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The low-lying level structures of nuclei in the vicinity of 78 Ni were investigated using in-beam γ -ray spectroscopy to clarify the nature of the nuclear magic numbers Z = 28 and N = 50 in systems close to the neutron drip line. Nucleon knockout reactions were employed to populate excited states in 80 were deduced to be 1.32(3) and 1.12 +80 −60 , respectively. These results imply that 80 Zn can be described in terms of two-proton configurations with a 78 Ni core and are consistent with a robust N = 50 magic number along the Zn isotopic chain. These observations, therefore, indicate a persistent N = 50 shell closure in nuclei far from the line of β stability, which in turn suggests a doubly magic structure for 78 Ni.

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During the expansion of a cell collective, such as the development of microbial colonies and tumor progression, the local cell growth increases the local pressure, which in turn suppresses cell growth. How this pressure-growth coupling affects the expansion of a cell collective remains unclear. Here, we answer this question using a continuum model of cell collective. We find that a fast-growing leading front and a slow-growing interior of the cell collective emerge due to the pressure-dependent growth rate. The leading front can exhibit fingering instability and we confirm the predicted instability criteria numerically with the leading front explicitly simulated. Intriguingly, we find that fingering instability is not only a consequence of local cell growth but also enhances the entire population’s growth rate as positive feedback. Our work unveils the fitness advantage of fingering formation quantitatively and suggests that the ability to form protrusion can be evolutionarily selected.