β-decay studies across N = 126

With the advent of the first Radioactive Ion Beam facilities of new generation, the investigation of the neutron-rich side of the nuclear chart has experienced an impressive progress. However, the discovery and study of new nuclear species in the region around the heaviest known neutron shell closure, N = 126, is still one of the most coveted experimental challenges. At a slower pace, the exploitation of alternative reaction mechanisms and/or advanced instrumentation has opened the possibility to investigate the isomeric and β decay of new, moderately neutron-rich N ∼ 126 nuclei. These are of relevance for the understanding of the nuclear structure below the doubly-magic 208Pb and for their role in the synthesis of the trans-bismuth fissile elements in the r process. In this contribution, a general overview of the β-decay experiments performed at both sides of N = 126 is provided, with a main focus on the experiments carried out at the fragmentation facilities GSI and RIBF.


Introduction
The spontaneous phenomenon of β decay has for a long time been a powerful tool to study newly synthesized exotic nuclei, since key properties such as β-decay half-lives or the lowestlying excited states in the descendants can be measured only with a few hundred decays [1,2].At present, it is often the first or even the only mechanism available to investigate structural properties of the most exotic neutron-rich nuclei produced in Radioactive Ion Beam (RIB) facilities.Furthermore, in the rapid neutron-capture process (r -process) of explosive nucleosynthesis, the (n, γ) rates drop quickly near the neutron shell closures with N = 50, 82 and 126, and β decay becomes the dominant nuclear mechanism, giving rise to the synthesis of heavier elements.Hence, understanding the formation of half the abundances of the existing chemical elements strongly depends on our knowledge of gross β decay properties such as halflives, β-delayed neutron emission probabilities, and Q β energies of very exotic neutron-rich nuclei [3].
Of particular interest is the nuclear region approaching the Terra Incognita, which lies far below the heaviest doubly magic 208 Pb and is related to the formation of the 3 rd r -process abundance peak and the crossing of the neutron shell closure with N = 126.Only a few nucleons away from 208 Pb, the most exotic heavy neutron-rich N ∼ 126 nuclei investigated thus far had been at the exclusive reach of the GSI Helmholtz Centre for Heavy Ion Research (Germany).For more than twenty years, GSI has been the only facility in the world with optimal operational conditions to produce and separate heavy N ∼ 126 nuclei.To this purpose, the fragmentation of relativistic 208 Pb and 238 U beams at 1GeV/nucleon colliding on light, thin targets has been exploited.This production mechanism has allowed for an unambiguous identification in flight of the reaction residues in mass A and charge Q using the high-resolution magnetic spectrometer Fragment Separator (FRS) [4].However, relevant recent advances exploiting new production mechanisms and methods of identification involving cutting-edge instrumentation have challenged the European leadership on the investigation of N ∼ 126 nuclei [5,6].In the present contribution, a general overview of the status of the β-decay studies across N = 126 is provided.The most important projects focusing on this mass region in fragmentation facilities are discussed [7,8,9], and a quick glance at near future perspectives is provided [10].
2. Scientific interest of the N ∼ 126 region below 208 Pb At present, the r -process calculations involving the A ∼ 195 peak must rely on theoretical predictions that can only be tested near stability, with no guarantee on their predictive power approaching the r -process reaction path.For this reason, new structural information on the properties of nuclei lying a few nucleons below 208 Pb, even if not extremely exotic, is crucial.Apart from the gross β-decay properties aforementioned, experimental observables such as the energies of excited nuclear states, spin and parities, and nuclear lifetimes are necessary to derive two-body matrix elements (TBME) and trace the evolution of the single-particle energies (SPE) for nuclei with N < 126.Reliable information on these parameters is essential to test the largescale shell model calculations towards the A∼195 bottleneck and calculate the more complex configurations of the r -process progenitors, which are completely out of experimental reach.
An important question open to debate is to what extent and how the first-forbidden (FF) transitions contribute to the β decay of these nuclei.FF decays are expected to be enhanced around the 3 rd r -abundance peak due to the ordering of the proton and neutron orbitals below 208 Pb.In a single-particle picture, the model space describing N < 126, Z < 82 nuclei involves only one allowed Gamow-Teller (GT) transition of low energy transforming a neutron in the 0νh 9/2 orbital into a proton in the 0πh 11/2 shell.This transition is further hampered by the partial filling of the 0πh 11/2 orbital and the location of the 0νh 9/2 sub-shell, which the deepest lying orbital of the 82 < N < 126 major shell.As a result, the appearance of fast FF transitions exceeding the GT strength is predicted in the N ∼ 126 region [11].These are expected to significantly reduce the theoretical half-lives [11,12,13,14,15], accelerating the nucleosynthesis of the actinides and the latter fission recycling.Improved simulations of the matter flow through the third r -process bottleneck are also important to constrain the relative abundances of the nuclear cosmo-chronometers of U and Th, which have for a long time been used to measure the age of stars [16] and identify r -process sites and stellar progenitors [17].

The production mechanisms. Multi-nucleon transfer versus fragmentation
Hitherto, the cold fragmentation of relativistic heavy stable projectiles of 208 Pb and 238 U on thin light targets has been used to synthesize the most exotic N ∼ 126 neutron-rich nuclei [19,20].Cold fragmentation reactions [21] are modeled as very peripheral relativistic nuclear collisions taking place in a participant-spectator picture that can be described in two steps.In the first stage, called abrasion, the projectile nucleus is cut by the target, becoming highly excited.In the second stage, called ablation, the projectile pre-fragment de-excites emitting particles and γ rays, even through fission, giving rise to the final fragment.There are two main advantages of this production mechanism.On the one hand, the neutron-rich reaction residues can be unambiguously identified in flight in a very short time period, down to ∼ 300ns; on the other hand, as the relativistic reaction takes place in inverse kinematics, the fragmentation residues are forwarded focused with small emission angles, resulting in high transmission rates, close to 100%, in zero-degree magnetic spectrometers [22].The detection efficiency of the tracking detectors is also good, resulting in small losses during the particle identification.In contrast, the cold fragmentation cross sections of the N = 126 isotones decrease rapidly as protons are removed from the projectile, resulting in too small production cross sections, below the order of the nb for Z ≤ 77. .Layout of the in-flight setup used at GSI for isomer and β-decay studies, consisting of the magnetic spectrometer FRS for particle identification and the stopped RISING detection system for β and γ-ray detection [7]. Figure taken from [18].
An alternative production mechanism presently attracting much attention is the multinucleon transfer (MNT) [23].The pioneering KISS project at RIBF has shown that MNT reactions, in combination with ISOL techniques for particle identification, are optimal to study N < 126 nuclei [5].In these reactions, a large number of nucleons are exchanged between two heavy nuclei at energies near the Coulomb barrier, giving rise to very large production cross sections using combinations such as ( 136 Xe, 198 Pt) or ( 136 Xe, 208 Pb).However, the angular distributions of the products are broad, resulting in small collection efficiencies.Furthermore, the low emission energies of the target-like fragments (TLF) make their extraction and separation very difficult, with rather small extraction efficiencies and long identification times, ∼ 300 ms.

The quest for N = 126 nuclei
The number of active or planned research programs around the world aiming at reaching the N ∼ 126 nuclei below 208 Pb [5,6,24,10,25] is a clear sign that the Terra Incognita is one of the major milestones of the latest generation of RIB laboratories.Due to length limitations, only the most important projects carried out in fragmentation facilities will be discussed here.

The past: RISING at GSI
The main facility contributing thus far to β-decay studies across N = 126 has been GSI.There, the β decay of nearly 40 neutron-rich nuclei was investigated using different in-flight β-decay setups [1,26,27,28,18,2,29,30,31].The most relevant was RISING, the schematic layout of which is shown in Fig 1 .In RISING, the measured β-decay half-lives of N ≤ 126, Z < 82 nuclei were well reproduced by models including a microscopic treatment of the FF transitions, such as the DF3+cQRPA approach [11] or the RHB+pn-RQRPA model [13]; while the FRDM+QRPA model [15], extensively used in calculations of r -process nucleosynthesis, significantly overestimated the half-lives of N ≤ 126 nuclei.This excess is in line with the expected enhancement of the FF transitions discussed in Section 2, as the FRDM+QRPA model calculates the FF strength using the gross theory, a treatment that might not be sufficient.But surprisingly, for N > 126, Z ≥ 80 nuclei, the FRDM+QRPA agrees remarkably well with the half-lives in contrast to the DF3+cQRPA and RHB+pn-RQRPA models, which underestimate the experimental results -the later by orders of magnitude [27,31].
[s]  The systematics observed during the RISING campaign suggest a higher contribution of the GT strength beyond the N = 126 shell gap.It has been argued that the allowed singleparticle 0νi 11/2 → 0πi 13/2 β transition might be opened due to an increased occupation of the 0νi 11/2 orbital [30,32]; but the underlying mechanisms driving this striking change in the half-lives across N = 126 have not yet been understood.Fig. 2 displays the compilation of βdecay half-lives measured by the RISING collaboration [29].These are compared with the DF3+cQRPA approach, the FRDM+QRPA model, and the Shell Model calculations of Ref. [33].For 215 Pb, the FRDM+QRPA and DF3+cQRPA predictions are shown with filled and empty circles, respectively.

The present: DESPEC at FAIR
The DESPEC project aims at continuing the Nuclear Structure and Astrophysics research program started with RISING by extending the scope to more exotic neutron-rich nuclei and more varied observables, thus helping to advance our knowledge on the structural properties of nuclei crossing N = 126.This mass region has been targeted at GSI very recently, during the FAIR Phase 0 campaign in Spring 2022, using for the first time new instrumentation developed for DESPEC: the DEGAS and DTAS γ-ray detector arrays [10].The former is intended for highresolution γ spectroscopy and consists of a series of EUROBALL HPGe crystals rearranged in triple clusters packed in a high-efficiency configuration.The latter is a modular total-absorption spectrometer made of 16 NaI crystals that acts as a calorimeter.Hence, it is specifically designed to maximize the γ-ray detection efficiency for the measurement of β intensities in fragmentation facilities.Pictures of the two setups are shown in Fig. 3.With DTAS, the first worldwide systematic measurement of β strengths for neutron-rich nuclei across N = 126 has been performed at GSI.The β strengths, derived from the measured β intensities, will provide an excellent experimental probe to test how the β decay proceeds for N ∼ 126 nuclei, as a complete picture of the wave-function overlap between parent and daughter states in the decay energy window can be obtained.They are hence better suited to understand the underlying mechanisms leading to the discrepancies in β half-lives observed in RISING (see Fig. 2).With DEGAS, the isomeric and β decay of the most exotic N = 126 isotones 203 Ir and 202 Os will soon be investigated.As a result, the knowledge of excitation energies, transition strengths, and β-decay properties downward N = 125-127 will be extended by the DESPEC collaboration in the incoming years.These findings, in turn, might help improve the nuclear models in their predictions towards the unknown r -process progenitors.At RIBF, the only heavy stable primary beam available is 238 U, with an energy of 345 MeV/nucleon and an intensity reaching 100 pnA.These conditions have allowed the observation of the first isomeric γ rays in N 126, Z < 82 nuclei since 2009 [34].The first experiment with such capabilities was run in spring 2021 by the BRIKEN collaboration [6].BRIKEN is made of 140 3 He tubes surrounded by a polyethylene (PE) moderator matrix.Two CLOVER-type HPGe detectors are inserted into the PE matrix transversely to the beam direction at an angle of 90 • for γ spectroscopy studies [9].The main technical challenge to identify in-flight heavy nuclei is related to the contamination arising from the atomic charge states produced in the interaction of the nuclei with the matter of the optical elements and detectors placed along the BigRIPS magnetic spectrometer [35].The required resolution in A/Q has been achieved by minimizing the matter placed along the spectrometer, whilst that in Z has been reached with a novel Si telescope system consisting of a stack of four wedge-shaped Si detectors of dimensions 93×93 mm 2 and 0.6-mm thick each.The particle-identification (PID) cluster matrix of the exotic heavy fragments produced, with Z ranging from 77 to 83, is shown in Fig. 4. The PID has been confirmed by the observation of the previously reported (8 + ) seniority isomer in 216 Pb [34] and other known transitions in 210 Hg and 213 Tl [36,37].Newly observed isomers have also been identified in 213 Tl-215 Tl, 211−212 Hg and 206 Pt.

Conclusions
Until recently, GSI has been the only facility where the β decay of N ∼ 126 nuclei could be investigated.However, the great progress carried out recently at RIBF via both multi-nucleon transfer and fragmentation of 238 U establishes it as both a competitive and complementary facility in the quest for the most exotic heavy systems towards the Terra Incognita.

Figure 1
Figure1.Layout of the in-flight setup used at GSI for isomer and β-decay studies, consisting of the magnetic spectrometer FRS for particle identification and the stopped RISING detection system for β and γ-ray detection[7].Figure taken from[18].

Figure 2 .
Figure 2. Systematics of β half-lives of nuclei crossing N = 126.The shaded region indicates the typical deviation between DF3+cQRPA and experiment in N∼82 nuclei.Figure adapted from Ref. [29].

Figure 3 .
Figure 3. Left: DTAS γ-ray calorimeter and narrow AIDA implant-decay detector.Right: DEGAS HPGe spectrometer surrounding the wide AIDA active stopper.All the systems are part of the advanced instrumentation developed for DESPEC [10].

4. 3 .Figure 4 .
Figure 4. Two-dimensional particle identification matrix showing the atomic charge Z as a function of the A/Q ratio for fully-stripped ions.Setting centered in 202 Os [6].