First complete shell-model description of $^{254}$No: a new paradigm for superheavy nuclear structure studies

In this letter, we report the latest developments in the beyond mean-field methods applied to the shell-model framework for the the description of heavy deformed nuclei. We extend our recent DNO-SM approach within the Variation-After-Projection (VAP) scheme, dubbed as DNO-SM(VAP). This approach naturally enables to a priori capture correlations more efficiently than the Projection-After-Variation (PAV) scheme which is commonly used in current theoretical modelings of nuclei. Using the Kuo-Herling effective interaction, we first examine the extended method by a systematic comparison of the binding energies, the yrast spectra and electromagnetic moments of some representative nuclei of masses ranging from $A=251$ to $A=256$. The results show that the VAP scheme variationally provides more bound solutions with respect to the PAV scheme, reflecting the additional correlations that were captured. Both spectra, dipole and spectroscopic quadrupole moments are reproduced favorably. We then focus on the case of $^{254}$No, one of the most studied elements experimentally, which can be considered as the portal to the superheavy region. The calculations show a striking agreement with the complete experimentally known spectroscopy: the yrast band, the isomers and K bands, providing new insights into its shell structure. The present successful description opens a new way for forthcoming spectroscopic studies of heavy and superheavy nuclei.