Momentum Distributions and Spatial Signatures of Proton Halos in the sd Shell
We perform a theoretical study of intermediate-energy quasifree one-proton knockout reactions on proton targets. Single-particle wave functions constrained by the experimental proton separation energies are employed to calculate longitudinal momentum distributions, one-proton removal cross sections, and full momentum-space profiles for $^{26}$P, $^{27}$S and $^{31}$Ar nuclei. To establish robust criteria to identify proton halos, the analysis is extended beyond the traditional momentum-width approach by investigating the spatial extension of the valence proton through root-mean-square radii and the probability that the proton resides outside the core nucleus, $P(r>R_{\rm core})$. We also examine Coulomb-barrier systematics, mirror-nucleus comparisons, realistic spectroscopic mixtures, finite experimental momentum resolution, and uncertainties associated with the proton separation energy. Our calculations indicate that proton-halo structure cannot be identified reliably from a single observable. A consistent interpretation emerges only when momentum distributions, spatial observables, Coulomb effects, and many-body structure are considered simultaneously. Within the present model, $^{26}$P exhibits the strongest proton-halo signatures, while $^{27}$S retains pronounced halo-like features despite its larger Coulomb barrier. The more strongly confined $^{31}$Ar provides a useful comparison and illustrates the progressive suppression of halo observables with increasing binding and core charge.