Relativistic medium effects and spectroscopic factor systematics in proton radioactivity near the drip line

Proton radioactivity provides a powerful probe of nuclear structure beyond the proton drip line and offers stringent tests for nuclear interaction models. We demonstrate that the relativistic density-dependent DDR3Y interaction, combined with Relativistic Hartree Bogoliubov (RHB) densities obtained with the DD-ME2 parameter set, yields the lowest MSE among the examined folding approaches in reproducing experimental proton-decay half-lives across 43 distinct measured states in the range 53 ≤ Z ≤ 83. Nuclear potentials are constructed within the single-folding model using Skyrme density distributions (SLy7, BSk14, and SkM*) folded with the M3Y–Paris interaction, alongside RHB densities folded with the density-dependent DDR3Y interaction. Proton decay half- lives are calculated using the WKB approximation. The role of the attractive component of the NN interaction in determining the depth of the potential pocket is analyzed in detail, with particular attention to high-angular-momentum (lp = 5) emitters for which the Bohr–Sommerfeld quantization condition provides a consistency check on independently assigned proton configurations and potential pockets, with renormalization defined relative to the adopted unscaled interaction and no universal upper bound of unity. A new empirical spectroscopic factor (Sp) formula incorporating four variables (decay energy, angular momentum, isospin asymmetry, and quadrupole deformation) is proposed as a principal result of this work. The formula is calibrated empirically within the DDR3Y(DD-ME2) framework and introduces a term coupling angular momentum to the decay-energy scale, with deformation dependence that may include omitted barrier effects. When applied to DDR3Y half-lives, the formula achieves training MSE = 0.1393 and SD = 0.3777; fixed-form leave-one-out cross-validation gives MSE = 0.1616, compared with 0.2304 for the Universal Decay Law for Protons (UDLP). The Qp-value sensitivity is reported for each measured state, spanning 0.63–2.37 decades per 0.1 MeV, identifying three sensitivity groups and the mass measurements most critical for improving predictive power. Half-lives for 12 unobserved or unquantified proton emitters near the drip line are predicted, with local barrier uncertainty estimates derived from Qp-value sensitivity.