For decades, nuclear physicists have known that so called islands of inversion mark regions of the nuclear chart where standard shell structure breaks down and magic numbers vanish in favor of strongly deformed shapes. In earlier work these islands were identified mainly in neutron rich isotopes such as beryllium 12 with N = 8, magnesium 32 with N = 20, and chromium 64 with N = 40, all distant f Tokyo, Japan (SPX) Dec 09, 2025
For decades, nuclear physicists have known that so called islands of inversion mark regions of the nuclear chart where standard shell structure breaks down and magic numbers vanish in favor of strongly deformed shapes. In earlier work these islands were identified mainly in neutron rich isotopes such as beryllium 12 with N = 8, magnesium 32 with N = 20, and chromium 64 with N = 40, all distant from the line of stable nuclei found in nature.
An international team from the Center for Exotic Nuclear Studies at the Institute for Basic Science, the University of Padova, Michigan State University, the University of Strasbourg and other partners has now identified an island of inversion in a very different part of the chart, where the number of protons and neutrons is nearly balanced. The group reports clear signatures of an island of inversion in molybdenum 84, a nuclide with Z = N = 42, while a neighboring isotope with only two extra neutrons, molybdenum 86, shows much more conventional behavior.
The researchers focused on isotopes along the N = Z line, a key testing ground for nuclear structure theories but one that is difficult to access experimentally because such nuclides are hard to produce. Using rare isotope beams at Michigan State University and precision gamma ray spectroscopy, they determined the lifetimes of excited states in both Mo 84 and Mo 86 with picosecond resolution. These lifetimes provide direct information on how strongly the nuclei are deformed and how their protons and neutrons move collectively.
To produce the necessary beams, accelerated molybdenum 92 ions were directed onto a primary beryllium target, creating a range of reaction products that included molybdenum 86. The A1900 fragment separator at Michigan State University was used to isolate the desired Mo 86 beam from the many other nuclides created in the collision. This secondary beam then struck a second beryllium target, where some nuclei were excited or converted into molybdenum 84 by the removal of two neutrons before emitting gamma rays as they returned to their ground states.
Gamma rays from the excited molybdenum isotopes were measured with the GRETINA high purity germanium detector array, which can track individual gamma ray interactions with high resolution. The experiment also used the TRIPLEX device, which enables lifetime measurements down to timescales of trillionths of a second and is well suited to fast rare isotope beams. By comparing the measured spectra and time distributions with detailed GEANT4 Monte Carlo simulations, the team extracted the lifetimes of the first excited states and quantified the deformation of each nucleus.
The data show that molybdenum 84 exhibits a much higher degree of collective motion than molybdenum 86, even though the two isotopes differ by only two neutrons. In Mo 84, many protons and neutrons are promoted together across a major shell gap in coordinated particle hole excitations, where nucleons move to higher energy orbitals and leave vacancies behind. The high level of collectivity indicates that a large number of nucleons participate in these excitations, producing a strongly deformed nuclear shape that contrasts sharply with the more modest deformation seen in Mo 86.
Theoretical calculations carried out alongside the measurements reproduce this sharp contrast between the two isotopes and clarify its origin. For Mo 84 the models require very large simultaneous particle hole excitations involving both protons and neutrons, corresponding to an effective 8 particle 8 hole configuration that drives strong deformation. This behavior is linked to a combination of proton neutron symmetry effects and a narrowed shell gap around N = Z = 40, which lowers the energy cost of such coordinated rearrangements.
A key outcome of the modeling is that three nucleon forces are essential to account for the observed structure in Mo 84. When the calculations include only conventional two nucleon interactions they fail to generate the large deformations indicated by the experimental lifetimes and gamma ray strengths. Including interactions in which three nucleons act together allows the theory to reproduce the measured properties, highlighting the importance of these forces in shaping nuclear structure near the N = Z line.
In molybdenum 86 the calculations and measurements agree on much smaller 4 particle 4 hole excitations and correspondingly weaker deformation. Together with the Mo 84 results, this pattern indicates that Mo 84 lies inside a newly defined island of inversion, while Mo 86 falls outside its boundary despite their close proximity in neutron number. The presence of such different structures in neighboring isotopes underscores how rapidly shell ordering and collectivity can change with small shifts in nucleon count.
The team describes this region as an isospin symmetric island of inversion because it appears in a nucleus where proton and neutron numbers are equal, in contrast to earlier islands identified mainly in neutron rich systems. This discovery challenges previous assumptions that inversion behavior is confined to exotic, neutron heavy nuclides and opens a new window on how nuclear forces operate when protons and neutrons play fully symmetric roles. The work provides a sensitive test ground for modern nuclear interaction models and may guide future experiments on other N = Z isotopes.
Research Report:Abrupt structural transition in exotic molybdenum isotopes unveils an isospin-symmetric island of inversion
Related Links
Institute for Basic Science
Understanding Time and Space