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 ∼ 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 Hg have been probed using the neutron-adding ( d , p ) reaction in inverse kinematics. The radioactive beam of 206 Hg was delivered to the new ISOLDE Solenoidal Spectrometer at an energy above the Coulomb barrier. The spectroscopy of 207 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.

The nucleus 207 Hg lies in the almost completely unexplored region of the nuclear chart below proton number 82 and just above neutron number 126, both "magic" numbers representing closed shells in the nuclear shell model [1].The doubly-magic nucleus 208 Pb is the cornerstone of this region, a benchmark nucleus in our understanding of the single-particle foundation of nuclear structure.This region, highlighted on the nuclear chart in Fig. 1, is unique in that its single-particle structure remains unexplored.
The nucleosynthesis of heavy elements via the rapid neutron-capture (r-) process path [2] crosses this region, as shown in Fig. 1.The robustness of the N = 126 neutron shell closure plays a crucial role in the nucleosynthesis of the actinides [3][4][5][6][7].The recent observation of a neutron star merger has provided a new focus of interest [8,9], suggesting a possible astrophysical environment for r-process nucleosynthesis [10][11][12][13].
Approaching the r-process path along the N = 126 isotonic chain from Pb, the binding energies (the degree to which neutrons are bound by the mean-field potential created by the decreasing number of all other nucleons) decrease, eventually crossing zero binding and becoming unbound.Near closed shells, the level density is low, so the usual statistical assumptions of many resonances participating in neutron capture is not valid, and specific nuclear-structure properties become important.Knowledge of ground-state binding energies of nuclei with N = 126 + n is important in defining the waiting point caused by the N = 126 closure, the bottleneck which is responsible for the third peak in solar system elemental abundances at nuclear mass A ∼ 195 [14].The binding energies are critical to how the r-process evolves.The energies of ground and excited states have significant consequences for the rate at which direct s-, p-, (and possibly d-) wave neutron-capture (n,γ) reactions proceed [15][16][17].This was discussed recently in the context of the N = 82 shell closure in Ref. [18].
As zero binding is approached, the energies of s orbitals increase less rapidly than those of states with higher angular momenta [19].This behavior has been studied for light nuclei [20,21] and, in the vicinity of N = 126, it is likely to play an important role in neutron-capture reactions.Direct measurements of properties of nuclei in the r-process path in this region will not be possible for many years, if not decades.Experimentally, this region of the FIG. 1.The chart of nuclides color coded to show the stable nuclei (288) in black and nuclei that have been shown to exist in grey (∼3350).Approximately 7000 nuclei, inside the drip lines, are predicted to exist [22].Nuclei estimated to be involved in the astrophysical r process [23] are shown in blue.The isotope 207 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 Hg.In the inset only, nuclei with at least one known excited state (∼2100 across the entire chart) are shown in green [24,25].
nuclear chart has remained largely inaccessible.Fragmentation and isotope separation online, which are the methods of choice at current and next generation radioactive ion beam facilities, only produce low-intensity beams of neutron-rich (N ≥ 126) nuclei below 208 Pb.Techniques that could produce these nuclei with significant yields, such as multi-nucleon transfer, look promising although technological developments are necessary to manipulate the reaction products for spectroscopy [26,27].New data on 207 Hg marks a first step in the study of these systems.
Only one transfer-reaction study has probed the Z < 82, N > 126 region using a long-lived radioactive target of 210 Pb [28], providing some limited information on proton-hole states in 209 Tl.Beyond the simple existence of some nuclei, derived from decay studies, only limited knowledge of a few excitations in 208−210 Tl (neighboring Pb isotopes) and 208,210 Hg are known [24,29].Most recently, γ-ray transitions have been seen in 211,213 Tl [30].In no instance is any direct knowledge of single-neutron structure known.All that has been previously established about 207 Hg, the next even-proton member of the N = 127 isotonic chain below Pb, is an estimate of its lifetime (T 1/2 = 2.9 m), its mass [31,32], and that its ground state decays via β decay.
In this work, we report the first study of single-neutron excitations beyond N = 126 for elements below Pb, achieved using a transfer reaction in inverse kinematics with a radioactive beam of 206 Hg, accelerated to energies above the Coulomb barrier for collisions with deuterium.This study was made possible by new advances in technology at the ISOLDE radioactive-beam facility at CERN [33][34][35] and with the development of the ISOLDE Solenoidal Spectrometer (ISS) [36] based on a technique pioneered at Argonne National Laboratory (ANL).As was demonstrated with HELIOS at ANL [37], factors of 2-3 improvements in Q-value resolution can be achieved in the study of these types of reactions using the solenoidal-spectrometer technique [38,39].
In this study, about 6000 protons were identified from the 206 Hg(d,p) 207 Hg reaction.These result from the bombardment of approximately 1.5 × 10 11 206 Hg ions with deuterated polyethylene targets of nominal thickness 165 µg/cm 2 at a rate of around 3 to 8×10 5 206 Hg ions per second and an energy of 1.52 GeV (7.38 MeV/u), the highest energy available at the time.
The preparation of the radioactive Hg ions is described elsewhere [40,41].The Hg ions (46 + ) were injected into the REX/HIE-ISOLDE linear accelerator in bursts of width ∼800-µs, every 450 ms.The beam was contaminated with 130 Xe at a level of < 2%.The level of the Xe impurity was determined from background runs with the ion-source lasers off.A measurement using a pure 130 Xe beam, at the same MeV/u as the Hg, was carried out to corroborate this.
(a) The low-lying excitation-energy spectrum of 207 Hg as measured via the (d,p) reaction on 206 Hg at 7.38 MeV/u.States are labeled by their energies in keV and value.Plot (b) is the same spectrum with a linear background subtracted and with fits shown [42].
Thin deuterated polyethylene targets are susceptible to damage even with relatively low ( 10 9 pps) intensity beams.The damage is reasonably well characterized for light and medium mass beams [43,44] but not for heavier beams.In the experiment described here, the target was replaced every 4 hours, on average, resulting in the use of 20 targets in the 82-hour duration.No evidence of target degradation was observed via elastically scattered deuterons and carbon ions in a monitor detector.
The ISS, in this first stage of its development, was set up in a manner similar to that described in Ref. [44] using the HELIOS detector system.A 2.5-T magnetic field was used.The data acquisition was triggered by signals in the on-axis Si array [37].A signal from the REXEBIS was used to gate the data acquisition system during the beam release, disabling it during the chargebreeding process.This suppressed spurious background, such as α decays present due to nuclei produced in fusionevaporation reactions.
The excitation-energy spectrum for 207 Hg is shown in Fig. 2 both with and without a background subtraction.The background is predominately prompt protons from fusion-evaporation reactions of the beam and 12 C in the target.The Q-value resolution was ∼140 keV FWHM.The spectrum represents a sum of all detectors on the Si array which corresponds to center-of-mass angles, 20  θ cm 40 • .From the data, seven states have been observed below 3 MeV, which are associated with adding a neutron in the vacant 1g 9/2 , 2d 5/2 , 3s 1/2 , 2d 3/2 , and 1g 7/2 orbitals beyond N = 126, as shown in Table I.The high-j 0i 11/2 = 6 strength, estimated to lie at around 0.8 MeV, is not seen; at an incident beam energy of 7.38 MeV/u, (d,p) yields corresponding to = 6 transfer are expected to be <10 counts (for a pure single-particle state) in total.The negative parity 0j 15/2 orbital is expected to lie around 1.2 MeV, but yields would be smaller still.The absolute cross sections have uncertainties of around 30%.Only relative cross sections were used in the analysis, which are known to better than 5%.
Calculations used to extract spectroscopic factors and predict angular distributions were performed using the distorted-wave Born approximation (DWBA) with the code Ptolemy [45].The bound-state form factors were taken from Ref. [46] and optical-model potentials from Refs.[47] and [48] were used.Normalized spectroscopic factors are listed in Table I; the uncertainties are dominated by the relative variation due to different choices in the optical-model potentials.a The centroid of the 2d 5/2 strength lies at 1500(50) keV, with (17).
The calculated angular distributions are fitted to the experimental data in Fig. 3.While at 7.38 MeV/u the distributions are relatively indistinct, tentative -value assignments have been made.Each state was fitted with = 0, 2, and 4 shapes using a χ 2 minimization technique.The -value for the resulting best-fit shape was adopted.In the case of the = 0 state, while having the smallest χ 2 , the value was similar to the values for = 2 and 4, but because of its large cross section, an assignment other than = 0 would cause serious inconsistencies in the sum rules.The ground state is identified as = 4 and corresponds to J π = 9/2 + .The states at 1195, 1600, and 1810 keV, are assigned as = 2, which is similar to the pattern seen in Z = 84, 211 Po [49].The core 2 + excitations in 206 Hg and 210 Po are at similar energies of ∼1.1 MeV.This can cause fragmentation of the excited states and is likely to be responsible for the three 5/2 + fragments and for any other fragmentation of the 2d 3/2 and 1g 7/2 strengths.The details, of course, depend on specific structural considerations.The 3s 1/2 strength is carried by the state at 1960 keV and the = 2 transfer to the 2335-keV state is presumed to carry the full 2d 3/2 strength, lying just over 0.8 MeV above the 2d 5/2 centroid.The state at 2530 keV is populated via = 4 transfer, and is assigned J π = 7/2 + , a major fragment of the spin-orbit partner to the ground state.
A sum-rule analysis of the spectroscopic factors gives a consistent picture of the assignments.The spectroscopic factors in Table I are normalized, arbitrarily, such that the 1960-keV = 0 transition has S ≡ 1.00.The summed strength for 1g 9/2 , 2d 5/2 , 3s 1/2 , 2d 3/2 , and 1g 7/2 are then 0.82 (13), 1.02 (14), 1.00, 1.00 (17), and 0.62 (12), respectively, implying that the bulk of the strength is carried by these states.The observed 1g 7/2 strength is notably lower than others, suggesting fragments of this strength lie at higher excitation energy than was probed here.The ordering of states is consistent with trends seen in 209 Pb and 211 Po, and that expected of single-neutron orbitals outside of the N = 126 shell closure.
The binding energies of the neutron orbitals at N = 127 have been calculated using a Woods-Saxon potential, with an asymmetry term in the potential depth as defined in Ref. [50].The potential depth, spin-orbit strength, radius, and diffuseness parameters were determined by fitting them to the experimental data for the five known single-particle centroids in 207 Hg and the seven in 209 Pb.The rms deviation of the fit from the experimental data was ∼200 keV and yielded physically sensible parameters.
The binding energies of the ground and excited states, using the parameters derived from the fitting described above, were extrapolated to zero binding along N = 127.These extrapolations suggest that below Gd (Z = 64), N = 127 nuclei are unbound.The uncertainties on this approach are about two units of Z.This assumption depends on the robustness of the closed shell at N = 126.Indeed, above Pb, the 2 + energies are essentially constant through to Th (Z = 90), beyond which there are no data [24].Heavier Th isotopes away from the closed shell are known to exhibit strong quadrupole deformation, much like the neutron-rich rare-earth nuclei (Z 70), but the shell closure seems to restore the spherical shape.
For the ground states, results from the Woods-Saxon calculations, constrained by the new experimental data, are compared to results from 21 models used for determining S n that are commonly used in r-process calculations [51].These are shown by the grey band in Fig. 4. Two models close to the extremes with regards to predicting zero binding energy at N = 127 nuclei are highlighted, UNEDF [52] and FRDM [53].The latter agrees well with the simple Woods-Saxon extrapolation guided by the experimental data.
The Woods-Saxon calculations suggest that between Gd (Z = 64) and Er (Z = 68), there are no bound excited states in these N = 127 nuclei.If there are no bound excited states and only a bound 9/2 + ground state it is difficult to see how capture would proceed.The level density in the continuum will be very low and the usual statistical estimates are not applicable.Direct capture can take place if there is an appreciable component of odd-parity phase shifts with = 4 ± 1.But such singleneutron excitations are far from the neutron threshold.Direct capture with higher than an E1 multipole is inhibited [16].In odd-Z nuclei, a member of a multiplet coupled to an h 11/2 proton hole may provide a basis for a neutron capture and subsequent β decays.A microscopic description of the bottleneck for the r-process will need considerably more data to allow for a more quantitative Experimentally determined binding energies of the neutron orbitals at N = 127 for 207 Hg (this measurement), 209 Pb [24], and 211 Po [49] compared to Woods-Saxon (WS) calculations of the same orbitals constrained by the Pb and new Hg data.The grey band represents the spread in 21 different models used to calculate Sn for the ground states of nuclei N = 127 that are commonly used in r-process studies [51].UNEDF0 [52] and FRDM2012 [53] are highlighted.
description.The bottleneck for N = 126 appears to be more significant than for N = 82, where for N > 82 there are odd-parity p orbitals [18].
Referring back to the r-process path shown in Fig. 1, the N = 126 bottleneck starts around Z = 54, and capture reactions beyond N = 126, starting in the first few tenths of a second into the r-process, occur around Z = 64 ± 2. The Woods-Saxon calculations shown here, constrained to new data at 207 Hg which includes excited states, are broadly in line with this picture.The UN-EDF0 and FRDM2012 models used to predict the neutron separation energy also agree with the experimental data at 80 < Z < 84, the latter consistent with the •

ℓ= 2 ×20FIG. 3 .
FIG. 3. Angular distributions for the outgoing protons from the (d,p) reaction on 206 Hg at 7.38 MeV/u.The color of the lines correspond to = 0 (orange), 2 (maroon), and 4 (yellow) transfer.Transitions are labeled by their excitation energies (in keV) in the residual nucleus and the -value corresponding to the best fit angular distribution.The thicker curves represent the best fit angular distribution for the -value quoted.Thinner lines are used to show other possible values.

TABLE I .
Excitation energies, tentative and J π assignments, and normalized spectroscopic factors S for states assigned to 207 Hg.The normalization is such that the 3s 1/2 strength is equal to unity.