First Exploration of Neutron Shell Structure below Lead and beyond $N=126$

The nuclei below lead but with more than 126 neutrons are crucial to an understanding of the astrophysical $r$ process in producing nuclei heavier than $A\sim 190$. Despite their importance, the structure and properties of these nuclei remain experimentally untested as they are difficult to produce in nuclear reactions with stable beams. In a first exploration of the shell structure of this region, neutron excitations in ${}^{207}\mathrm{Hg}$ have been probed using the neutron-adding ($d$,$p$) reaction in inverse kinematics. The radioactive beam of ${}^{206}\mathrm{Hg}$ was delivered to the new ISOLDE Solenoidal Spectrometer at an energy above the Coulomb barrier. The spectroscopy of ${}^{207}\mathrm{Hg}$ marks a first step in improving our understanding of the relevant structural properties of nuclei involved in a key part of the path of the $r$ process.

Figure 1

Chart of nuclides color coded to show the stable nuclei (288) in black and nuclei that have been shown to exist in gray ($\sim 3350$). Approximately 7000 nuclei, inside the drip lines, are predicted to exist [2]. Nuclei estimated to be involved in the astrophysical $r$ process [3] are shown in blue. The isotope ${}^{207}\mathrm{Hg}$ is marked with a red asterisk, lying in the region shaded yellow with boundaries at $Z=82$ and $N=126$. The bold lines show the traditional magic numbers. The inset shows the region around ${}^{207}\mathrm{Hg}$. In the inset only, nuclei with at least one known excited state ($\sim 2100$ across the entire chart) are shown in green [4, 5].

Figure 2

(a) The low-lying excitation-energy spectrum of ${}^{207}\mathrm{Hg}$ as measured via the ($d$,$p$) reaction on ${}^{206}\mathrm{Hg}$ at $7.38\mathrm{MeV}/\mathrm{u}$. States are labeled by their energies in keV and $\ell$ value. (b) Same spectrum with a linear background subtracted and with fits shown [44].

Figure 3

Angular distributions for the outgoing protons from the ($d$,$p$) reaction on ${}^{206}\mathrm{Hg}$ at $7.38\mathrm{MeV}/\mathrm{u}$. The color of the lines corresponds to $\ell =0$ (orange), 2 (maroon), and 4 (yellow) transfer. Transitions are labeled by their excitation energies (in keV) in the residual nucleus and the $\ell$ value corresponding to the best-fit angular distribution. The thicker curves represent the best-fit angular distribution for the $\ell$-value quoted. Thinner lines are used to show other possible $\ell$ values.

Figure 4

Experimentally determined binding energies of the neutron orbitals at $N=127$ for ${}^{207}\mathrm{Hg}$ (this measurement), ${}^{209}\mathrm{Pb}$ [4], and ${}^{211}\mathrm{Po}$ [49] compared to Woods-Saxon (WS) calculations of the same orbitals constrained by the Pb and new Hg data. The gray band represents the spread in 21 different models used to calculate $S_n$ for the ground states of nuclei $N=127$ that are commonly used in $r$-process studies [50]. UNEDF0 [51] and FRDM2012 [52] are highlighted.