Proton radioactivity in deformed nuclei with microscopic optical potential: a novel angular-dependent emission mechanism in the nanosecond-emitter $^{149}$Lu

We present the first microscopic description of proton radioactivity in $^{149}$Lu, the most oblate deformed proton emitter known, using a deformed microscopic optical potential derived from $ab\ initio$ nuclear matter calculations. We predict a novel angular-dependent phenomenon unprecedented in spherical proton emitters: the disappearance of classically allowed regions at small polar angles $(θ\leq 21^\circ)$. Combining the Wentzel-Kramers-Brillouin penetration probabilities and the assault frequency of the emitted proton estimated with a new harmonic-oscillator-inspired scheme, our framework yields a half-life $T_{1/2}=467^{+143}_{-108}$ ns for $^{149}$Lu, in excellent agreement within uncertainties with the experimental value $450^{+170}_{-100}$ ns. Deformation analysis rigorously excludes configurations with $|β_2|\geq 0.32$. Extensions to $^{150, 151}$Lu and their isomers also achieve excellent agreement with experimental half-life data. We further predict $^{148}$Lu as another highly oblate $(β_2 = -0.166)$ proton emitter with a half-life of 4.42 ns. This work validates deformed microscopic optical potentials as a robust predictive tool for drip-line proton emitters and provides quantitative evidence for deformation effects in exotic decays.