$nd$ scattering lengths from a quark-model based $NN$ interaction

TL;DR

This paper computes neutron-deuteron scattering lengths using a quark-model based nucleon-nucleon interaction, achieving good agreement with experimental data for the quartet case and consistent results with the Phillips line.

Contribution

It introduces a fully derived nonlocal nucleon-nucleon interaction from quark-quark interactions to calculate scattering lengths.

Findings

Quartet scattering length matches experimental value.

Doublet scattering length deviates from experiment but aligns with the Phillips line when combined with triton binding energy.

Method uses $NN$ partial waves from quark-model interactions.

Abstract

We calculate the doublet and quartet neutron-deuteron scattering lengths using a nonlocal nucleon-nucleon interaction fully derived from quark-quark interactions. We use as input the $NN$ $^1S_0$ and $^3S_1$-${}^3 D_1$ partial waves. Our result for the quartet scattering length agrees well with the experimental value while the result for the doublet scattering length does not. However, if we take the result for the doublet scattering length together with the one for the triton binding energy they agree well with the so-called Phillips line.