Testing nonlocal nucleon-nucleon interactions in four-nucleon systems

The Faddeev-Yakubovski equations are solved in configuration space for the $\alpha$-particle and $n-{}^3\mathrm{H}$ continuum states. We test the ability of nonlocal nucleon-nucleon interaction models to describe $3N$ and $4N$ systems.

Figure 1

(Color online) Comparison between the experimental and theoretical calculations with AV18 interaction in He isotopes. Results are taken from Refs. 6, 7.

Figure 2

(Color online) (a) FY components $K$ and $H$. Asymptotically, as $z\to \infty$, components $K$ describe $3+1$ particle channels, whereas components $H$ contain asymptotic states of $2+2$ channels. (b) The $j\text{−}j$ coupling schemes used when developing FYC $K$ and $H$ into a partial wave basis.

Figure 3

(Color online) Tjon line for the local and nonlocal NN potentials.

Figure 4

(Color online) Negative-parity resonance above the $n+t$ threshold.

Figure 5

(Color online) Extraction procedure for $n+{}^3\mathrm{H}$ singlet $\left(a_{0^{+}}\right)$ and triplet $\left(a_{1^{+}}\right)$ scattering lengths from measurements of zero-energy cross section (elliptic band) [38] and coherent scattering length (linear bands) [39, 40, 41]. The values of $a_i$ are given by the intersection of these two curves. Bandwidths are related to experimental errors and, even being small, they make their determination very unstable.

Figure 6

(Color online) Comparison between experimental and theoretical $n-{}^3\mathrm{H}$ total cross section calculated with several local and nonlocal NN potentials.