We present a systematic survey of even-even nuclei with $Z>50$ to identify where a very large prolate configuration driven by the second intruder orbit emerges. Within the energy density functional theory framework, we find in representative cases a pronounced prolate minimum at quadrupole deformation ${\beta }_2\approx$ 0.3–0.4. A characteristic feature of these minima is a local enhancement of the hexadecapole (${\beta }_4$) component relative to nearby deformations, which is a clear fingerprint of the ${\beta }_2\text{−}{\beta }_4$ coupling expected for the second intruder orbit. Representative comparisons among three Skyrme interactions show a similar appearance of the highly deformed minimum and a local enhancement of ${\beta }_4$ at the prolate minimum, indicating qualitative robustness with respect to the interaction. The resulting maps highlight specific heavy nuclei where highly deformed ground states are anticipated.

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• Nuclear structure & decays