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This white paper is the result of a collaboration by many of those that attended a workshop at the facility for rare isotope beams (FRIB), organized by the FRIB Theory Alliance (FRIB-TA), on ‘Theoretical Justifications and Motivations for Early High-Profile FRIB Experiments’. It covers a wide range of topics related to the science that will be explored at FRIB. After a brief introduction, the sections address: section 2: Overview of theoretical methods, section 3: Experimental capabilities, section 4: Structure, section 5: Near-threshold Physics, section 6: Reaction mechanisms, section 7: Nuclear equations of state, section 8: Nuclear astrophysics, section 9: Fundamental symmetries, and section 10: Experimental design and uncertainty quantification. 

Abstract The nucleus²⁰⁶Po was studied in the two proton transfer reaction²⁰⁴Pb(¹⁶O,¹⁴C)²⁰⁶Po and the lifetime of the first excited 2⁺state was determined by utilizing the Recoil Distance Doppler Shift method. The experimental results are compared with shell-model calculations based on different effective interactions. The calculations qualitatively reproduced the experimentally observed $B(E2;2_1^{+}\to 0_1^{+})$value, suggesting that the $2_1^{+}$state of²⁰⁶Po exhibits a collective nature. However, the employed effective interactions revealed some limitations, particularly in their description of the $4_{1,2}^{+}$states. These results emphasize the importance of understanding the properties of low-lying states, especially their evolution from single-particle dynamics to collective modes, in evaluating various effective nuclear interactions. 

Applications of configuration-mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new “outposts” are highlighted: 28O, 42Si, 60Ca and 78Ni. Topics include shell gaps, single-particle properties, islands of inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions. 

Abstract The observation of a weak proton-emission branch in the decay of the 3174-keV^53mCo isomeric state marked the discovery of proton radioactivity in atomic nuclei in 1970. Here we show, based on the partial half-lives and the decay energies of the possible proton-emission branches, that the exceptionally high angular momentum barriers,$${{{{{{\mathcal{l}}}}}}}_{{{{{{\rm{p}}}}}}}=9$$ $l_p=9$and$${{{{{{\mathcal{l}}}}}}}_{{{{{{\rm{p}}}}}}}=7$$ $l_p=7$, play a key role in hindering the proton radioactivity from^53mCo, making them very challenging to observe and calculate. Indeed, experiments had to wait decades for significant advances in accelerator facilities and multi-faceted state-of-the-art decay stations to gain full access to all observables. Combining data taken with the TASISpec decay station at the Accelerator Laboratory of the University of Jyväskylä, Finland, and the ACTAR TPC device on LISE3 at GANIL, France, we measured their branching ratios as b_p1= 1.3(1)% and b_p2= 0.025(4)%. These results were compared to cutting-edge shell-model and barrier penetration calculations. This description reproduces the order of magnitude of the branching ratios and partial half-lives, despite their very small spectroscopic factors.