Searching for the origin of the rare-earth peak with precision mass measurements across Ce–Eu isotopic chains

A nuclear mass survey of rare-earth isotopes has been conducted with the Canadian Penning Trap mass spectrometer using the most neutron-rich nuclei thus far extracted from the CARIBU facility. We present a collection of 12 nuclear masses determined with a precision of $\le 10$ keV/$c{}^2$ for $Z=58–63$ nuclei near $N=100$. Independently, a detailed study exploring the role of nuclear masses in the formation of the $r$-process rare-earth abundance peak has been performed. Employing a Markov chain Monte Carlo (MCMC) technique, mass predictions of lanthanide isotopes have been made which uniquely reproduce the observed solar abundances near $A=164$ under three distinct astrophysical outflow conditions. We demonstrate that the mass surface trends thus far mapped out by our measurements are most consistent with MCMC mass predictions given an $r$ process that forms the rare-earth peak during an extended $(n,\gamma )\rightleftarrows (\gamma ,n)$ equilibrium.

Figure 1

Highlights from the ${\nu }_c$ measurement of ${}^{157}\mathrm{Pr}^{2+}$. Panel (a) is a histogram of detected ion locations on the face of the MCP during a $t_{\mathrm{acc}}=90.447$ ms final phase measurement. The orbital positions of ${}^{157}\mathrm{Pr}^{2+}$ and ${}^{157}\mathrm{Nd}^{2+}$ ions are labeled alongside a central cluster of unexcited ions. In panel (b) the ${\nu }_c$ values of ${}^{157}\mathrm{Pr}^{2+}$ from five distinct final phase measurements near $t_{\mathrm{acc}}=90$ ms are fitted to a model, described in Ref. [22], to reveal the true ${\nu }_c$ (gray dashed line).

Figure 2

Rare-earth peak abundances given the average masses predicted in Ref. [16] when two distinct astrophysical outflow conditions (“hot” in red and “cold” in blue) are considered in the MCMC calculations (solid lines). Dotted lines show results when the average masses found to produce the rare-earth peak in a given condition are applied in a distinctly different condition.

Figure 3

Precision CPT mass measurements of neutron-rich lanthanides with $Z=58–63$ from this work alongside Refs. [19, 20] as compared to the masses predicted by the MCMC calculations of Ref. [16] (shown relative to the Duflo-Zuker mass model) given three distinct astrophysical outflow conditions: a “hot” outflow with $s=30k_B$/baryon and $\tau =70$ ms (red), a “cold” outflow with $s=10k_B$/baryon and $\tau =3$ ms (blue), and a “hot/cold” outflow with $s=20k_B$/baryon and $\tau =10$ ms (green).