First direct mass measurements of nuclides around $Z=100$ with a Multireflection Time-of-Flight Mass Spectrograph

The masses of $^{246}$Es, $^{251}$Fm and the transfermium nuclei $^{249-252}$Md, and $^{254}$No, produced by hot- and cold-fusion reactions, in the vicinity of the deformed $N=152$ neutron shell closure, have been directly measured using a multireflection time-of-flight mass spectrograph. The masses of $^{246}$Es and $^{249,250,252}$Md were measured for the first time. Using the masses of $^{249,250}$Md as anchor points for $\alpha$ decay chains, the masses of heavier nuclei, up to $^{261}$Bh and $^{266}$Mt, were determined. These new masses were compared with theoretical global mass models and demonstrated to be in good agreement with macroscopic-microscopic models in this region. The empirical shell gap parameter $\delta_{2n}$ derived from three isotopic masses was updated with the new masses and corroborate the existence of the deformed $N=152$ neutron shell closure for Md and Lr.

Precision mass measurements of unstable nuclei, providing a direct measure of the nuclear binding energy, are invaluable for the study of nuclear shell evolution and collective effects, such as deformations, far from stability [1,2]. For transfermium nuclei and the yet poorly investigated region towards the superheavy nuclei (SHN), where proton repulsion becomes a generally dominant feature, the description of nuclear lifetimes depends crucially on shell stabilization effects mainly driven by deformed shells [3][4][5]. Theoretical studies with increasing particle numbers investigate the so-called "island of stability" [6], where features like the continuing decrease of energy gaps [7] and the emergence of shape coexistence [8] have crucial impact on the predicted position and localization of stability regions and the corresponding lifetimes of the nuclei. Although first experimental evidence for SHN has reached the region of the predicted sub-shell closure at N = 162 [9][10][11], the deformed shell closure at N = 152 for transfermium nuclei (see e.g. [12]) and, as recently pointed out, weaker shell effects in the vicinity [13], still represents the cutting edge for thorough experimental investigations. The transfermium nuclei, however, can only be produced online, in heavy-ion fusion and nucleon transfer reactions, and consequently only low yields are available for study, necessitating highly efficient techniques. Direct mass measurements of trans- The squares indicate nuclei synthesized so far. Nuclei whose masses were determined in this work are indicated by the solid (direct) and the left-hatched (indirect) red squares. Similarly, nuclei whose masses were determined by SHIPTRAP measurements are indicated by the solid (direct) and the righthatched (indirect) black squares.
fermium nuclei have so far been performed for only six nuclei -four isotopes of nobelium and two isotopes of lawrencium -with the Penning trap mass spectrometer SHIPTRAP [14,15].
In this letter we report the first implementation of a multireflection time-of-flight mass spectrograph (MRTOF-MS) for transfermium nuclei as shown in Fig. 1, including new mass measurements of 246 Es, 251 Fm, 249−252 Md, and 254 No, performed with sub-ppm precision. This represents the first determination of the masses of 249−250,252 Md, closing a gap of unmeasured nuclei which could not be linked by corresponding decay chains. Through combining the masses of the dominantly β-decaying nuclei 249−250 Md with previously-known Q αvalues, the masses of nuclei up to 261 Bh and 266 Mt could be experimentally determined for the first time. These results support the existence of the N = 152 shell gap in Md and Lr, while also providing the first experimental data at the shell gap for Db isotopes.
As shown in Fig. 2, the MRTOF-MS [16,17] was installed behind a cryogenic helium gas cell and ion trap system coupled with the gas-filled recoil ion separator GARIS-II [18]. Primary beams provided by the RIKEN heavy-ion linear accelerator RILAC impinged upon a rotating target to produce fusion-evaporation residues (ER). The stopping of high-energy ER in the gas cell was optimized by adjusting the thickness of a Mylar degrader while the gas cell was filled with 150 mbar helium at a temperature of 150 K. The ions were transported to a radiofrequency carpet (RFC) [19], located on the exit wall, by a static electric field and then extracted by means of a traveling-wave (TW) mode RFC technique [20][21][22]. The extracted ions were transported through a differential pumping section by a sextupole ion guide  (SPIG) and then accumulated in the first ion trap system. After accumulating and cooling in the flat trap, ion bunches were orthogonally ejected, accelerated to a kinetic energy of ≈1.7 keV by a pulsed drift tube (Acc-PDT), transported through an electrostatic multiple lens and a Bradbury-Nielsen gate (BN gate) [23] and decelerated to tens of electron-volts by a second pulsed drift tube (Dec-PDT) before being retrapped in the second ion trap system, located in the experimental room underneath GARIS-II. The first and second ion trap systems, each consisting of a pair of linear Paul traps on either side of a "flat" ion trap [24], have the same geometry and were filled with helium buffer gas at ∼10 −2 mbar. In the first trap system, the fore and aft linear Paul traps accumulated the continuous ion beams from the gas cell and from a thermal ionization ion source, respectively, in order to pre-cool and pre-bunch the ion beam prior to transfer to the flat trap. The thermal ionization ion source in the first trap system provided both Cs + and Ba + ions for beam-line tuning. In the second trap system, the fore and aft linear Paul traps accumulated and pre-cooled the pulsed beam delivered from the first trap and the continuous beam from a reference ion source, respectively. The second trap system's thermal ionization ion source provided reference Cs + ions for the mass measurements.
The novel flat trap geometry allowed implementation of a concomitant measurement scheme, shown in Fig. 3(a). While ions from the gas cell were being analyzed with the MRTOF-MS, reference ions stored in the second trap system's aft linear Paul trap were transferred to the flat ion trap and cooled, while pulses of ions sent from the first trap system continue to accumulate in the lower trap system's fore linear Paul trap. In this way, measurements of analyte ions from the gas cell were interleaved with measurements of reference ions within a 30 ms cycle (15 ms for each). In addition to providing a nearly 100% duty cycle, the times-of-flight (ToF) of the reference ions provide precise corrections of ToF drifts for both reference ions and analyte ions.
The ToF drift correction was performed in a manner we refer to as the "Slice-by-Event" method (see Fig. 3(b)). Because analyte detection events were sparse, it was not necessary to consider all reference events. Rather, the reference ions detected 50 cycles (1.5 s) before and after each analyte detection event were combined to produce a reference spectrum. The centroid of reference events in each slice was used to determine the reference ToF t ri for each analyte ToF t xi . Drift-corrected spectra can then be produced for reference and analyte by multiplying the ToF of each detected ion in subset i by t r0 /t ri . A detailed review of this analytical method will be provided in a future publication. Spectra were fitted with an unbinned maximum-likelihood estimator using an asymmetric combined Gaussian-Lorentzian function [25].
Due to the multireflection nature of the MRTOF-MS, there is not a one-to-one correspondence between ToF and A/q; unambiguous identification cannot be made from a single spectrum. This is a consequence of the possibility that two ion species differing in mass-to-charge ratio by ∆A/q will also differ in number of laps made in the MRTOF-MS by ∆n laps such that they have essentially the same ToF. To avoid misidentifications, therefore, we employed confirmation measurements of each analyte ion at different numbers of laps (generally ±1 laps), and additionally for low count-rate measurements of 249,250 Md further confirmations with a dummy target of lower Z which is unable to produce the desired ER but that can be presumed to provide otherwise similar conditions. Figure 4 demonstrates this process in the case of 250 Md. After 6000 s, within ±50 ns of the expected ToF of 250 Md 2+ 7 and 5 counts, respectively, were observed at n = 144 and n = 145 laps while using nat Tl (Z = 81) targets; no counts were observed when using 197 Au (Z = 79) targets in 4000 s for both. This provides strong evidence that the observed spectral peak truly belongs to 250 Md 2+ with the probability of no detected events being only 0.03%. The raw and binned spectrum observed for 250 Md at n = 145 laps, along with the resultant fitting curve by an unbinned maximum-likelihood routine [26], is shown in Fig. 5. This process was employed for each isotope measured.
Experimental conditions, reactions, and primary beam energies, for each measured isotopes are included in Table I. 246 Es, 251 Fm and 252 Md were produced with hotfusion reactions using 18 O and 19 F primary beams with intensities of ∼3 pµA on 232 Th and nat U targets. A 48 Ca primary beam of ∼0.3 pµA intensity was used to produce 249,250,251 Md and 254 No via cold-fusion reactions with nat Tl and 208 Pb targets. All targets had a thickness of ∼500 µg/cm 2 with 1.4-mg/cm 2 Ti backings for actinide targets and 60-µg/cm 2 C backing for other targets, and were mounted on a 300-mm wheel [27] which  Table I; the mass values are compared with AME16 [33] values in Fig. 6. The masses were derived using the single-reference analysis method described in [16]. The listed systematic uncertainties derive from ambiguity in the origin of the time-of-flight. As expected from the short measurement cycle, ToF spectra for 254 No included a ∼30% admixture [34] of the 1.295(2) MeV isomer. While the isomer and ground state could only be partially resolved, the mass of 254g No is consistent with prior direct measurements at the Penning trap mass spectrometer SHIPTRAP [14]. Furthermore, the masses of 251 Fm and 251 Md are in good agreement with those determined by Q α [28] using SHIP-TRAP values for the masses of 255 Lr and 255 No; this work provides the first direct mass measurements of 251 Fm and 251 Md. In the cases of 246 Es and 249,250,252 Md, no previous experimental mass data exist, however our values are consistent with extrapolated mass values in AME16 with similar or higher mass precisions.
One important test applied to theoretical models is  their ability to reproduce the shell gap parameter δ 2n [35]. The shell gap parameter δ 2n is calculated as   sure. For comparison to theory, we have selected global mass models representative of various common theoretical techniques: a shell model (DZ10 [36]), macroscopicmicroscopic model (FRDM12 [37], and WS4 RBF [38]), a self-consistent mean-field model (HFB32 [39]) and a phenomenological mass model (KTUY05 [40]). Both macroscopic-microscopic mass models (FRDM12 and WS4 RBF ) reasonably predict the experimentally determined δ 2n trends, although the peaking at N = 152 is best reproduced by the FRDM12 model. HFB32 and KTUY05 peak beyond N = 152, while DZ10 shows a flat trend with no peak. For lawrencium, WS4 RBF agrees well with both the general trend and the peak at N = 152.
The location of the island of stability remains ambiguous. While experimental mass measurements of nuclei located within the hot-fusion superheavy island including the next deformed shell-closure predicted at N = 162 would be particularly valuable for this, in general more experimentally determined masses in the trans-uranium region will allow for improved extrapolation of mass values into the presumed region of the island of stability. By   Table II. For future efforts to approach to the island of stability, reliable theoretical predictions are crucial. Figure 8 shows the deviations between the various theoretical models and our experimental values. The best average agreement, with a mean deviation below 500 keV/c 2 , is obtained from the WS4 RBF mass model, which is based on the WS4 mass model [41]  This work demonstrates the ability to perform direct mass measurements of both cold-and hot-fusion products, even with low recoil energy products (E recoil ≈ 7 MeV), by coupling a gas cell with GARIS-II. This technique could be applied to most nuclei produced with fusion-evaporation reactions in the SHN region. The overall system efficiency behind GARIS-II, excluding GARIS-II efficiency, from stopping in the gas cell to detection, was ∼2% limited by the double trap system. In the near future, modification to a single trap setup at a new experimental location should provide improved system efficiency of more than 10% and shorter measurement time. This will allow us to measure the masses of hot-fusion SHN having cross sections on the order of ten picobarn. We wish to express gratitude to the Nishina Center for Accelerator-based Research at RIKEN and the Center for Nuclear Science at the University of Tokyo for their support during the online experiments. This work was financially supported by the Japan Society for the Promotion of Science KAKENHI (Grant Nos. 2200823, 24224008, 24740142, 15H02096, 15K05116, and 17H06090).