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Neutron-deuteron scattering revisited with the EKM chiral nuclear force and the WPCD method

Qing-Yu Zhai, Dan-Yang Pang, Wen-Di Chen, O. A. Rubtsova, Rui-Rui Xu, Jun-Xu Lu, Haozhao Liang, Li-Sheng Geng

Abstract

We revisit the neutron-deuteron scattering using the Wave-Packet Continuum Discretization (WPCD) method with the EKM chiral nuclear force at various chiral orders. We rederive the permutation operator and solve the Faddeev-AGS equations directly, without rewriting the initial Faddeev kernel $tG_0$ and introducing pseudo-states, thereby rendering the approach easily extendable to a relativistic framework. We find that up to the next-to-next-to-next-to-leading order (N$^3$LO), although one can well describe the differential cross sections, one cannot resolve the long-standing $A_y$ puzzle, consistent with previous studies. The fact that the N$^3$LO chiral forces can well describe the $NN$ phase shifts and the results obtained with the EKM and Idaho N$^3$LO chiral forces agree with each other underscores the need for further investigations to resolve the $A_y$ puzzle, e.g., considering three-body forces or relativistic effects.

Neutron-deuteron scattering revisited with the EKM chiral nuclear force and the WPCD method

Abstract

We revisit the neutron-deuteron scattering using the Wave-Packet Continuum Discretization (WPCD) method with the EKM chiral nuclear force at various chiral orders. We rederive the permutation operator and solve the Faddeev-AGS equations directly, without rewriting the initial Faddeev kernel and introducing pseudo-states, thereby rendering the approach easily extendable to a relativistic framework. We find that up to the next-to-next-to-next-to-leading order (NLO), although one can well describe the differential cross sections, one cannot resolve the long-standing puzzle, consistent with previous studies. The fact that the NLO chiral forces can well describe the phase shifts and the results obtained with the EKM and Idaho NLO chiral forces agree with each other underscores the need for further investigations to resolve the puzzle, e.g., considering three-body forces or relativistic effects.

Paper Structure

This paper contains 12 sections, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Formalism
  3. Faddeev-AGS equations in momentum space
  4. Setting up the WPCD basis
  5. Computational implementation
  6. $G_0$ matrix
  7. $t$ matrix
  8. $P$ matrix
  9. Spin-scattering matrix and observables
  10. Numerical Results and Discussions
  11. Summary and outlook
  12. Acknowledgments

Figures (4)

  • Figure 1: Momentum assignments of the three nucleons.
  • Figure 2: Neutron analyzing power $A_y(n)$ at $E_\mathrm{lab}=10\ \mathrm{MeV}$ with Nijmegen-I $NN$ interactions. The results denoted by the solid black lines are taken from Ref. Gloeckle:1995jg.
  • Figure 3: Differential cross sections $\mathrm{d}\sigma/\mathrm{d}\Omega$ and the neutron analyzing powers $A_y(n)$ for elastic $nd$ scattering obtained with different chiral orders of the EKM $NN$ interaction. The experimental data at $E_{\mathrm{lab}}=5$ and $10\ \mathrm{MeV}$ are taken from the EXFOR database Otuka:2014wzu, while the data at $E_{\mathrm{lab}}=14.1$ and $53\ \mathrm{MeV}$ are taken from Refs. Berick:1968zzRomero:1982zzWatson:1982zz. The yellow and red bands at $E_{\mathrm{lab}}=10\ \mathrm{MeV}$ are taken from Ref. LENPIC:2015qsz, which show the estimated theoretical uncertainties at NLO and N$^3$LO, respectively.
  • Figure 4: Differential cross section $\mathrm{d}\sigma/\mathrm{d}\Omega$ and neutron analyzing power $A_y(n)$ at $E_\mathrm{lab}=10\ \mathrm{MeV}$ with two $\mathrm{N^3LO}$ chiral $NN$ interactions. The results of $\mathrm{Idaho\text{-}N^3LO}$ are taken from Ref. Miller:2022beg, and the experimental data are taken from the EXFOR database Otuka:2014wzu.