Exploring highly-deformed ground states involving the second intruder orbit in Z>50 even-even nuclei

Abstract: 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 $β_2\approx$ 0.3--0.4. A characteristic feature of these minima is a local enhancement of the hexadecapole ($β_4$) component relative to nearby deformations, which is a clear fingerprint of the $β_2$--$β_4$ 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 $β_4$ 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.