Determination of low energy parameters for NN-scattering at $N^{4}LO$ in all partial waves with $j\le 5$

Abstract

The Variable S-matrix approach offers a unique way to extract low energy threshold parameters for a given NN potential. We extract those parameters for the np system from the NijmII and Reid93 potentials, to all partial waves with total angular momentum $j\le m5$, using the generalized effective range expansion % $$({\mathbf{f}}^{sj}{)}_{l,l^{\prime }}{k}^l{k}^{l^{\prime }}=-({{\mathbf{a}}^{sj}}^{-1}{)}_{l,l^{\prime }}+\frac{1}{2}({\mathbf{r}}^{sj}{)}_{l,l^{\prime }}{k}^2+({{\mathbf{v}}_2}^{sj}{)}_{l,l^{\prime }}{k}^4++({{\mathbf{v}}_3}^{sj}{)}_{l,l^{\prime }}{k}^6++({{\mathbf{v}}_4}^{sj}{)}_{l,l^{\prime }}{k}^8+...-\mathrm{i}{k}^{l+l^{\prime }+1}$$ % where ${\mathbf{f}}^{sj}=({\mathbf{S}}^{sj}-1)/(2\mathrm{i}k)$ is the scattering amplitude and ${\mathbf{S}}^{sj}$ is the unitary S-matrix in coupled channel space with total spin $s$ and total angular momentum $j$. Our calculation includes all the relevant contributions of the full amplitude to order $\mathcal{O}(k^8)$ in the CM momentum. We also discuss the validity of the generalized effective range expansion in the region of analyticity $k\le m_{\pi }/2$.

Comments: 7 figures, 5 tables