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.
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,…
We present a perturbative approach to solving the three-nucleon continuum Faddeev equation. This approach is particularly well suited to dealing with variable strengths of contact terms in a chiral three-nucleon force. We use examples of observables in the elastic nucleon-deuteron scattering as well as in the deuteron breakup reaction to demonstrate high precision of the proposed procedure and its capability to reproduce exact results. A significant reduction of computer time achieved by the perturbative approach in comparison to exact treatment makes this approach valuable for fine-tuning of …
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 reprodu…
We obtain a minimal form of the two-derivative three-nucleon contact Lagrangian, by imposing all constraints deriving from discrete symmetries, Fierz identities and Poincare' covariance. The resulting interaction, depending on 13 unknown low-energy constants, leads to a three-nucleon potential which we give in a local form in configuration space. We also consider the leading (no-derivative) four-nucleon interaction and show that there exists only one independent operator.
General expressions for all parity-conserving polarization observables of elastic electron-nucleon scattering in the one-photon exchange approximation are derived for a general frame of reference, i.e.\ not assumming scattering off a nucleon at rest and not specializing to a specific system of coordinates. Essentially, the given expressions are also valid for the inverse process, i.e.\ nucleon scattering off electrons.
The high-momentum antisymmetrized molecular dynamics (HMAMD) is a new promising framework with significant analytical simplicity and efficiency inherited from its antisymmetrized molecular dynamics in describing the high momentum correlations in various nuclear states. In the aim of further improving the numerical efficiency for the description of nucleon-nucleon correlation, we introduce a new formulation by including a new Gaussian weighted basis of high momentum pairs in the HMAMD wave function, with which very rapid convergence is obtained in numerical calculation. It is surprising that th…
Partial-wave decomposition of isospin-projected subleading three-nucleon contact interactions
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT ∗ ) and Fondazione Bruno Kessler（欧洲核物理及相关领域理论研究中心和布鲁诺·凯塞尔基金会）；Department of Mathematics and Physics “E. De Giorgi”, University of Salento（萨莱托大学“E. 德乔治”数学与物理系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Lecce（意大利国家核物理研究所莱切分部）
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 scatter…
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.
In this work the elastic scattering of two nucleons is calculated in chiral effective field theory at next-to-leading order taking into account the coupled N$Δ$-, $Δ$N- and $ΔΔ$-channels. To solve the coupled channel scattering equation one needs as input the potentials for all combinations of these initial and final states. Up to next-to leading order these (transition) potentials arise from one-pion exchange, two-pion exchange and contact interactions. For the two-pion exchange we give analytic expressions for the spectral functions derived from all contributing one-loop diagrams. The forms …
Theoretical uncertainties of various types are discussed for the nucleon-deuteron elastic scattering observables at the incoming nucleon laboratory energies up to 200 MeV. We are especially interested in the statistical errors arising from uncertainties of parameters of a nucleon-nucleon interaction. The obtained uncertainties of the differential cross section and numerous scattering observables are in general small, grow with the reaction energy and amount up to a few percent at 200 MeV. We compare these uncertainties with the other types of theoretical errors like truncation errors, numerica…
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, w…
Propagation of uncertainties from two-nucleon potential parameters to three-nucleon observables, that is statistical errors for the neutron-deuteron elastic scattering and the deuteron breakup reaction at neutron laboratory energies up to 200 MeV is investigated. To that end we use the chiral nucleon-nucleon interaction with the semi-local momentum-space regularization at various orders of the chiral expansion, exploiting knowledge of the covariance matrix of its parameters. For both reactions we compare statistical uncertainties for chiral predictions with the uncertainties obtained in the sa…
We adopt a covariant version of the naive dimensional analysis and construct the chiral two-nucleon contact Lagrangian constrained by Lorentz, parity, charge conjugation, hermitian conjugation, and chiral symmetries. We show that at $\mathcal{O}(q^0)$, $\mathcal{O}(q^2)$, $\mathcal{O}(q^4)$, where $q$ denotes a generic small quantity, there are 4, 13, and 23 terms, respectively. We find that by performing $1/m_N$ expansions, the covariant Lagrangian reduces to the conventional non-relativistic one, which includes 2, 7, and 15 terms at each corresponding order.
Dineutron and the three-nucleon continuum observables
我们研究如何强大的一个假设的1 S 0束缚态的两个中子会影响不同的可观测的中子-氘核反应。为了这个目的，我们扩展我们的动量空间方案解决三核子Faddeev方程纳入除了氘核也1 S 0双中子束缚态。讨论了双中子对中子-氘弹性散射角分布和氘破裂截面的影响。与中子-氘核总截面和弹性散射角分布的现有数据的比较不能决定性地排除两个中子可以形成1 S 0束缚态的可能性。然而，强烈的修改时，从负到正的值的中子-中子散射长度的中子-氘分裂的最终状态相互作用峰似乎排除双中子的存在。
The standard way to demonstrate the relevance of chiral symmetry for the NN interaction is to consider higher partial waves of NN scattering which are controlled entirely by chiral pion-exchanges (since contacts vanish). However, in applications of NN-potentials to nuclear structure and reactions, the lower partial waves are the important ones, making the largest contributions. Lower partial waves are sensitive to the short-range potential, and so, when the short-range contacts were to dominate over the chiral pion-contributions in lower partial waves, then the predictions from "chiral potenti…
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 $R_1\,$=$(…
