${k}_{rel}gtrsim 2,,fm^{-1}$ and small values of ${K}_{CM} lesssim 1.0,,fm^{-1}$, both distributions are angle independent and decrease with increasing $K_{CM}$, with the $pn$ distribution factorizing into the deuteron momentum distribution times a rapidly decreasing function of $K_{CM}$, in agreement with the two-nucleon (2N) short range correlation (SRC) picture. When $K_{CM}$ and $k_{rel}$ are both large, the distributions exhibit a strong angle dependence, which is evidence of three-nucleon (3N) SRC. The predicted center-of-mass and angular dependence of 2N and 3N SRC should be observable in two-nucleon knock-out processes $A(e,epN)X$.
We apply improved nucleon-nucleon potentials up to fifth order in chiral effective field theory, along with a new analysis of the theoretical truncation errors, to study nucleon-deuteron (Nd) scattering and selected low-energy observables in 3H, 4He, and 6Li. Calculations beyond second order differ from experiment well outside the range of quantified uncertainties, providing truly unambiguous evidence for missing three-nucleon forces within the employed framework. The sizes of the required three-nucleon force contributions agree well with expectations based on Weinbergs power counting. We identify the energy range in elastic Nd scattering best suited to study three-nucleon force effects and estimate the achievable accuracy of theoretical predictions for various observables.
We investigate the roles of chiral three-nucleon force (3NF) in nucleon-nucleus elastic scattering, using the standard framework based on the Brueckner-Hartree-Fock method for nuclear matter and the $g$-matrix folding model for the nucleon-nucleus scattering. In nuclear matter, chiral 3NF at NNLO level (mainly the 2$pi$-exchange diagram) makes the single particle potential less attractive for the singlet-even channel and more absorptive for the triplet channels. The single-particle potential calculated from chiral two-nucleon force (2NF) at N$^{3}$LO level is found to be close to that from Bonn-B 2NF. The Melbourne $g$-matrix interaction is a practical effective interaction constructed by localizing the $g$-matrices calculated from Bonn-B 2NF. We then introduce the chiral-3NF effects to the local Melbourne $g$-matrix interaction. For nucleon-nucleus elastic scattering on various targets at 65 MeV, chiral 3NF makes the folding potential less attractive and more absorptive. The novel property for the imaginary part is originated in the enhancement of tensor correlations due to chiral 3NF. The two effects are small for differential cross sections and vector analyzing powers at the forward and middle angles where the experimental data are available. If backward measurements are done, the data will reveal the effects of chiral 3NF.
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