Extended Data Figure 1: Calculated proton and neutron single-particle energy levels in ¹⁰⁵Zr as functions of nuclear deformation.

Left panel, proton levels; right panel, neutron levels. The 40 protons and 65 neutrons in ¹⁰⁵Zr fill all levels up to the Fermi levels corresponding to these nucleon numbers in the two diagrams (red dots). Levels corresponding to even parity are shown as solid lines, those corresponding to odd parity as dashed lines. Shell gaps are characterized by a particularly large separation in energy between two adjacent single-particle levels. The numbers of protons or neutrons that occupy levels up to the shell gap are indicated by circled numbers. The single-particle levels are shown for a spherical nucleus in spectroscopic standard notation (left side of each panel), and for a deformation near the calculated ground-state shape of ¹⁰⁵Zr with quadrupole and hexadecapole shape-parameter values ε₂ = 0.333 and ε₄ = 0.06, respectively²³ (right side of each panel). The middle section of each panel shows the change in level energies as ε₂ and ε₄ change from spherical values ε₂ = ε₄ = 0 to deformed values²⁸. The well-known “magic numbers” 50 and 82 corresponding to particularly large gaps stand out at zero deformation²⁹. When the nuclear shape becomes deformed, the spherical shell gaps disappear resulting in a large density of levels in the vicinity of the Fermi level. This gives rise to a large number of states at low excitation in ¹⁰⁵Zr. Some of these states can be populated by strong β⁻ decay transitions from the ground state of ¹⁰⁵Y. The situation is similar for the electron capture on ¹⁰⁵Zr into deformed ¹⁰⁵Y.