Neutron-deuteron scattering cross sections with chiral $NN$ interactions using wave-packet continuum discretization

In this work we present a framework that allows one to solve the Faddeev equations for three-nucleon scattering using the wave-packet continuum-discretization method. We perform systematic benchmarks using results in the literature and study in detail the convergence of this method with respect to the number of wave packets. We compute several different elastic neutron-deuteron scattering cross-section observables for a variety of energies using chiral nucleon-nucleon interactions. For the optimized next-to-next-to-leading order interaction ${\text{N2LO}}_{\text{opt}}$ we find good agreement with data for nucleon scattering-energies $E_{\text{Lab}}\le 70$ MeV and a slightly larger maximum of the neutron analyzing power $A_y\left(n\right)$ at $E_{\text{Lab}}=10$ and 21 MeV compared with other interactions. This work represents a first step towards a systematic inclusion of three-nucleon scattering observables in the construction of next-generation nuclear interactions.

Figure 1

The $nd$ scattering phase shifts (real and imaginary parts) in the doublet and quartet spin channels of the ${\frac{1}{2}}^{+}$ (left panel) and ${\frac{5}{2}}^{-}$ (right panel) $NNN$ partial waves, respectively. Standard Faddeev results at $E_{\text{Lab}}=13$ MeV are from Ref. [2]. See Appendix pp5 for more on the notation.

Figure 2

The neutron analyzing power $A_y\left(n\right)$ at $E_{\text{Lab}}=35$ MeV vs c.m. scattering angle ${\theta }_{\text{c.m.}}$ using the Nijmegen-I $NN$ potential. The WPCD prediction approaches the standard Faddeev result [2] with an increasing number of wave packets $N_{\text{WP}}$ and they overlap for $N_{\text{WP}}\gtrsim 125$.

Figure 3

The convergence of WPCD predictions for typical elastic $nd$ differential scattering cross sections and polarization observables for increasing neutron scattering energies with respect to an increasing number of wave packets using the Idaho-N3LO $NN$ interaction [21].

Figure 4

Total $nd$ cross sections computed using the WPCD method and the optical theorem; see, e.g., Ref. [42]. Experimental $nd$ data were retrieved via EXFOR [43].

Figure 5

The neutron analyzing power $A_y\left(n\right)$ at $E_{\text{Lab}}=10$ MeV computed using the WPCD method with $N_{\text{WP}}=125$ wave packets. At the maximum, the top dashed line is the ${\text{N2LO}}_{\text{opt}}$ result. Experimental $nd$ data are from Ref. [44].

Figure 6

The differential cross section for elastic $nd$ scattering computed using the WPCD method with $N_{\text{WP}}=125$ wave packets. The experimental $nd$ data (empty markers) at $E_{\text{Lab}}=6,12,25$ MeV in the left panel are from Ref. [45] and the $pd$ data (filled markers) at $E_{\text{Lab}}=64.5$ MeV in the right panel are from Ref. [46]. For $E_{\text{Lab}}=64.5$ MeV (right panel) the Idaho-N3LO predicts a slightly smaller cross section at the minimum.

Figure 7

Spin observables for elastic $nd$ scattering computed using the WPCD method with $N_{\text{WP}}=125$ wave packets and the ${\text{N2LO}}_{\text{opt}}$ and the Idaho-N3LO potentials. The experimental $nd$ data (empty markers) at $E_{\text{Lab}}=21,22.5$, and 65 MeV are from Refs. [50], [51], and [52], respectively. The $pd$ data (filled markers) at $E_{\text{Lab}}=13,35,47.5,65$, and 70 MeV are from Refs. [53], [54], [55], [46], and [56], respectively. See the main text for detailed discussion.