1. Department of Physics, Florida State University, Tallahassee, Florida 32306-4350, USA
2. National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1321, USA
3. Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
4. Department of Physics, School of Electronics and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, UK

Correspondence to: P. D. Cottle¹ Correspondence and requests for materials should be addressed to P.D.C. (Email: cottle@phy.fsu.edu).

Nuclear shell structures—the distribution of the quantum states of individual protons and neutrons—provide one of our most important guides for understanding the stability of atomic nuclei. Nuclei with 'magic numbers' of protons and/or neutrons (corresponding to closed shells of strongly bound nucleons) are particularly stable^{1, 2}. Whether the major shell closures and magic numbers change in very neutron-rich nuclei (potentially causing shape deformations) is a fundamental, and at present open, question^{3, 4}. A unique opportunity to study these shell effects is offered by the ⁴²Si nucleus, which has 28 neutrons—a magic number in stable nuclei—and 14 protons. This nucleus has a 12-neutron excess over the heaviest stable silicon nuclide, and has only one neutron fewer than the heaviest silicon nuclide observed so far⁵. Here we report measurements of ⁴²Si and two neighbouring nuclei using a technique involving one- and two-nucleon knockout from beams of exotic nuclei^{6, 7}. We present strong evidence for a well-developed proton subshell closure at Z = 14 (14 protons), the near degeneracy of two different (s _1/2 and d _3/2) proton orbits in the vicinity of ⁴²Si, and a nearly spherical shape for ⁴²Si.

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