CERN Accelerating science

Resolving a long-standing question at ISOLDE

Among the many pioneering results that have been published at ISOLDE was the discovery of odd-even staggering in the mean-square charge radius in neutron deficient Hg isotopes in the 1970s, as part of the RADOP experiment which measured the isotopic shifts using optical spectroscopy [1], [2]. Since then, this phenomenon has been called “shape staggering” and is thought to be unprecedented elsewhere in the nuclear landscape.

Figure 1 Example of the first observation of odd-even staggering at ISOLDE [1]

Further study revealed that this region of the nuclear chart displays a multitude of different shapes and the mercury isotopes are now known to be one of the richest regions in terms of shape coexistence. Since this discovery, numerous other studies were conducted into probing this staggering phenomena using a variety of techniques such as Coulomb Excitation, beta-decay and mass measurements. However, the theoretical basis for the staggering mechanism along with an experimental extension to ever more neutron deficient isotopes had not been attempted due to the inherent difficulties in modelling such heavy isotopes and challenges in measuring such exotic isotopes. Furthermore, measurements had only been extended down to 181Hg. While the ground-state deformation has been indirectly inferred for neutron deficient mercury isotopes from in-beam recoil-decay tagging measurements, hinting towards less-deformed shapes for A<180, this had not been confirmed by a direct ground-state isotope-shift measurement. The missing mean-square charge-radii data for the lighter mercury isotopes left the key question of where the shape staggering ends.

These hurdles have now been overcome at ISOLDE [3] where target and ion source developments  have allowed for the production of ever more exotic isotopes, down to 177Hg. Similarly, improvements in spectroscopic methods have allowed for high precision measurements of even weakly produced radioactive ions: down to rates of only a few per minute. The neutron deficient series of Hg isotopes has been characterized using an impressive combination of decay, optical and mass spectroscopies and spectrometry. Faraday cup measurements allowed for the measurement of the stable 198Hg isotope – which was the reference isotope for the current study – along with other strongly produced Hg isotopes. Isomer shifts and hyperfine parameters were measured using either the ISOLDE “Windmill” setup – allowing isotopes with a production rate of only 0.1/s to be determined – and the Multi-Reflection Time of Flight spectrometer (MR-TOF) at ISOLTRAP [4]. The experimental scheme is shown in Figure 2.

Mercury isotopes were produced via spallation reactions induced by a1.4-GeV proton beam from the PS-Booster impinging upon a molten-lead target. The neutral reaction products effused from the heated target via the transfer line. Traditionally, Hg ions can be produced using a plasma ion source, but this gives rise to strong stable contamination. In this experiment, the Hg ions were produced using the ISOLDE laser ion source in the plasma ion source: the so-called VADLIS mode. This allowed for high purity beams to be ionized which were subsequently sent to the various experimental stations. High quality Hg beams are a specialty of ISOLDE and are one of the many instances where the facility is unique worldwide.

Figure 2. Overview of the various experimental techniques, which have been employed in the investigation of neutron deficient isotopes at ISOLDE (a) and the ISOLDE laser ion source (RILIS) in operation (b).

Examples of the results from the experimental campaign are shown in Figure 3. As can be clearly seen, the pronounced staggering is observed until A=101. Extending the measurements down to 177Hg has allowed this sequence to be extended for the first time with the observation that the deformation comes to an end at 181Hg. Below this, the nuclei return to a spherical shape. In addition, the measured nuclei, this finding is supported by magnetic nad quadrupole measurements in 177Hg and 179Hg. In order to understand further the mechanism that explains this unusual behavior, extensive calculations using density functional theory and large scale Monte-Carlo shell model (MCSM) were undertaken. This was the first time that such calculations were performed for such a heavy system such as Hg and were the heaviest MCSM so far. The calculations were carried out on the massively parallel K-supercomputer at RIKEN. Both the magnetic and quadrupole moments and the radii changes calculated with the MCSM agree with the experimental results to a remarkable extent. Full details of the results can be found in [4] but, in essence, the origin of the shape staggering is attributed to a subtle variation on the “usual” normal shell theory predictions for such isotopes. So-called type II shell evolution – where significant changes in nucleon occupation number produce large shifts of effective single-particle energies – is found to be responsible for the existence of near-degenerate coexistence of strongly and weakly bound deformed states, which gives rise to the observed staggering in neutron deficient Hg isotopes.

This work has highlighted not only the advances that have been made at ISOLDE in producing neutron deficient isotopes in the Hg region, but also the considerable advances in spectroscopy which have allowed these isotopes to be characterized using a host of experimental techniques. The detailed modelling using MCSM has for the first calculations of spectroscopic properties of the heaviest isotopes yet and will surely inspire additional work in this region and on heavier isotopes. Given the improvements in computing power this will likely become the norm and fits in well with the experimental programmes at ISOLDE where – with the advent of HIE-ISOLDE – the study of such isotopes using Coulomb excitation and multi-nucleon reactions will address new areas of the nuclear chart and will benefit from this close relation to theory.

Figure 3. Measured changes in mean-square charge radius for neutron deficient Hg and Pb isotopes.

Figure 4 MCSM calculations showing remarkable agreement with experimentally measured radii.



[1] J. Bonn et al., Physics Letters B 38, 308 (1972).

[2] T. Kuhl et al., Phys. Rev. Lett. 39, 180 (1977).

[3]  B. Marsh et al., Nature Physics 14, 1163 (2018).

[4] S. Sels et al. arXiv:1902.11211v1 (2019).