Vortex Nucleons as Partial-Wave Filters in Nucleon--Nucleon Scattering

We propose vortex nucleon scattering as an angular-momentum-resolved probe of nucleon–nucleon partial waves. Using the standard $LSJ$ partial-wave $S$ matrix as input, we show that an on-axis vortex incident state with a fixed orbital angular-momentum projection $m_L=\mathrm{\ell }$ imposes the direct selection rule $L\ge \mathrm{\mid }\mathrm{\ell }\mathrm{\mid }$ on the initial nucleon–nucleon partial waves. As a result, the initial $S$ wave is excluded for $\mathrm{\ell }=1$, while both the initial $S$ and $P$ waves are excluded for $\mathrm{\ell }=2$. The underlying phase shifts are not modified. Instead, the vortex external state changes how the ordinary partial waves are projected into the scattering amplitude. We further analyze off-axis scattering, where the displacement of the target from the vortex axis introduces Bessel-function weights and partially relaxes the on-axis selection rule. These results suggest that vortex nucleons can provide a new experimental handle on the partial-wave content of the strong nucleon–nucleon interaction.