Mass measurements of $^{179-184}$Yb identify an anomalous proton-neutron interaction

Abstract

Mass measurements of nuclei can identify structurally-driven trends in binding energy across isotopic chains, and can also isolate specific nucleon-nucleon interactions, such as the $δV_{\mathrm{pn}}$ interaction of the last two valence protons with the last two valence neutrons. Below $^{208}$Pb, investigation of the local binding energy and $δV_{\mathrm{pn}}$ systematics can facilitate a better understanding of the behaviour of the proton-neutron interaction in the 'hole-hole' regime (where valence interactions can be modelled in hole-space rather than particle-space) and provide insight on the potential onset of a prolate-to-oblate shape transition. However, measurement of the necessary nuclei has been exceptionally challenging. Here we present six first-time measurements of neutron-rich ytterbium, using advanced rare isotope production and mass spectrometry techniques, leading to the identification of an anomalously strong proton-neutron interaction in the 'hole-hole' quadrant below $^{208}$Pb. The scale of this interaction, at $^{186}$Hf, is comparable to that of similar signals at doubly-magic nuclei and shape transitions. The experimental results are compared with contemporary mean-field model predictions, that do not accurately reproduce the anomaly. The results are also used to benchmark predictions from several models, to facilitate more accurate descriptions towards a key r-process waiting point at $N = 126$.

Figures (7)

• Figure 1: Schematic of TITAN and the upstream ISAC beamline at TRIUMF, not to scale. An intense 480MeV, 18µ H+ beam was provided by the TRIUMF main cyclotron, and impinged onto a thick UCX target to produce an array of radioactive species. These species were extracted and ionised to form a cocktail radioactive ion beam (RIB), with selective ionisation of ytterbium species achieved through application of TRIUMF's Resonant Ionisation Laser Ion Source (TRILIS). This cocktail RIB was twice mass separated and transported to TITAN's RFQ Cooler and Buncher, which then delivered the beam as radioactive ion bunches to TITAN's Multiple-Reflection Time-of-Flight Mass Spectrometer (MR-ToF-MS). Here narrow ion bunches, with calibrant ions injected from an internal source, were reflected for multiple turns between a set of two isochronous ion mirrors, facilitating precise mass measurement with a high mass resolving power. A mass spectrum for the reported results at $A=184$ is shown. The identified species are labelled, including 184Yb, the most exotic species measured. 'Mass-selective re-trapping' centred on 184Yb was used to cut the rates of the major contaminant peaks by four orders of magnitude. See the main text for further details0.
• Figure 2: Top: Experimental two-neutron separation energies for the local even-$Z$ species, with data from the AME2020 Wang2021, GSI Shubina2013, and this work. Theoretical predictions are overlaid for the 70Yb and 72Hf chains, from the BSkG03 model Grams2023 and this work. Note that for the ytterbium $S_{2\mathrm{n}}$, after $N=115$, the HF-BCS-Sk-1 and HF-BCS-Sk-2 values are shown only for the even-$N$ ytterbium species. Red squares are the new ytterbium data. Bottom: Experimental $\beta_{2}$ deformations for 70Yb and 72Hf, with data from the NNDC NNDC. Theoretical predictions are overlaid, from the BSkG03 Grams2023 model and this work. Note that for the ytterbium $\beta_{2}$, only the HF-BCS-Sk-1 values are shown, as the two sets of $\beta_{2}$ predictions are not distinguishable; after $N=115$ these values are shown for only the even-$N$ ytterbium species.
• Figure 3: Experimental $\delta V_{\mathrm{pn}}$ values for the even-even species of the region between 132Sn and 208Pb, with data from the AME2020 Wang2021, CPT Orford2022, and this work. Top: A 2-dimensional plot of $\delta V_{\mathrm{pn}}$ against $N$ for all isotopic chains in this region. The 60Nd and 72Hf chains are drawn in black, or red where data are from this work, with species discussed in the text labelled. All other chains are shown in light grey for reference. Theoretical predictions are overlaid for the 72Hf chain, from the BSkG03 model Grams2023 and this work. Bottom: A 3-dimensional heat-map of $\delta V_{\mathrm{pn}}$ against $N$ and $Z$. New values from this work are indicated with a red box. The solid line corresponds to equal numbers of valence protons and valence neutrons; the dashed line corresponds to equal numbers of proton holes and neutron holes. Dotted mid-shell lines at $N=104$ and $Z=66$ demarcate the particle-particle, particle-hole, hole-hole, and hole-particle quadrants (from bottom-left clockwise). Elemental maxima according to the existing literature are marked with white circles from 52Te to 74W; this highlights the known effect along the line of nuclei with approximately equal numbers of valence protons and valence neutrons. The newly identified maximum in the hafnium chain, from this work, is marked with a white diamond; this highlights the new effect identified in this work, in a nucleus with approximately equal numbers of proton holes and neutron holes.
• Figure 4: Experimental $\delta V_{\mathrm{pn}}$ (top) and $R_{42}$ (bottom) between 76Ni and 210Pb. Notable species discussed in the text are labelled, with the relevant sections of the $\delta V_{\mathrm{pn}}$ chains drawn in black. Data from the AME Wang2021, NNDC NNDC, CPT Orford2022, ISOLTRAP Lunney2025, and this work.
• Figure 5: Ytterbium mass excesses from various theoretical models Duflo1995Pearson1996Goriely2010Moller2016Grams2023, including blind HF-BCS-Sk predictions from this work, presented as differences from the experimental values. Experimental values are from the AME Wang2021 and first time mass measurements from this work. For the HF-BCS-Sk model the theoretical values plotted are obtained through a systematic correction of $-5MeV$; see the text for details.